diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..a5c0f87 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +multiagent1/ \ No newline at end of file diff --git a/docs/A*.md b/docs/A*.md new file mode 100644 index 0000000..e8b8f75 --- /dev/null +++ b/docs/A*.md @@ -0,0 +1,103 @@ +# 启发式函数与A*搜索算法 + +## 介绍 + +在人工智能和路径规划中，启发式函数和A*搜索算法是两个重要的概念。启发式函数用于估计从当前状态到目标状态的代价，而A\*搜索算法则利用这些估计来找到最优路径。 + +## 启发式函数 + +### 什么是启发式函数？ + +启发式函数（Heuristic Function）是用于估计当前状态到目标状态之间的最小成本的函数。它的设计是为了加速搜索算法，使其更高效地找到解决方案。 + +### 启发式函数的性质 + +1. **可接受性（Admissibility）**： + - 一个启发式函数是可接受的，如果它从不高估从节点到目标节点的实际最小成本。 + - 数学定义：对于所有节点 \(n\)，启发式函数 \(h(n)\) 必须满足 \(h(n) \leq h^*(n)\)，其中 \(h^*(n)\) 是从节点 \(n\) 到目标节点的实际成本。 + +2. **一致性（Consistency）**： + - 一致性的启发式函数也称为单调性启发式函数。如果对于所有节点 \(n\) 和其每个子节点 \(m\)，启发式函数 \(h\) 满足 \(h(n) \leq c(n, m) + h(m)\)，其中 \(c(n, m)\) 是从节点 \(n\) 到节点 \(m\) 的实际成本。 + - 数学定义：\(h(n) \leq c(n, m) + h(m)\)。 + +### 启发式函数的示例 + +1. **曼哈顿距离（Manhattan Distance）**： + - 在网格路径规划中，曼哈顿距离是两个点之间沿轴线方向的总距离。 + - 公式：\(h(n) = |x_1 - x_2| + |y_1 - y_2|\)。 + +2. **欧几里得距离（Euclidean Distance）**： + - 欧几里得距离是两点之间的直线距离。 + - 公式：\(h(n) = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)。 + +## A*搜索算法 + +### 什么是A*搜索？ + +A*搜索是一种图搜索算法，它结合了Dijkstra算法和贪婪最佳优先搜索的优点。A*搜索使用启发式函数来引导搜索方向，从而找到从起始点到目标点的最优路径。 + +### A*搜索的工作原理 + +1. **初始化**： + - 将起始节点添加到优先队列中，初始代价为0。 + +2. **搜索过程**： + - 从优先队列中取出总代价最小的节点作为当前节点。 + - 如果当前节点是目标节点，则搜索结束。 + - 否则，扩展当前节点的所有邻居节点，并更新它们的代价和优先级。 + - 重复上述步骤，直到找到目标节点或优先队列为空。 + +3. **代价函数**： + - A*搜索使用一个代价函数 \(f(n) = g(n) + h(n)\) 来评估每个节点的优先级。 + - 其中，\(g(n)\) 是从起始节点到节点 \(n\) 的实际代价，\(h(n)\) 是从节点 \(n\) 到目标节点的启发式估计代价。 + +### A*搜索的伪代码 + +```pseudo +function A*(start, goal) + openSet := {start} + cameFrom := empty map + + gScore := map with default value of Infinity + gScore[start] := 0 + + fScore := map with default value of Infinity + fScore[start] := heuristic(start, goal) + + while openSet is not empty + current := node in openSet with lowest fScore[current] + if current == goal + return reconstruct_path(cameFrom, current) + + openSet.remove(current) + for each neighbor of current + tentative_gScore := gScore[current] + d(current, neighbor) + if tentative_gScore < gScore[neighbor] + cameFrom[neighbor] := current + gScore[neighbor] := tentative_gScore + fScore[neighbor] := gScore[neighbor] + heuristic(neighbor, goal) + if neighbor not in openSet + openSet.add(neighbor) + + return failure + +function reconstruct_path(cameFrom, current) + total_path := {current} + while current in cameFrom + current := cameFrom[current] + total_path.prepend(current) + return total_path +``` + +### A*搜索的应用 + +- **视频游戏**：用于角色路径规划。 +- **路径规划问题**：如地图导航、机器人路径规划等。 +- **资源规划问题**：如物流和供应链管理。 +- **语言分析**：如句法分析。 +- **机器翻译和语音识别**：用于寻找最优匹配和路径。 + +## 结论 + +启发式函数和A\*搜索算法是解决复杂路径规划和搜索问题的重要工具。通过设计有效的启发式函数，可以显著提高搜索算法的效率。A*搜索算法结合了路径代价和启发式估计，是找到最优路径的强大方法。 + diff --git a/docs/minmax.md b/docs/minmax.md new file mode 100644 index 0000000..e3105c8 --- /dev/null +++ b/docs/minmax.md @@ -0,0 +1,140 @@ +# Minimax 搜索算法 + +## 介绍 + +Minimax 是一种用于两人对弈游戏的决策算法，如国际象棋、井字棋和跳棋。它帮助确定玩家的最佳行动，假设对手也在最优地进行游戏。Minimax 算法的目标是在最小化可能损失的情况下最大化玩家的得分（因此得名 "minimax"）。 + +## 基本概念 + +### 游戏树 + +游戏树表示游戏中所有可能的移动。从当前状态开始，每个节点代表一个游戏状态，每条边代表一个移动。 + +### 最大化和最小化玩家 + +- **最大化玩家（Max）**：这个玩家试图获得尽可能高的分数。 +- **最小化玩家（Min）**：这个玩家试图最小化最大化玩家的得分。 + +## Minimax 如何工作 + +1. **生成游戏树**：从当前游戏状态开始，生成所有可能的未来状态，直到某个预定深度。 +2. **评估叶节点**：使用评估函数为每个叶节点（终止状态或最大深度的状态）分配一个分数。 +3. **回溯分数**： + - 对于 Max 节点，选择子节点中得分最高的。 + - 对于 Min 节点，选择子节点中得分最低的。 +4. **选择最佳移动**：在根节点（当前游戏状态），选择导致 Max 玩家得分最高的移动。 + +## 示例 + +让我们以井字棋为例。假设现在是 Max 的回合，当前棋盘如下： + +``` + X | O | X +----------- + O | X | +----------- + | | O +``` + +### 步骤 1：生成游戏树 + +生成 Max 的所有可能移动。由于是 Max 的回合，在每个空位上放置一个 "X"： + +``` + X | O | X X | O | X X | O | X +----------- ----------- ----------- + O | X | X O | X | O | X | +----------- ----------- ----------- + | | O X | | O X | | O +``` + +### 步骤 2：评估叶节点 + +为叶节点分配分数。假设： +- Max 获胜得 +10 分 +- Min 获胜得 -10 分 +- 平局得 0 分 + +``` + X | O | X X | O | X X | O | X +----------- ----------- ----------- + O | X | X O | X | O | X | +----------- ----------- ----------- + | | O X | | O X | | O + +得分: 0 得分: 10 得分: 10 +``` + +### 步骤 3：回溯分数 + +由于根节点是 Max 的回合，选择子节点中得分最高的： + +``` + Max + | + V + 10 +``` + +### 步骤 4：选择最佳移动 + +Max 将选择导致得分为 10 的移动。 + +## 伪代码 + +以下是 Minimax 算法的简单伪代码： + +```pseudo +function minimax(node, depth, maximizingPlayer) + if depth == 0 or node is a terminal node + return evaluate(node) + + if maximizingPlayer + maxEval = -∞ + for each child of node + eval = minimax(child, depth - 1, false) + maxEval = max(maxEval, eval) + return maxEval + else + minEval = +∞ + for each child of node + eval = minimax(child, depth - 1, true) + minEval = min(minEval, eval) + return minEval +``` + +## Alpha-Beta 剪枝 + +Alpha-Beta 剪枝是 Minimax 算法的一种优化。它通过剪枝那些不会影响最终决策的分支，减少需要评估的节点数量。 + +### 带 Alpha-Beta 剪枝的伪代码 + +```pseudo +function alphabeta(node, depth, α, β, maximizingPlayer) + if depth == 0 or node is a terminal node + return evaluate(node) + + if maximizingPlayer + maxEval = -∞ + for each child of node + eval = alphabeta(child, depth - 1, α, β, false) + maxEval = max(maxEval, eval) + α = max(α, eval) + if β <= α + break + return maxEval + else + minEval = +∞ + for each child of node + eval = alphabeta(child, depth - 1, α, β, true) + minEval = min(minEval, eval) + β = min(β, eval) + if β <= α + break + return minEval +``` + +## 结论 + +Minimax 是一种在两人对弈游戏中做出最佳决策的强大算法。通过考虑所有可能的移动及其结果，它确保玩家在假设对手也在最优地进行游戏的情况下做出最佳移动。Alpha-Beta 剪枝进一步提高了 Minimax 的效率，减少了需要评估的节点数量。 + diff --git a/multiagent/VERSION b/multiagent/VERSION new file mode 100644 index 0000000..259e855 --- /dev/null +++ b/multiagent/VERSION @@ -0,0 +1 @@ +v1.004 diff --git a/multiagent/autograder.py b/multiagent/autograder.py new file mode 100644 index 0000000..03a048a --- /dev/null +++ b/multiagent/autograder.py @@ -0,0 +1,362 @@ +# autograder.py +# ------------- +# Licensing Information: You are free to use or extend these projects for +# educational purposes provided that (1) you do not distribute or publish +# solutions, (2) you retain this notice, and (3) you provide clear +# attribution to UC Berkeley, including a link to http://ai.berkeley.edu. +# +# Attribution Information: The Pacman AI projects were developed at UC Berkeley. +# The core projects and autograders were primarily created by John DeNero +# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu). +# Student side autograding was added by Brad Miller, Nick Hay, and +# Pieter Abbeel (pabbeel@cs.berkeley.edu). + + +# imports from python standard library +import grading +import importlib.util +import optparse +import os +import pprint +import re +import sys +import projectParams +import random +random.seed(0) +try: + from pacman import GameState +except: + pass + +# register arguments and set default values +def readCommand(argv): + parser = optparse.OptionParser( + description='Run public tests on student code') + parser.set_defaults(generateSolutions=False, edxOutput=False, gsOutput=False, + muteOutput=False, printTestCase=False, noGraphics=False) + parser.add_option('--test-directory', + dest='testRoot', + default='test_cases', + help='Root test directory which contains subdirectories corresponding to each question') + parser.add_option('--student-code', + dest='studentCode', + default=projectParams.STUDENT_CODE_DEFAULT, + help='comma separated list of student code files') + parser.add_option('--code-directory', + dest='codeRoot', + default="", + help='Root directory containing the student and testClass code') + parser.add_option('--test-case-code', + dest='testCaseCode', + default=projectParams.PROJECT_TEST_CLASSES, + help='class containing testClass classes for this project') + parser.add_option('--generate-solutions', + dest='generateSolutions', + action='store_true', + help='Write solutions generated to .solution file') + parser.add_option('--edx-output', + dest='edxOutput', + action='store_true', + help='Generate edX output files') + parser.add_option('--gradescope-output', + dest='gsOutput', + action='store_true', + help='Generate GradeScope output files') + parser.add_option('--mute', + dest='muteOutput', + action='store_true', + help='Mute output from executing tests') + parser.add_option('--print-tests', '-p', + dest='printTestCase', + action='store_true', + help='Print each test case before running them.') + parser.add_option('--test', '-t', + dest='runTest', + default=None, + help='Run one particular test. Relative to test root.') + parser.add_option('--question', '-q', + dest='gradeQuestion', + default=None, + help='Grade one particular question.') + parser.add_option('--no-graphics', + dest='noGraphics', + action='store_true', + help='No graphics display for pacman games.') + (options, args) = parser.parse_args(argv) + return options + + +# confirm we should author solution files +def confirmGenerate(): + print('WARNING: this action will overwrite any solution files.') + print('Are you sure you want to proceed? (yes/no)') + while True: + ans = sys.stdin.readline().strip() + if ans == 'yes': + break + elif ans == 'no': + sys.exit(0) + else: + print('please answer either "yes" or "no"') + + +# TODO: Fix this so that it tracebacks work correctly +# Looking at source of the traceback module, presuming it works +# the same as the intepreters, it uses co_filename. This is, +# however, a readonly attribute. +def setModuleName(module, filename): + functionType = type(confirmGenerate) + classType = type(optparse.Option) + + for i in dir(module): + o = getattr(module, i) + if hasattr(o, '__file__'): + continue + + if type(o) == functionType: + setattr(o, '__file__', filename) + elif type(o) == classType: + setattr(o, '__file__', filename) + # TODO: assign member __file__'s? + # print i, type(o) + + +#from cStringIO import StringIO + +def loadModuleString(moduleSource): + # Below broken, imp doesn't believe its being passed a file: + # ValueError: load_module arg#2 should be a file or None + # + #f = StringIO(moduleCodeDict[k]) + #tmp = imp.load_module(k, f, k, (".py", "r", imp.PY_SOURCE)) + tmp = imp.new_module(k) + exec(moduleCodeDict[k], tmp.__dict__) + setModuleName(tmp, k) + return tmp + + +def loadModuleFile(moduleName, filePath): + # https://docs.python.org/3/library/importlib.html#importing-a-source-file-directly + spec = importlib.util.spec_from_file_location(moduleName, filePath) + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + return module + + +def readFile(path, root=""): + "Read file from disk at specified path and return as string" + with open(os.path.join(root, path), 'r') as handle: + return handle.read() + + +####################################################################### +# Error Hint Map +####################################################################### + +# TODO: use these +ERROR_HINT_MAP = { + 'q1': { + "": """ + We noticed that your project threw an IndexError on q1. + While many things may cause this, it may have been from + assuming a certain number of successors from a state space + or assuming a certain number of actions available from a given + state. Try making your code more general (no hardcoded indices) + and submit again! + """ + }, + 'q3': { + "": """ + We noticed that your project threw an AttributeError on q3. + While many things may cause this, it may have been from assuming + a certain size or structure to the state space. For example, if you have + a line of code assuming that the state is (x, y) and we run your code + on a state space with (x, y, z), this error could be thrown. Try + making your code more general and submit again! + + """ + } +} + + +def splitStrings(d): + d2 = dict(d) + for k in d: + if k[0:2] == "__": + del d2[k] + continue + if d2[k].find("\n") >= 0: + d2[k] = d2[k].split("\n") + return d2 + + +def printTest(testDict, solutionDict): + pp = pprint.PrettyPrinter(indent=4) + print("Test case:") + for line in testDict["__raw_lines__"]: + print(" |", line) + print("Solution:") + for line in solutionDict["__raw_lines__"]: + print(" |", line) + + +def runTest(testName, moduleDict, printTestCase=False, display=None): + import testParser + import testClasses + for module in moduleDict: + setattr(sys.modules[__name__], module, moduleDict[module]) + + testDict = testParser.TestParser(testName + ".test").parse() + solutionDict = testParser.TestParser(testName + ".solution").parse() + test_out_file = os.path.join('%s.test_output' % testName) + testDict['test_out_file'] = test_out_file + testClass = getattr(projectTestClasses, testDict['class']) + + questionClass = getattr(testClasses, 'Question') + question = questionClass({'max_points': 0}, display) + testCase = testClass(question, testDict) + + if printTestCase: + printTest(testDict, solutionDict) + + # This is a fragile hack to create a stub grades object + grades = grading.Grades(projectParams.PROJECT_NAME, [(None, 0)]) + testCase.execute(grades, moduleDict, solutionDict) + + +# returns all the tests you need to run in order to run question +def getDepends(testParser, testRoot, question): + allDeps = [question] + questionDict = testParser.TestParser( + os.path.join(testRoot, question, 'CONFIG')).parse() + if 'depends' in questionDict: + depends = questionDict['depends'].split() + for d in depends: + # run dependencies first + allDeps = getDepends(testParser, testRoot, d) + allDeps + return allDeps + +# get list of questions to grade +def getTestSubdirs(testParser, testRoot, questionToGrade): + problemDict = testParser.TestParser( + os.path.join(testRoot, 'CONFIG')).parse() + if questionToGrade != None: + questions = getDepends(testParser, testRoot, questionToGrade) + if len(questions) > 1: + print('Note: due to dependencies, the following tests will be run: %s' % + ' '.join(questions)) + return questions + if 'order' in problemDict: + return problemDict['order'].split() + return sorted(os.listdir(testRoot)) + + +# evaluate student code +def evaluate(generateSolutions, testRoot, moduleDict, exceptionMap=ERROR_HINT_MAP, + edxOutput=False, muteOutput=False, gsOutput=False, + printTestCase=False, questionToGrade=None, display=None): + # imports of testbench code. note that the testClasses import must follow + # the import of student code due to dependencies + import testParser + import testClasses + for module in moduleDict: + setattr(sys.modules[__name__], module, moduleDict[module]) + + questions = [] + questionDicts = {} + test_subdirs = getTestSubdirs(testParser, testRoot, questionToGrade) + for q in test_subdirs: + subdir_path = os.path.join(testRoot, q) + if not os.path.isdir(subdir_path) or q[0] == '.': + continue + + # create a question object + questionDict = testParser.TestParser( + os.path.join(subdir_path, 'CONFIG')).parse() + questionClass = getattr(testClasses, questionDict['class']) + question = questionClass(questionDict, display) + questionDicts[q] = questionDict + + # load test cases into question + tests = [t for t in os.listdir( + subdir_path) if re.match(r'[^#~.].*\.test\Z', t)] + tests = [re.match(r'(.*)\.test\Z', t).group(1) for t in tests] + for t in sorted(tests): + test_file = os.path.join(subdir_path, '%s.test' % t) + solution_file = os.path.join(subdir_path, '%s.solution' % t) + test_out_file = os.path.join(subdir_path, '%s.test_output' % t) + testDict = testParser.TestParser(test_file).parse() + if testDict.get("disabled", "false").lower() == "true": + continue + testDict['test_out_file'] = test_out_file + testClass = getattr(projectTestClasses, testDict['class']) + testCase = testClass(question, testDict) + + def makefun(testCase, solution_file): + if generateSolutions: + # write solution file to disk + return lambda grades: testCase.writeSolution(moduleDict, solution_file) + else: + # read in solution dictionary and pass as an argument + testDict = testParser.TestParser(test_file).parse() + solutionDict = testParser.TestParser(solution_file).parse() + if printTestCase: + return lambda grades: printTest(testDict, solutionDict) or testCase.execute(grades, moduleDict, solutionDict) + else: + return lambda grades: testCase.execute(grades, moduleDict, solutionDict) + question.addTestCase(testCase, makefun(testCase, solution_file)) + + # Note extra function is necessary for scoping reasons + def makefun(question): + return lambda grades: question.execute(grades) + setattr(sys.modules[__name__], q, makefun(question)) + questions.append((q, question.getMaxPoints())) + + grades = grading.Grades(projectParams.PROJECT_NAME, questions, + gsOutput=gsOutput, edxOutput=edxOutput, muteOutput=muteOutput) + if questionToGrade == None: + for q in questionDicts: + for prereq in questionDicts[q].get('depends', '').split(): + grades.addPrereq(q, prereq) + + grades.grade(sys.modules[__name__], bonusPic=projectParams.BONUS_PIC) + return grades.points + + +def getDisplay(graphicsByDefault, options=None): + graphics = graphicsByDefault + if options is not None and options.noGraphics: + graphics = False + if graphics: + try: + import graphicsDisplay + return graphicsDisplay.PacmanGraphics(1, frameTime=.05) + except ImportError: + pass + import textDisplay + return textDisplay.NullGraphics() + + +if __name__ == '__main__': + options = readCommand(sys.argv) + if options.generateSolutions: + confirmGenerate() + codePaths = options.studentCode.split(',') + + moduleDict = {} + for cp in codePaths: + moduleName = re.match(r'.*?([^/]*)\.py', cp).group(1) + moduleDict[moduleName] = loadModuleFile( + moduleName, os.path.join(options.codeRoot, cp)) + moduleName = re.match(r'.*?([^/]*)\.py', options.testCaseCode).group(1) + moduleDict['projectTestClasses'] = loadModuleFile( + moduleName, os.path.join(options.codeRoot, options.testCaseCode)) + + if options.runTest != None: + runTest(options.runTest, moduleDict, printTestCase=options.printTestCase, + display=getDisplay(True, options)) + else: + evaluate(options.generateSolutions, options.testRoot, moduleDict, + gsOutput=options.gsOutput, + edxOutput=options.edxOutput, muteOutput=options.muteOutput, printTestCase=options.printTestCase, + questionToGrade=options.gradeQuestion, display=getDisplay(options.gradeQuestion != None, options)) diff --git a/multiagent/game.py b/multiagent/game.py new file mode 100644 index 0000000..00adb7a --- /dev/null +++ b/multiagent/game.py @@ -0,0 +1,778 @@ +# game.py +# ------- +# Licensing Information: You are free to use or extend these projects for +# educational purposes provided that (1) you do not distribute or publish +# solutions, (2) you retain this notice, and (3) you provide clear +# attribution to UC Berkeley, including a link to http://ai.berkeley.edu. +# +# Attribution Information: The Pacman AI projects were developed at UC Berkeley. +# The core projects and autograders were primarily created by John DeNero +# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu). +# Student side autograding was added by Brad Miller, Nick Hay, and +# Pieter Abbeel (pabbeel@cs.berkeley.edu). + + +# game.py +# ------- +# Licensing Information: Please do not distribute or publish solutions to this +# project. You are free to use and extend these projects for educational +# purposes. The Pacman AI projects were developed at UC Berkeley, primarily by +# John DeNero (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu). +# For more info, see http://inst.eecs.berkeley.edu/~cs188/sp09/pacman.html + +from util import * +import time +import os +import traceback +import sys + +####################### +# Parts worth reading # +####################### + + +class Agent: + """ + An agent must define a getAction method, but may also define the + following methods which will be called if they exist: + + def registerInitialState(self, state): # inspects the starting state + """ + + def __init__(self, index=0): + self.index = index + + def getAction(self, state): + """ + The Agent will receive a GameState (from either {pacman, capture, sonar}.py) and + must return an action from Directions.{North, South, East, West, Stop} + """ + raiseNotDefined() + + +class Directions: + NORTH = 'North' + SOUTH = 'South' + EAST = 'East' + WEST = 'West' + STOP = 'Stop' + + LEFT = {NORTH: WEST, + SOUTH: EAST, + EAST: NORTH, + WEST: SOUTH, + STOP: STOP} + + RIGHT = dict([(y, x) for x, y in list(LEFT.items())]) + + REVERSE = {NORTH: SOUTH, + SOUTH: NORTH, + EAST: WEST, + WEST: EAST, + STOP: STOP} + + +class Configuration: + """ + A Configuration holds the (x,y) coordinate of a character, along with its + traveling direction. + + The convention for positions, like a graph, is that (0,0) is the lower left corner, x increases + horizontally and y increases vertically. Therefore, north is the direction of increasing y, or (0,1). + """ + + def __init__(self, pos, direction): + self.pos = pos + self.direction = direction + + def getPosition(self): + return (self.pos) + + def getDirection(self): + return self.direction + + def isInteger(self): + x, y = self.pos + return x == int(x) and y == int(y) + + def __eq__(self, other): + if other == None: + return False + return (self.pos == other.pos and self.direction == other.direction) + + def __hash__(self): + x = hash(self.pos) + y = hash(self.direction) + return hash(x + 13 * y) + + def __str__(self): + return "(x,y)="+str(self.pos)+", "+str(self.direction) + + def generateSuccessor(self, vector): + """ + Generates a new configuration reached by translating the current + configuration by the action vector. This is a low-level call and does + not attempt to respect the legality of the movement. + + Actions are movement vectors. + """ + x, y = self.pos + dx, dy = vector + direction = Actions.vectorToDirection(vector) + if direction == Directions.STOP: + direction = self.direction # There is no stop direction + return Configuration((x + dx, y+dy), direction) + + +class AgentState: + """ + AgentStates hold the state of an agent (configuration, speed, scared, etc). + """ + + def __init__(self, startConfiguration, isPacman): + self.start = startConfiguration + self.configuration = startConfiguration + self.isPacman = isPacman + self.scaredTimer = 0 + # state below potentially used for contest only + self.numCarrying = 0 + self.numReturned = 0 + + def __str__(self): + if self.isPacman: + return "Pacman: " + str(self.configuration) + else: + return "Ghost: " + str(self.configuration) + + def __eq__(self, other): + if other == None: + return False + return self.configuration == other.configuration and self.scaredTimer == other.scaredTimer + + def __hash__(self): + return hash(hash(self.configuration) + 13 * hash(self.scaredTimer)) + + def copy(self): + state = AgentState(self.start, self.isPacman) + state.configuration = self.configuration + state.scaredTimer = self.scaredTimer + state.numCarrying = self.numCarrying + state.numReturned = self.numReturned + return state + + def getPosition(self): + if self.configuration == None: + return None + return self.configuration.getPosition() + + def getDirection(self): + return self.configuration.getDirection() + + +class Grid: + """ + A 2-dimensional array of objects backed by a list of lists. Data is accessed + via grid[x][y] where (x,y) are positions on a Pacman map with x horizontal, + y vertical and the origin (0,0) in the bottom left corner. + + The __str__ method constructs an output that is oriented like a pacman board. + """ + + def __init__(self, width, height, initialValue=False, bitRepresentation=None): + if initialValue not in [False, True]: + raise Exception('Grids can only contain booleans') + self.CELLS_PER_INT = 30 + + self.width = width + self.height = height + self.data = [[initialValue for y in range( + height)] for x in range(width)] + if bitRepresentation: + self._unpackBits(bitRepresentation) + + def __getitem__(self, i): + return self.data[i] + + def __setitem__(self, key, item): + self.data[key] = item + + def __str__(self): + out = [[str(self.data[x][y])[0] for x in range(self.width)] + for y in range(self.height)] + out.reverse() + return '\n'.join([''.join(x) for x in out]) + + def __eq__(self, other): + if other == None: + return False + return self.data == other.data + + def __hash__(self): + # return hash(str(self)) + base = 1 + h = 0 + for l in self.data: + for i in l: + if i: + h += base + base *= 2 + return hash(h) + + def copy(self): + g = Grid(self.width, self.height) + g.data = [x[:] for x in self.data] + return g + + def deepCopy(self): + return self.copy() + + def shallowCopy(self): + g = Grid(self.width, self.height) + g.data = self.data + return g + + def count(self, item=True): + return sum([x.count(item) for x in self.data]) + + def asList(self, key=True): + list = [] + for x in range(self.width): + for y in range(self.height): + if self[x][y] == key: + list.append((x, y)) + return list + + def packBits(self): + """ + Returns an efficient int list representation + + (width, height, bitPackedInts...) + """ + bits = [self.width, self.height] + currentInt = 0 + for i in range(self.height * self.width): + bit = self.CELLS_PER_INT - (i % self.CELLS_PER_INT) - 1 + x, y = self._cellIndexToPosition(i) + if self[x][y]: + currentInt += 2 ** bit + if (i + 1) % self.CELLS_PER_INT == 0: + bits.append(currentInt) + currentInt = 0 + bits.append(currentInt) + return tuple(bits) + + def _cellIndexToPosition(self, index): + x = index / self.height + y = index % self.height + return x, y + + def _unpackBits(self, bits): + """ + Fills in data from a bit-level representation + """ + cell = 0 + for packed in bits: + for bit in self._unpackInt(packed, self.CELLS_PER_INT): + if cell == self.width * self.height: + break + x, y = self._cellIndexToPosition(cell) + self[x][y] = bit + cell += 1 + + def _unpackInt(self, packed, size): + bools = [] + if packed < 0: + raise ValueError("must be a positive integer") + for i in range(size): + n = 2 ** (self.CELLS_PER_INT - i - 1) + if packed >= n: + bools.append(True) + packed -= n + else: + bools.append(False) + return bools + + +def reconstituteGrid(bitRep): + if type(bitRep) is not type((1, 2)): + return bitRep + width, height = bitRep[:2] + return Grid(width, height, bitRepresentation=bitRep[2:]) + +#################################### +# Parts you shouldn't have to read # +#################################### + + +class Actions: + """ + A collection of static methods for manipulating move actions. + """ + # Directions + _directions = {Directions.WEST: (-1, 0), + Directions.STOP: (0, 0), + Directions.EAST: (1, 0), + Directions.NORTH: (0, 1), + Directions.SOUTH: (0, -1)} + + _directionsAsList = [('West', (-1, 0)), ('Stop', (0, 0)), ('East', (1, 0)), ('North', (0, 1)), ('South', (0, -1))] + + TOLERANCE = .001 + + def reverseDirection(action): + if action == Directions.NORTH: + return Directions.SOUTH + if action == Directions.SOUTH: + return Directions.NORTH + if action == Directions.EAST: + return Directions.WEST + if action == Directions.WEST: + return Directions.EAST + return action + reverseDirection = staticmethod(reverseDirection) + + def vectorToDirection(vector): + dx, dy = vector + if dy > 0: + return Directions.NORTH + if dy < 0: + return Directions.SOUTH + if dx < 0: + return Directions.WEST + if dx > 0: + return Directions.EAST + return Directions.STOP + vectorToDirection = staticmethod(vectorToDirection) + + def directionToVector(direction, speed=1.0): + dx, dy = Actions._directions[direction] + return (dx * speed, dy * speed) + directionToVector = staticmethod(directionToVector) + + def getPossibleActions(config, walls): + possible = [] + x, y = config.pos + x_int, y_int = int(x + 0.5), int(y + 0.5) + + # In between grid points, all agents must continue straight + if (abs(x - x_int) + abs(y - y_int) > Actions.TOLERANCE): + return [config.getDirection()] + + for dir, vec in Actions._directionsAsList: + dx, dy = vec + next_y = y_int + dy + next_x = x_int + dx + if not walls[next_x][next_y]: + possible.append(dir) + + return possible + + getPossibleActions = staticmethod(getPossibleActions) + + def getLegalNeighbors(position, walls): + x, y = position + x_int, y_int = int(x + 0.5), int(y + 0.5) + neighbors = [] + for dir, vec in Actions._directionsAsList: + dx, dy = vec + next_x = x_int + dx + if next_x < 0 or next_x == walls.width: + continue + next_y = y_int + dy + if next_y < 0 or next_y == walls.height: + continue + if not walls[next_x][next_y]: + neighbors.append((next_x, next_y)) + return neighbors + getLegalNeighbors = staticmethod(getLegalNeighbors) + + def getSuccessor(position, action): + dx, dy = Actions.directionToVector(action) + x, y = position + return (x + dx, y + dy) + getSuccessor = staticmethod(getSuccessor) + + +class GameStateData: + + def __init__(self, prevState=None): + """ + Generates a new data packet by copying information from its predecessor. + """ + if prevState != None: + self.food = prevState.food.shallowCopy() + self.capsules = prevState.capsules[:] + self.agentStates = self.copyAgentStates(prevState.agentStates) + self.layout = prevState.layout + self._eaten = prevState._eaten + self.score = prevState.score + + self._foodEaten = None + self._foodAdded = None + self._capsuleEaten = None + self._agentMoved = None + self._lose = False + self._win = False + self.scoreChange = 0 + + def deepCopy(self): + state = GameStateData(self) + state.food = self.food.deepCopy() + state.layout = self.layout.deepCopy() + state._agentMoved = self._agentMoved + state._foodEaten = self._foodEaten + state._foodAdded = self._foodAdded + state._capsuleEaten = self._capsuleEaten + return state + + def copyAgentStates(self, agentStates): + copiedStates = [] + for agentState in agentStates: + copiedStates.append(agentState.copy()) + return copiedStates + + def __eq__(self, other): + """ + Allows two states to be compared. + """ + if other == None: + return False + # TODO Check for type of other + if not self.agentStates == other.agentStates: + return False + if not self.food == other.food: + return False + if not self.capsules == other.capsules: + return False + if not self.score == other.score: + return False + return True + + def __hash__(self): + """ + Allows states to be keys of dictionaries. + """ + for i, state in enumerate(self.agentStates): + try: + int(hash(state)) + except TypeError as e: + print(e) + # hash(state) + return int((hash(tuple(self.agentStates)) + 13*hash(self.food) + 113 * hash(tuple(self.capsules)) + 7 * hash(self.score)) % 1048575) + + def __str__(self): + width, height = self.layout.width, self.layout.height + map = Grid(width, height) + if type(self.food) == type((1, 2)): + self.food = reconstituteGrid(self.food) + for x in range(width): + for y in range(height): + food, walls = self.food, self.layout.walls + map[x][y] = self._foodWallStr(food[x][y], walls[x][y]) + + for agentState in self.agentStates: + if agentState == None: + continue + if agentState.configuration == None: + continue + x, y = [int(i) for i in nearestPoint(agentState.configuration.pos)] + agent_dir = agentState.configuration.direction + if agentState.isPacman: + map[x][y] = self._pacStr(agent_dir) + else: + map[x][y] = self._ghostStr(agent_dir) + + for x, y in self.capsules: + map[x][y] = 'o' + + return str(map) + ("\nScore: %d\n" % self.score) + + def _foodWallStr(self, hasFood, hasWall): + if hasFood: + return '.' + elif hasWall: + return '%' + else: + return ' ' + + def _pacStr(self, dir): + if dir == Directions.NORTH: + return 'v' + if dir == Directions.SOUTH: + return '^' + if dir == Directions.WEST: + return '>' + return '<' + + def _ghostStr(self, dir): + return 'G' + if dir == Directions.NORTH: + return 'M' + if dir == Directions.SOUTH: + return 'W' + if dir == Directions.WEST: + return '3' + return 'E' + + def initialize(self, layout, numGhostAgents): + """ + Creates an initial game state from a layout array (see layout.py). + """ + self.food = layout.food.copy() + #self.capsules = [] + self.capsules = layout.capsules[:] + self.layout = layout + self.score = 0 + self.scoreChange = 0 + + self.agentStates = [] + numGhosts = 0 + for isPacman, pos in layout.agentPositions: + if not isPacman: + if numGhosts == numGhostAgents: + continue # Max ghosts reached already + else: + numGhosts += 1 + self.agentStates.append(AgentState( + Configuration(pos, Directions.STOP), isPacman)) + self._eaten = [False for a in self.agentStates] + + +try: + import boinc + _BOINC_ENABLED = True +except: + _BOINC_ENABLED = False + + +class Game: + """ + The Game manages the control flow, soliciting actions from agents. + """ + + def __init__(self, agents, display, rules, startingIndex=0, muteAgents=False, catchExceptions=False): + self.agentCrashed = False + self.agents = agents + self.display = display + self.rules = rules + self.startingIndex = startingIndex + self.gameOver = False + self.muteAgents = muteAgents + self.catchExceptions = catchExceptions + self.moveHistory = [] + self.totalAgentTimes = [0 for agent in agents] + self.totalAgentTimeWarnings = [0 for agent in agents] + self.agentTimeout = False + import io + self.agentOutput = [io.StringIO() for agent in agents] + + def getProgress(self): + if self.gameOver: + return 1.0 + else: + return self.rules.getProgress(self) + + def _agentCrash(self, agentIndex, quiet=False): + "Helper method for handling agent crashes" + if not quiet: + traceback.print_exc() + self.gameOver = True + self.agentCrashed = True + self.rules.agentCrash(self, agentIndex) + + OLD_STDOUT = None + OLD_STDERR = None + + def mute(self, agentIndex): + if not self.muteAgents: + return + global OLD_STDOUT, OLD_STDERR + import io + OLD_STDOUT = sys.stdout + OLD_STDERR = sys.stderr + sys.stdout = self.agentOutput[agentIndex] + sys.stderr = self.agentOutput[agentIndex] + + def unmute(self): + if not self.muteAgents: + return + global OLD_STDOUT, OLD_STDERR + # Revert stdout/stderr to originals + sys.stdout = OLD_STDOUT + sys.stderr = OLD_STDERR + + def run(self): + """ + Main control loop for game play. + """ + self.display.initialize(self.state.data) + self.numMoves = 0 + + # self.display.initialize(self.state.makeObservation(1).data) + # inform learning agents of the game start + for i in range(len(self.agents)): + agent = self.agents[i] + if not agent: + self.mute(i) + # this is a null agent, meaning it failed to load + # the other team wins + print("Agent %d failed to load" % i, file=sys.stderr) + self.unmute() + self._agentCrash(i, quiet=True) + return + if ("registerInitialState" in dir(agent)): + self.mute(i) + if self.catchExceptions: + try: + timed_func = TimeoutFunction( + agent.registerInitialState, int(self.rules.getMaxStartupTime(i))) + try: + start_time = time.time() + timed_func(self.state.deepCopy()) + time_taken = time.time() - start_time + self.totalAgentTimes[i] += time_taken + except TimeoutFunctionException: + print("Agent %d ran out of time on startup!" % + i, file=sys.stderr) + self.unmute() + self.agentTimeout = True + self._agentCrash(i, quiet=True) + return + except Exception as data: + self._agentCrash(i, quiet=False) + self.unmute() + return + else: + agent.registerInitialState(self.state.deepCopy()) + # TODO: could this exceed the total time + self.unmute() + + agentIndex = self.startingIndex + numAgents = len(self.agents) + + while not self.gameOver: + # Fetch the next agent + agent = self.agents[agentIndex] + move_time = 0 + skip_action = False + # Generate an observation of the state + if 'observationFunction' in dir(agent): + self.mute(agentIndex) + if self.catchExceptions: + try: + timed_func = TimeoutFunction(agent.observationFunction, int( + self.rules.getMoveTimeout(agentIndex))) + try: + start_time = time.time() + observation = timed_func(self.state.deepCopy()) + except TimeoutFunctionException: + skip_action = True + move_time += time.time() - start_time + self.unmute() + except Exception as data: + self._agentCrash(agentIndex, quiet=False) + self.unmute() + return + else: + observation = agent.observationFunction( + self.state.deepCopy()) + self.unmute() + else: + observation = self.state.deepCopy() + + # Solicit an action + action = None + self.mute(agentIndex) + if self.catchExceptions: + try: + timed_func = TimeoutFunction(agent.getAction, int( + self.rules.getMoveTimeout(agentIndex)) - int(move_time)) + try: + start_time = time.time() + if skip_action: + raise TimeoutFunctionException() + action = timed_func(observation) + except TimeoutFunctionException: + print("Agent %d timed out on a single move!" % + agentIndex, file=sys.stderr) + self.agentTimeout = True + self._agentCrash(agentIndex, quiet=True) + self.unmute() + return + + move_time += time.time() - start_time + + if move_time > self.rules.getMoveWarningTime(agentIndex): + self.totalAgentTimeWarnings[agentIndex] += 1 + print("Agent %d took too long to make a move! This is warning %d" % ( + agentIndex, self.totalAgentTimeWarnings[agentIndex]), file=sys.stderr) + if self.totalAgentTimeWarnings[agentIndex] > self.rules.getMaxTimeWarnings(agentIndex): + print("Agent %d exceeded the maximum number of warnings: %d" % ( + agentIndex, self.totalAgentTimeWarnings[agentIndex]), file=sys.stderr) + self.agentTimeout = True + self._agentCrash(agentIndex, quiet=True) + self.unmute() + return + + self.totalAgentTimes[agentIndex] += move_time + # print "Agent: %d, time: %f, total: %f" % (agentIndex, move_time, self.totalAgentTimes[agentIndex]) + if self.totalAgentTimes[agentIndex] > self.rules.getMaxTotalTime(agentIndex): + print("Agent %d ran out of time! (time: %1.2f)" % ( + agentIndex, self.totalAgentTimes[agentIndex]), file=sys.stderr) + self.agentTimeout = True + self._agentCrash(agentIndex, quiet=True) + self.unmute() + return + self.unmute() + except Exception as data: + self._agentCrash(agentIndex) + self.unmute() + return + else: + action = agent.getAction(observation) + self.unmute() + + # Execute the action + self.moveHistory.append((agentIndex, action)) + if self.catchExceptions: + try: + self.state = self.state.generateSuccessor( + agentIndex, action) + except Exception as data: + self.mute(agentIndex) + self._agentCrash(agentIndex) + self.unmute() + return + else: + self.state = self.state.generateSuccessor(agentIndex, action) + + # Change the display + self.display.update(self.state.data) + ###idx = agentIndex - agentIndex % 2 + 1 + ###self.display.update( self.state.makeObservation(idx).data ) + + # Allow for game specific conditions (winning, losing, etc.) + self.rules.process(self.state, self) + # Track progress + if agentIndex == numAgents + 1: + self.numMoves += 1 + # Next agent + agentIndex = (agentIndex + 1) % numAgents + + if _BOINC_ENABLED: + boinc.set_fraction_done(self.getProgress()) + + # inform a learning agent of the game result + for agentIndex, agent in enumerate(self.agents): + if "final" in dir(agent): + try: + self.mute(agentIndex) + agent.final(self.state) + self.unmute() + except Exception as data: + if not self.catchExceptions: + raise + self._agentCrash(agentIndex) + self.unmute() + return + self.display.finish() diff --git a/multiagent/ghostAgents.py b/multiagent/ghostAgents.py new file mode 100644 index 0000000..0b84b50 --- /dev/null +++ b/multiagent/ghostAgents.py @@ -0,0 +1,93 @@ +# ghostAgents.py +# -------------- +# Licensing Information: You are free to use or extend these projects for +# educational purposes provided that (1) you do not distribute or publish +# solutions, (2) you retain this notice, and (3) you provide clear +# attribution to UC Berkeley, including a link to http://ai.berkeley.edu. +# +# Attribution Information: The Pacman AI projects were developed at UC Berkeley. +# The core projects and autograders were primarily created by John DeNero +# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu). +# Student side autograding was added by Brad Miller, Nick Hay, and +# Pieter Abbeel (pabbeel@cs.berkeley.edu). + + +from game import Agent +from game import Actions +from game import Directions +import random +from util import manhattanDistance +import util + + +class GhostAgent(Agent): + def __init__(self, index): + self.index = index + + def getAction(self, state): + dist = self.getDistribution(state) + if len(dist) == 0: + return Directions.STOP + else: + return util.chooseFromDistribution(dist) + + def getDistribution(self, state): + "Returns a Counter encoding a distribution over actions from the provided state." + util.raiseNotDefined() + + +class RandomGhost(GhostAgent): + "A ghost that chooses a legal action uniformly at random." + + def getDistribution(self, state): + dist = util.Counter() + for a in state.getLegalActions(self.index): + dist[a] = 1.0 + dist.normalize() + return dist + + +class DirectionalGhost(GhostAgent): + "A ghost that prefers to rush Pacman, or flee when scared." + + def __init__(self, index, prob_attack=0.8, prob_scaredFlee=0.8): + self.index = index + self.prob_attack = prob_attack + self.prob_scaredFlee = prob_scaredFlee + + def getDistribution(self, state): + # Read variables from state + ghostState = state.getGhostState(self.index) + legalActions = state.getLegalActions(self.index) + pos = state.getGhostPosition(self.index) + isScared = ghostState.scaredTimer > 0 + + speed = 1 + if isScared: + speed = 0.5 + + actionVectors = [Actions.directionToVector( + a, speed) for a in legalActions] + newPositions = [(pos[0]+a[0], pos[1]+a[1]) for a in actionVectors] + pacmanPosition = state.getPacmanPosition() + + # Select best actions given the state + distancesToPacman = [manhattanDistance( + pos, pacmanPosition) for pos in newPositions] + if isScared: + bestScore = max(distancesToPacman) + bestProb = self.prob_scaredFlee + else: + bestScore = min(distancesToPacman) + bestProb = self.prob_attack + bestActions = [action for action, distance in zip( + legalActions, distancesToPacman) if distance == bestScore] + + # Construct distribution + dist = util.Counter() + for a in bestActions: + dist[a] = bestProb / len(bestActions) + for a in legalActions: + dist[a] += (1-bestProb) / len(legalActions) + dist.normalize() + return dist diff --git a/multiagent/grading.py b/multiagent/grading.py new file mode 100644 index 0000000..30d628a --- /dev/null +++ b/multiagent/grading.py @@ -0,0 +1,328 @@ +# grading.py +# ---------- +# Licensing Information: You are free to use or extend these projects for +# educational purposes provided that (1) you do not distribute or publish +# solutions, (2) you retain this notice, and (3) you provide clear +# attribution to UC Berkeley, including a link to http://ai.berkeley.edu. +# +# Attribution Information: The Pacman AI projects were developed at UC Berkeley. +# The core projects and autograders were primarily created by John DeNero +# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu). +# Student side autograding was added by Brad Miller, Nick Hay, and +# Pieter Abbeel (pabbeel@cs.berkeley.edu). + + +"Common code for autograders" + +import html +import time +import sys +import json +import traceback +import pdb +from collections import defaultdict +import util + + +class Grades: + "A data structure for project grades, along with formatting code to display them" + + def __init__(self, projectName, questionsAndMaxesList, + gsOutput=False, edxOutput=False, muteOutput=False): + """ + Defines the grading scheme for a project + projectName: project name + questionsAndMaxesDict: a list of (question name, max points per question) + """ + self.questions = [el[0] for el in questionsAndMaxesList] + self.maxes = dict(questionsAndMaxesList) + self.points = Counter() + self.messages = dict([(q, []) for q in self.questions]) + self.project = projectName + self.start = time.localtime()[1:6] + self.sane = True # Sanity checks + self.currentQuestion = None # Which question we're grading + self.edxOutput = edxOutput + self.gsOutput = gsOutput # GradeScope output + self.mute = muteOutput + self.prereqs = defaultdict(set) + + # print 'Autograder transcript for %s' % self.project + print('Starting on %d-%d at %d:%02d:%02d' % self.start) + + def addPrereq(self, question, prereq): + self.prereqs[question].add(prereq) + + def grade(self, gradingModule, exceptionMap={}, bonusPic=False): + """ + Grades each question + gradingModule: the module with all the grading functions (pass in with sys.modules[__name__]) + """ + + completedQuestions = set([]) + for q in self.questions: + print('\nQuestion %s' % q) + print('=' * (9 + len(q))) + print() + self.currentQuestion = q + + incompleted = self.prereqs[q].difference(completedQuestions) + if len(incompleted) > 0: + prereq = incompleted.pop() + print("""*** NOTE: Make sure to complete Question %s before working on Question %s, +*** because Question %s builds upon your answer for Question %s. +""" % (prereq, q, q, prereq)) + continue + + if self.mute: + util.mutePrint() + try: + util.TimeoutFunction(getattr(gradingModule, q), 1800)( + self) # Call the question's function + # TimeoutFunction(getattr(gradingModule, q),1200)(self) # Call the question's function + except Exception as inst: + self.addExceptionMessage(q, inst, traceback) + self.addErrorHints(exceptionMap, inst, q[1]) + except: + self.fail('FAIL: Terminated with a string exception.') + finally: + if self.mute: + util.unmutePrint() + + if self.points[q] >= self.maxes[q]: + completedQuestions.add(q) + + print('\n### Question %s: %d/%d ###\n' % + (q, self.points[q], self.maxes[q])) + + print('\nFinished at %d:%02d:%02d' % time.localtime()[3:6]) + print("\nProvisional grades\n==================") + + for q in self.questions: + print('Question %s: %d/%d' % (q, self.points[q], self.maxes[q])) + print('------------------') + print('Total: %d/%d' % + (self.points.totalCount(), sum(self.maxes.values()))) + if bonusPic and self.points.totalCount() == 25: + print(""" + + ALL HAIL GRANDPAC. + LONG LIVE THE GHOSTBUSTING KING. + + --- ---- --- + | \ / + \ / | + | + \--/ \--/ + | + | + + | + | + + + | + @@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + \ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + \ / @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + V \ @@@@@@@@@@@@@@@@@@@@@@@@@@@@ + \ / @@@@@@@@@@@@@@@@@@@@@@@@@@ + V @@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@ + /\ @@@@@@@@@@@@@@@@@@@@@@ + / \ @@@@@@@@@@@@@@@@@@@@@@@@@ + /\ / @@@@@@@@@@@@@@@@@@@@@@@@@@@ + / \ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + / @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@ + +""") + print(""" +Your grades are NOT yet registered. To register your grades, make sure +to follow your instructor's guidelines to receive credit on your project. +""") + + if self.edxOutput: + self.produceOutput() + if self.gsOutput: + self.produceGradeScopeOutput() + + def addExceptionMessage(self, q, inst, traceback): + """ + Method to format the exception message, this is more complicated because + we need to html.escape the traceback but wrap the exception in a 
 tag
+        """
+        self.fail('FAIL: Exception raised: %s' % inst)
+        self.addMessage('')
+        for line in traceback.format_exc().split('\n'):
+            self.addMessage(line)
+
+    def addErrorHints(self, exceptionMap, errorInstance, questionNum):
+        typeOf = str(type(errorInstance))
+        questionName = 'q' + questionNum
+        errorHint = ''
+
+        # question specific error hints
+        if exceptionMap.get(questionName):
+            questionMap = exceptionMap.get(questionName)
+            if (questionMap.get(typeOf)):
+                errorHint = questionMap.get(typeOf)
+        # fall back to general error messages if a question specific
+        # one does not exist
+        if (exceptionMap.get(typeOf)):
+            errorHint = exceptionMap.get(typeOf)
+
+        # dont include the HTML if we have no error hint
+        if not errorHint:
+            return ''
+
+        for line in errorHint.split('\n'):
+            self.addMessage(line)
+
+    def produceGradeScopeOutput(self):
+        out_dct = {}
+
+        # total of entire submission
+        total_possible = sum(self.maxes.values())
+        total_score = sum(self.points.values())
+        out_dct['score'] = total_score
+        out_dct['max_score'] = total_possible
+        out_dct['output'] = "Total score (%d / %d)" % (
+            total_score, total_possible)
+
+        # individual tests
+        tests_out = []
+        for name in self.questions:
+            test_out = {}
+            # test name
+            test_out['name'] = name
+            # test score
+            test_out['score'] = self.points[name]
+            test_out['max_score'] = self.maxes[name]
+            # others
+            is_correct = self.points[name] >= self.maxes[name]
+            test_out['output'] = "  Question {num} ({points}/{max}) {correct}".format(
+                num=(name[1] if len(name) == 2 else name),
+                points=test_out['score'],
+                max=test_out['max_score'],
+                correct=('X' if not is_correct else ''),
+            )
+            test_out['tags'] = []
+            tests_out.append(test_out)
+        out_dct['tests'] = tests_out
+
+        # file output
+        with open('gradescope_response.json', 'w') as outfile:
+            json.dump(out_dct, outfile)
+        return
+
+    def produceOutput(self):
+        edxOutput = open('edx_response.html', 'w')
+        edxOutput.write("
")
+
+        # first sum
+        total_possible = sum(self.maxes.values())
+        total_score = sum(self.points.values())
+        checkOrX = ''
+        if (total_score >= total_possible):
+            checkOrX = ''
+        header = """
+        

+            Total score ({total_score} / {total_possible})
+        

+    """.format(total_score=total_score,
+               total_possible=total_possible,
+               checkOrX=checkOrX
+               )
+        edxOutput.write(header)
+
+        for q in self.questions:
+            if len(q) == 2:
+                name = q[1]
+            else:
+                name = q
+            checkOrX = ''
+            if (self.points[q] >= self.maxes[q]):
+                checkOrX = ''
+            #messages = '\n
\n'.join(self.messages[q])
+            messages = "
%s
" % '\n'.join(self.messages[q])
+            output = """
+        

+          

+          

+            Question {q} ({points}/{max}) {checkOrX}
+          

+        

+          {messages}
+        

+        

+      

+      """.format(q=name,
+                 max=self.maxes[q],
+                 messages=messages,
+                 checkOrX=checkOrX,
+                 points=self.points[q]
+                 )
+            # print "*** output for Question %s " % q[1]
+            # print output
+            edxOutput.write(output)
+        edxOutput.write("
")
+        edxOutput.close()
+        edxOutput = open('edx_grade', 'w')
+        edxOutput.write(str(self.points.totalCount()))
+        edxOutput.close()
+
+    def fail(self, message, raw=False):
+        "Sets sanity check bit to false and outputs a message"
+        self.sane = False
+        self.assignZeroCredit()
+        self.addMessage(message, raw)
+
+    def assignZeroCredit(self):
+        self.points[self.currentQuestion] = 0
+
+    def addPoints(self, amt):
+        self.points[self.currentQuestion] += amt
+
+    def deductPoints(self, amt):
+        self.points[self.currentQuestion] -= amt
+
+    def assignFullCredit(self, message="", raw=False):
+        self.points[self.currentQuestion] = self.maxes[self.currentQuestion]
+        if message != "":
+            self.addMessage(message, raw)
+
+    def addMessage(self, message, raw=False):
+        if not raw:
+                # We assume raw messages, formatted for HTML, are printed separately
+            if self.mute:
+                util.unmutePrint()
+            print('*** ' + message)
+            if self.mute:
+                util.mutePrint()
+            message = html.escape(message)
+        self.messages[self.currentQuestion].append(message)
+
+    def addMessageToEmail(self, message):
+        print("WARNING**** addMessageToEmail is deprecated %s" % message)
+        for line in message.split('\n'):
+            pass
+            # print '%%% ' + line + ' %%%'
+            # self.messages[self.currentQuestion].append(line)
+
+
+class Counter(dict):
+    """
+    Dict with default 0
+    """
+
+    def __getitem__(self, idx):
+        try:
+            return dict.__getitem__(self, idx)
+        except KeyError:
+            return 0
+
+    def totalCount(self):
+        """
+        Returns the sum of counts for all keys.
+        """
+        return sum(self.values())
diff --git a/multiagent/graphicsDisplay.py b/multiagent/graphicsDisplay.py
new file mode 100644
index 0000000..b2a82e5
--- /dev/null
+++ b/multiagent/graphicsDisplay.py
@@ -0,0 +1,738 @@
+# graphicsDisplay.py
+# ------------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+from graphicsUtils import *
+import math
+import time
+from game import Directions
+
+###########################
+#  GRAPHICS DISPLAY CODE  #
+###########################
+
+# Most code by Dan Klein and John Denero written or rewritten for cs188, UC Berkeley.
+# Some code from a Pacman implementation by LiveWires, and used / modified with permission.
+
+DEFAULT_GRID_SIZE = 30.0
+INFO_PANE_HEIGHT = 35
+BACKGROUND_COLOR = formatColor(0, 0, 0)
+WALL_COLOR = formatColor(0.0/255.0, 51.0/255.0, 255.0/255.0)
+INFO_PANE_COLOR = formatColor(.4, .4, 0)
+SCORE_COLOR = formatColor(.9, .9, .9)
+PACMAN_OUTLINE_WIDTH = 2
+PACMAN_CAPTURE_OUTLINE_WIDTH = 4
+
+GHOST_COLORS = []
+GHOST_COLORS.append(formatColor(.9, 0, 0))  # Red
+GHOST_COLORS.append(formatColor(0, .3, .9))  # Blue
+GHOST_COLORS.append(formatColor(.98, .41, .07))  # Orange
+GHOST_COLORS.append(formatColor(.1, .75, .7))  # Green
+GHOST_COLORS.append(formatColor(1.0, 0.6, 0.0))  # Yellow
+GHOST_COLORS.append(formatColor(.4, 0.13, 0.91))  # Purple
+
+TEAM_COLORS = GHOST_COLORS[:2]
+
+GHOST_SHAPE = [
+    (0,     0.3),
+    (0.25,  0.75),
+    (0.5,   0.3),
+    (0.75,  0.75),
+    (0.75,  -0.5),
+    (0.5,   -0.75),
+    (-0.5,  -0.75),
+    (-0.75, -0.5),
+    (-0.75, 0.75),
+    (-0.5,  0.3),
+    (-0.25, 0.75)
+]
+GHOST_SIZE = 0.65
+SCARED_COLOR = formatColor(1, 1, 1)
+
+GHOST_VEC_COLORS = list(map(colorToVector, GHOST_COLORS))
+
+PACMAN_COLOR = formatColor(255.0/255.0, 255.0/255.0, 61.0/255)
+PACMAN_SCALE = 0.5
+#pacman_speed = 0.25
+
+# Food
+FOOD_COLOR = formatColor(1, 1, 1)
+FOOD_SIZE = 0.1
+
+# Laser
+LASER_COLOR = formatColor(1, 0, 0)
+LASER_SIZE = 0.02
+
+# Capsule graphics
+CAPSULE_COLOR = formatColor(1, 1, 1)
+CAPSULE_SIZE = 0.25
+
+# Drawing walls
+WALL_RADIUS = 0.15
+
+
+class InfoPane:
+    def __init__(self, layout, gridSize):
+        self.gridSize = gridSize
+        self.width = (layout.width) * gridSize
+        self.base = (layout.height + 1) * gridSize
+        self.height = INFO_PANE_HEIGHT
+        self.fontSize = 24
+        self.textColor = PACMAN_COLOR
+        self.drawPane()
+
+    def toScreen(self, pos, y=None):
+        """
+          Translates a point relative from the bottom left of the info pane.
+        """
+        if y == None:
+            x, y = pos
+        else:
+            x = pos
+
+        x = self.gridSize + x  # Margin
+        y = self.base + y
+        return x, y
+
+    def drawPane(self):
+        self.scoreText = text(self.toScreen(
+            0, 0), self.textColor, "SCORE:    0", "Times", self.fontSize, "bold")
+
+    def initializeGhostDistances(self, distances):
+        self.ghostDistanceText = []
+
+        size = 20
+        if self.width < 240:
+            size = 12
+        if self.width < 160:
+            size = 10
+
+        for i, d in enumerate(distances):
+            t = text(self.toScreen(self.width/2 + self.width/8 * i, 0),
+                     GHOST_COLORS[i+1], d, "Times", size, "bold")
+            self.ghostDistanceText.append(t)
+
+    def updateScore(self, score):
+        changeText(self.scoreText, "SCORE: % 4d" % score)
+
+    def setTeam(self, isBlue):
+        text = "RED TEAM"
+        if isBlue:
+            text = "BLUE TEAM"
+        self.teamText = text(self.toScreen(
+            300, 0), self.textColor, text, "Times", self.fontSize, "bold")
+
+    def updateGhostDistances(self, distances):
+        if len(distances) == 0:
+            return
+        if 'ghostDistanceText' not in dir(self):
+            self.initializeGhostDistances(distances)
+        else:
+            for i, d in enumerate(distances):
+                changeText(self.ghostDistanceText[i], d)
+
+    def drawGhost(self):
+        pass
+
+    def drawPacman(self):
+        pass
+
+    def drawWarning(self):
+        pass
+
+    def clearIcon(self):
+        pass
+
+    def updateMessage(self, message):
+        pass
+
+    def clearMessage(self):
+        pass
+
+
+class PacmanGraphics:
+    def __init__(self, zoom=1.0, frameTime=0.0, capture=False):
+        self.have_window = 0
+        self.currentGhostImages = {}
+        self.pacmanImage = None
+        self.zoom = zoom
+        self.gridSize = DEFAULT_GRID_SIZE * zoom
+        self.capture = capture
+        self.frameTime = frameTime
+
+    def checkNullDisplay(self):
+        return False
+
+    def initialize(self, state, isBlue=False):
+        self.isBlue = isBlue
+        self.startGraphics(state)
+
+        # self.drawDistributions(state)
+        self.distributionImages = None  # Initialized lazily
+        self.drawStaticObjects(state)
+        self.drawAgentObjects(state)
+
+        # Information
+        self.previousState = state
+
+    def startGraphics(self, state):
+        self.layout = state.layout
+        layout = self.layout
+        self.width = layout.width
+        self.height = layout.height
+        self.make_window(self.width, self.height)
+        self.infoPane = InfoPane(layout, self.gridSize)
+        self.currentState = layout
+
+    def drawDistributions(self, state):
+        walls = state.layout.walls
+        dist = []
+        for x in range(walls.width):
+            distx = []
+            dist.append(distx)
+            for y in range(walls.height):
+                (screen_x, screen_y) = self.to_screen((x, y))
+                block = square((screen_x, screen_y),
+                               0.5 * self.gridSize,
+                               color=BACKGROUND_COLOR,
+                               filled=1, behind=2)
+                distx.append(block)
+        self.distributionImages = dist
+
+    def drawStaticObjects(self, state):
+        layout = self.layout
+        self.drawWalls(layout.walls)
+        self.food = self.drawFood(layout.food)
+        self.capsules = self.drawCapsules(layout.capsules)
+        refresh()
+
+    def drawAgentObjects(self, state):
+        self.agentImages = []  # (agentState, image)
+        for index, agent in enumerate(state.agentStates):
+            if agent.isPacman:
+                image = self.drawPacman(agent, index)
+                self.agentImages.append((agent, image))
+            else:
+                image = self.drawGhost(agent, index)
+                self.agentImages.append((agent, image))
+        refresh()
+
+    def swapImages(self, agentIndex, newState):
+        """
+          Changes an image from a ghost to a pacman or vis versa (for capture)
+        """
+        prevState, prevImage = self.agentImages[agentIndex]
+        for item in prevImage:
+            remove_from_screen(item)
+        if newState.isPacman:
+            image = self.drawPacman(newState, agentIndex)
+            self.agentImages[agentIndex] = (newState, image)
+        else:
+            image = self.drawGhost(newState, agentIndex)
+            self.agentImages[agentIndex] = (newState, image)
+        refresh()
+
+    def update(self, newState):
+        agentIndex = newState._agentMoved
+        agentState = newState.agentStates[agentIndex]
+
+        if self.agentImages[agentIndex][0].isPacman != agentState.isPacman:
+            self.swapImages(agentIndex, agentState)
+        prevState, prevImage = self.agentImages[agentIndex]
+        if agentState.isPacman:
+            self.animatePacman(agentState, prevState, prevImage)
+        else:
+            self.moveGhost(agentState, agentIndex, prevState, prevImage)
+        self.agentImages[agentIndex] = (agentState, prevImage)
+
+        if newState._foodEaten != None:
+            self.removeFood(newState._foodEaten, self.food)
+        if newState._capsuleEaten != None:
+            self.removeCapsule(newState._capsuleEaten, self.capsules)
+        self.infoPane.updateScore(newState.score)
+        if 'ghostDistances' in dir(newState):
+            self.infoPane.updateGhostDistances(newState.ghostDistances)
+
+    def make_window(self, width, height):
+        grid_width = (width-1) * self.gridSize
+        grid_height = (height-1) * self.gridSize
+        screen_width = 2*self.gridSize + grid_width
+        screen_height = 2*self.gridSize + grid_height + INFO_PANE_HEIGHT
+
+        begin_graphics(screen_width,
+                       screen_height,
+                       BACKGROUND_COLOR,
+                       "CS188 Pacman")
+
+    def drawPacman(self, pacman, index):
+        position = self.getPosition(pacman)
+        screen_point = self.to_screen(position)
+        endpoints = self.getEndpoints(self.getDirection(pacman))
+
+        width = PACMAN_OUTLINE_WIDTH
+        outlineColor = PACMAN_COLOR
+        fillColor = PACMAN_COLOR
+
+        if self.capture:
+            outlineColor = TEAM_COLORS[index % 2]
+            fillColor = GHOST_COLORS[index]
+            width = PACMAN_CAPTURE_OUTLINE_WIDTH
+
+        return [circle(screen_point, PACMAN_SCALE * self.gridSize,
+                       fillColor=fillColor, outlineColor=outlineColor,
+                       endpoints=endpoints,
+                       width=width)]
+
+    def getEndpoints(self, direction, position=(0, 0)):
+        x, y = position
+        pos = x - int(x) + y - int(y)
+        width = 30 + 80 * math.sin(math.pi * pos)
+
+        delta = width / 2
+        if (direction == 'West'):
+            endpoints = (180+delta, 180-delta)
+        elif (direction == 'North'):
+            endpoints = (90+delta, 90-delta)
+        elif (direction == 'South'):
+            endpoints = (270+delta, 270-delta)
+        else:
+            endpoints = (0+delta, 0-delta)
+        return endpoints
+
+    def movePacman(self, position, direction, image):
+        screenPosition = self.to_screen(position)
+        endpoints = self.getEndpoints(direction, position)
+        r = PACMAN_SCALE * self.gridSize
+        moveCircle(image[0], screenPosition, r, endpoints)
+        refresh()
+
+    def animatePacman(self, pacman, prevPacman, image):
+        if self.frameTime < 0:
+            print('Press any key to step forward, "q" to play')
+            keys = wait_for_keys()
+            if 'q' in keys:
+                self.frameTime = 0.1
+        if self.frameTime > 0.01 or self.frameTime < 0:
+            start = time.time()
+            fx, fy = self.getPosition(prevPacman)
+            px, py = self.getPosition(pacman)
+            frames = 4.0
+            for i in range(1, int(frames) + 1):
+                pos = px*i/frames + fx * \
+                    (frames-i)/frames, py*i/frames + fy*(frames-i)/frames
+                self.movePacman(pos, self.getDirection(pacman), image)
+                refresh()
+                sleep(abs(self.frameTime) / frames)
+        else:
+            self.movePacman(self.getPosition(pacman),
+                            self.getDirection(pacman), image)
+        refresh()
+
+    def getGhostColor(self, ghost, ghostIndex):
+        if ghost.scaredTimer > 0:
+            return SCARED_COLOR
+        else:
+            return GHOST_COLORS[ghostIndex]
+
+    def drawGhost(self, ghost, agentIndex):
+        pos = self.getPosition(ghost)
+        dir = self.getDirection(ghost)
+        (screen_x, screen_y) = (self.to_screen(pos))
+        coords = []
+        for (x, y) in GHOST_SHAPE:
+            coords.append((x*self.gridSize*GHOST_SIZE + screen_x,
+                           y*self.gridSize*GHOST_SIZE + screen_y))
+
+        colour = self.getGhostColor(ghost, agentIndex)
+        body = polygon(coords, colour, filled=1)
+        WHITE = formatColor(1.0, 1.0, 1.0)
+        BLACK = formatColor(0.0, 0.0, 0.0)
+
+        dx = 0
+        dy = 0
+        if dir == 'North':
+            dy = -0.2
+        if dir == 'South':
+            dy = 0.2
+        if dir == 'East':
+            dx = 0.2
+        if dir == 'West':
+            dx = -0.2
+        leftEye = circle((screen_x+self.gridSize*GHOST_SIZE*(-0.3+dx/1.5), screen_y -
+                          self.gridSize*GHOST_SIZE*(0.3-dy/1.5)), self.gridSize*GHOST_SIZE*0.2, WHITE, WHITE)
+        rightEye = circle((screen_x+self.gridSize*GHOST_SIZE*(0.3+dx/1.5), screen_y -
+                           self.gridSize*GHOST_SIZE*(0.3-dy/1.5)), self.gridSize*GHOST_SIZE*0.2, WHITE, WHITE)
+        leftPupil = circle((screen_x+self.gridSize*GHOST_SIZE*(-0.3+dx), screen_y -
+                            self.gridSize*GHOST_SIZE*(0.3-dy)), self.gridSize*GHOST_SIZE*0.08, BLACK, BLACK)
+        rightPupil = circle((screen_x+self.gridSize*GHOST_SIZE*(0.3+dx), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy)), self.gridSize*GHOST_SIZE*0.08, BLACK, BLACK)
+        ghostImageParts = []
+        ghostImageParts.append(body)
+        ghostImageParts.append(leftEye)
+        ghostImageParts.append(rightEye)
+        ghostImageParts.append(leftPupil)
+        ghostImageParts.append(rightPupil)
+
+        return ghostImageParts
+
+    def moveEyes(self, pos, dir, eyes):
+        (screen_x, screen_y) = (self.to_screen(pos))
+        dx = 0
+        dy = 0
+        if dir == 'North':
+            dy = -0.2
+        if dir == 'South':
+            dy = 0.2
+        if dir == 'East':
+            dx = 0.2
+        if dir == 'West':
+            dx = -0.2
+        moveCircle(eyes[0], (screen_x+self.gridSize*GHOST_SIZE*(-0.3+dx/1.5), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy/1.5)), self.gridSize*GHOST_SIZE*0.2)
+        moveCircle(eyes[1], (screen_x+self.gridSize*GHOST_SIZE*(0.3+dx/1.5), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy/1.5)), self.gridSize*GHOST_SIZE*0.2)
+        moveCircle(eyes[2], (screen_x+self.gridSize*GHOST_SIZE*(-0.3+dx), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy)), self.gridSize*GHOST_SIZE*0.08)
+        moveCircle(eyes[3], (screen_x+self.gridSize*GHOST_SIZE*(0.3+dx), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy)), self.gridSize*GHOST_SIZE*0.08)
+
+    def moveGhost(self, ghost, ghostIndex, prevGhost, ghostImageParts):
+        old_x, old_y = self.to_screen(self.getPosition(prevGhost))
+        new_x, new_y = self.to_screen(self.getPosition(ghost))
+        delta = new_x - old_x, new_y - old_y
+
+        for ghostImagePart in ghostImageParts:
+            move_by(ghostImagePart, delta)
+        refresh()
+
+        if ghost.scaredTimer > 0:
+            color = SCARED_COLOR
+        else:
+            color = GHOST_COLORS[ghostIndex]
+        edit(ghostImageParts[0], ('fill', color), ('outline', color))
+        self.moveEyes(self.getPosition(ghost),
+                      self.getDirection(ghost), ghostImageParts[-4:])
+        refresh()
+
+    def getPosition(self, agentState):
+        if agentState.configuration == None:
+            return (-1000, -1000)
+        return agentState.getPosition()
+
+    def getDirection(self, agentState):
+        if agentState.configuration == None:
+            return Directions.STOP
+        return agentState.configuration.getDirection()
+
+    def finish(self):
+        end_graphics()
+
+    def to_screen(self, point):
+        (x, y) = point
+        #y = self.height - y
+        x = (x + 1)*self.gridSize
+        y = (self.height - y)*self.gridSize
+        return (x, y)
+
+    # Fixes some TK issue with off-center circles
+    def to_screen2(self, point):
+        (x, y) = point
+        #y = self.height - y
+        x = (x + 1)*self.gridSize
+        y = (self.height - y)*self.gridSize
+        return (x, y)
+
+    def drawWalls(self, wallMatrix):
+        wallColor = WALL_COLOR
+        for xNum, x in enumerate(wallMatrix):
+            if self.capture and (xNum * 2) < wallMatrix.width:
+                wallColor = TEAM_COLORS[0]
+            if self.capture and (xNum * 2) >= wallMatrix.width:
+                wallColor = TEAM_COLORS[1]
+
+            for yNum, cell in enumerate(x):
+                if cell:  # There's a wall here
+                    pos = (xNum, yNum)
+                    screen = self.to_screen(pos)
+                    screen2 = self.to_screen2(pos)
+
+                    # draw each quadrant of the square based on adjacent walls
+                    wIsWall = self.isWall(xNum-1, yNum, wallMatrix)
+                    eIsWall = self.isWall(xNum+1, yNum, wallMatrix)
+                    nIsWall = self.isWall(xNum, yNum+1, wallMatrix)
+                    sIsWall = self.isWall(xNum, yNum-1, wallMatrix)
+                    nwIsWall = self.isWall(xNum-1, yNum+1, wallMatrix)
+                    swIsWall = self.isWall(xNum-1, yNum-1, wallMatrix)
+                    neIsWall = self.isWall(xNum+1, yNum+1, wallMatrix)
+                    seIsWall = self.isWall(xNum+1, yNum-1, wallMatrix)
+
+                    # NE quadrant
+                    if (not nIsWall) and (not eIsWall):
+                        # inner circle
+                        circle(screen2, WALL_RADIUS * self.gridSize,
+                               wallColor, wallColor, (0, 91), 'arc')
+                    if (nIsWall) and (not eIsWall):
+                        # vertical line
+                        line(add(screen, (self.gridSize*WALL_RADIUS, 0)), add(screen,
+                                                                              (self.gridSize*WALL_RADIUS, self.gridSize*(-0.5)-1)), wallColor)
+                    if (not nIsWall) and (eIsWall):
+                        # horizontal line
+                        line(add(screen, (0, self.gridSize*(-1)*WALL_RADIUS)), add(screen,
+                                                                                   (self.gridSize*0.5+1, self.gridSize*(-1)*WALL_RADIUS)), wallColor)
+                    if (nIsWall) and (eIsWall) and (not neIsWall):
+                        # outer circle
+                        circle(add(screen2, (self.gridSize*2*WALL_RADIUS, self.gridSize*(-2)*WALL_RADIUS)),
+                               WALL_RADIUS * self.gridSize-1, wallColor, wallColor, (180, 271), 'arc')
+                        line(add(screen, (self.gridSize*2*WALL_RADIUS-1, self.gridSize*(-1)*WALL_RADIUS)),
+                             add(screen, (self.gridSize*0.5+1, self.gridSize*(-1)*WALL_RADIUS)), wallColor)
+                        line(add(screen, (self.gridSize*WALL_RADIUS, self.gridSize*(-2)*WALL_RADIUS+1)),
+                             add(screen, (self.gridSize*WALL_RADIUS, self.gridSize*(-0.5))), wallColor)
+
+                    # NW quadrant
+                    if (not nIsWall) and (not wIsWall):
+                        # inner circle
+                        circle(screen2, WALL_RADIUS * self.gridSize,
+                               wallColor, wallColor, (90, 181), 'arc')
+                    if (nIsWall) and (not wIsWall):
+                        # vertical line
+                        line(add(screen, (self.gridSize*(-1)*WALL_RADIUS, 0)), add(screen,
+                                                                                   (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(-0.5)-1)), wallColor)
+                    if (not nIsWall) and (wIsWall):
+                        # horizontal line
+                        line(add(screen, (0, self.gridSize*(-1)*WALL_RADIUS)), add(screen,
+                                                                                   (self.gridSize*(-0.5)-1, self.gridSize*(-1)*WALL_RADIUS)), wallColor)
+                    if (nIsWall) and (wIsWall) and (not nwIsWall):
+                        # outer circle
+                        circle(add(screen2, (self.gridSize*(-2)*WALL_RADIUS, self.gridSize*(-2)*WALL_RADIUS)),
+                               WALL_RADIUS * self.gridSize-1, wallColor, wallColor, (270, 361), 'arc')
+                        line(add(screen, (self.gridSize*(-2)*WALL_RADIUS+1, self.gridSize*(-1)*WALL_RADIUS)),
+                             add(screen, (self.gridSize*(-0.5), self.gridSize*(-1)*WALL_RADIUS)), wallColor)
+                        line(add(screen, (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(-2)*WALL_RADIUS+1)),
+                             add(screen, (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(-0.5))), wallColor)
+
+                    # SE quadrant
+                    if (not sIsWall) and (not eIsWall):
+                        # inner circle
+                        circle(screen2, WALL_RADIUS * self.gridSize,
+                               wallColor, wallColor, (270, 361), 'arc')
+                    if (sIsWall) and (not eIsWall):
+                        # vertical line
+                        line(add(screen, (self.gridSize*WALL_RADIUS, 0)), add(screen,
+                                                                              (self.gridSize*WALL_RADIUS, self.gridSize*(0.5)+1)), wallColor)
+                    if (not sIsWall) and (eIsWall):
+                        # horizontal line
+                        line(add(screen, (0, self.gridSize*(1)*WALL_RADIUS)), add(screen,
+                                                                                  (self.gridSize*0.5+1, self.gridSize*(1)*WALL_RADIUS)), wallColor)
+                    if (sIsWall) and (eIsWall) and (not seIsWall):
+                        # outer circle
+                        circle(add(screen2, (self.gridSize*2*WALL_RADIUS, self.gridSize*(2)*WALL_RADIUS)),
+                               WALL_RADIUS * self.gridSize-1, wallColor, wallColor, (90, 181), 'arc')
+                        line(add(screen, (self.gridSize*2*WALL_RADIUS-1, self.gridSize*(1)*WALL_RADIUS)),
+                             add(screen, (self.gridSize*0.5, self.gridSize*(1)*WALL_RADIUS)), wallColor)
+                        line(add(screen, (self.gridSize*WALL_RADIUS, self.gridSize*(2)*WALL_RADIUS-1)),
+                             add(screen, (self.gridSize*WALL_RADIUS, self.gridSize*(0.5))), wallColor)
+
+                    # SW quadrant
+                    if (not sIsWall) and (not wIsWall):
+                        # inner circle
+                        circle(screen2, WALL_RADIUS * self.gridSize,
+                               wallColor, wallColor, (180, 271), 'arc')
+                    if (sIsWall) and (not wIsWall):
+                        # vertical line
+                        line(add(screen, (self.gridSize*(-1)*WALL_RADIUS, 0)), add(screen,
+                                                                                   (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(0.5)+1)), wallColor)
+                    if (not sIsWall) and (wIsWall):
+                        # horizontal line
+                        line(add(screen, (0, self.gridSize*(1)*WALL_RADIUS)), add(screen,
+                                                                                  (self.gridSize*(-0.5)-1, self.gridSize*(1)*WALL_RADIUS)), wallColor)
+                    if (sIsWall) and (wIsWall) and (not swIsWall):
+                        # outer circle
+                        circle(add(screen2, (self.gridSize*(-2)*WALL_RADIUS, self.gridSize*(2)*WALL_RADIUS)),
+                               WALL_RADIUS * self.gridSize-1, wallColor, wallColor, (0, 91), 'arc')
+                        line(add(screen, (self.gridSize*(-2)*WALL_RADIUS+1, self.gridSize*(1)*WALL_RADIUS)),
+                             add(screen, (self.gridSize*(-0.5), self.gridSize*(1)*WALL_RADIUS)), wallColor)
+                        line(add(screen, (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(2)*WALL_RADIUS-1)),
+                             add(screen, (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(0.5))), wallColor)
+
+    def isWall(self, x, y, walls):
+        if x < 0 or y < 0:
+            return False
+        if x >= walls.width or y >= walls.height:
+            return False
+        return walls[x][y]
+
+    def drawFood(self, foodMatrix):
+        foodImages = []
+        color = FOOD_COLOR
+        for xNum, x in enumerate(foodMatrix):
+            if self.capture and (xNum * 2) <= foodMatrix.width:
+                color = TEAM_COLORS[0]
+            if self.capture and (xNum * 2) > foodMatrix.width:
+                color = TEAM_COLORS[1]
+            imageRow = []
+            foodImages.append(imageRow)
+            for yNum, cell in enumerate(x):
+                if cell:  # There's food here
+                    screen = self.to_screen((xNum, yNum))
+                    dot = circle(screen,
+                                 FOOD_SIZE * self.gridSize,
+                                 outlineColor=color, fillColor=color,
+                                 width=1)
+                    imageRow.append(dot)
+                else:
+                    imageRow.append(None)
+        return foodImages
+
+    def drawCapsules(self, capsules):
+        capsuleImages = {}
+        for capsule in capsules:
+            (screen_x, screen_y) = self.to_screen(capsule)
+            dot = circle((screen_x, screen_y),
+                         CAPSULE_SIZE * self.gridSize,
+                         outlineColor=CAPSULE_COLOR,
+                         fillColor=CAPSULE_COLOR,
+                         width=1)
+            capsuleImages[capsule] = dot
+        return capsuleImages
+
+    def removeFood(self, cell, foodImages):
+        x, y = cell
+        remove_from_screen(foodImages[x][y])
+
+    def removeCapsule(self, cell, capsuleImages):
+        x, y = cell
+        remove_from_screen(capsuleImages[(x, y)])
+
+    def drawExpandedCells(self, cells):
+        """
+        Draws an overlay of expanded grid positions for search agents
+        """
+        n = float(len(cells))
+        baseColor = [1.0, 0.0, 0.0]
+        self.clearExpandedCells()
+        self.expandedCells = []
+        for k, cell in enumerate(cells):
+            screenPos = self.to_screen(cell)
+            cellColor = formatColor(
+                *[(n-k) * c * .5 / n + .25 for c in baseColor])
+            block = square(screenPos,
+                           0.5 * self.gridSize,
+                           color=cellColor,
+                           filled=1, behind=2)
+            self.expandedCells.append(block)
+            if self.frameTime < 0:
+                refresh()
+
+    def clearExpandedCells(self):
+        if 'expandedCells' in dir(self) and len(self.expandedCells) > 0:
+            for cell in self.expandedCells:
+                remove_from_screen(cell)
+
+    def updateDistributions(self, distributions):
+        "Draws an agent's belief distributions"
+        # copy all distributions so we don't change their state
+        distributions = [x.copy() for x in distributions]
+        if self.distributionImages == None:
+            self.drawDistributions(self.previousState)
+        for x in range(len(self.distributionImages)):
+            for y in range(len(self.distributionImages[0])):
+                image = self.distributionImages[x][y]
+                weights = [dist[(x, y)] for dist in distributions]
+
+                if sum(weights) != 0:
+                    pass
+                # Fog of war
+                color = [0.0, 0.0, 0.0]
+                colors = GHOST_VEC_COLORS[1:]  # With Pacman
+                if self.capture:
+                    colors = GHOST_VEC_COLORS
+                for weight, gcolor in zip(weights, colors):
+                    color = [min(1.0, c + 0.95 * g * weight ** .3)
+                             for c, g in zip(color, gcolor)]
+                changeColor(image, formatColor(*color))
+        refresh()
+
+
+class FirstPersonPacmanGraphics(PacmanGraphics):
+    def __init__(self, zoom=1.0, showGhosts=True, capture=False, frameTime=0):
+        PacmanGraphics.__init__(self, zoom, frameTime=frameTime)
+        self.showGhosts = showGhosts
+        self.capture = capture
+
+    def initialize(self, state, isBlue=False):
+
+        self.isBlue = isBlue
+        PacmanGraphics.startGraphics(self, state)
+        # Initialize distribution images
+        walls = state.layout.walls
+        dist = []
+        self.layout = state.layout
+
+        # Draw the rest
+        self.distributionImages = None  # initialize lazily
+        self.drawStaticObjects(state)
+        self.drawAgentObjects(state)
+
+        # Information
+        self.previousState = state
+
+    def lookAhead(self, config, state):
+        if config.getDirection() == 'Stop':
+            return
+        else:
+            pass
+            # Draw relevant ghosts
+            allGhosts = state.getGhostStates()
+            visibleGhosts = state.getVisibleGhosts()
+            for i, ghost in enumerate(allGhosts):
+                if ghost in visibleGhosts:
+                    self.drawGhost(ghost, i)
+                else:
+                    self.currentGhostImages[i] = None
+
+    def getGhostColor(self, ghost, ghostIndex):
+        return GHOST_COLORS[ghostIndex]
+
+    def getPosition(self, ghostState):
+        if not self.showGhosts and not ghostState.isPacman and ghostState.getPosition()[1] > 1:
+            return (-1000, -1000)
+        else:
+            return PacmanGraphics.getPosition(self, ghostState)
+
+
+def add(x, y):
+    return (x[0] + y[0], x[1] + y[1])
+
+
+# Saving graphical output
+# -----------------------
+# Note: to make an animated gif from this postscript output, try the command:
+# convert -delay 7 -loop 1 -compress lzw -layers optimize frame* out.gif
+# convert is part of imagemagick (freeware)
+
+SAVE_POSTSCRIPT = False
+POSTSCRIPT_OUTPUT_DIR = 'frames'
+FRAME_NUMBER = 0
+import os
+
+
+def saveFrame():
+    "Saves the current graphical output as a postscript file"
+    global SAVE_POSTSCRIPT, FRAME_NUMBER, POSTSCRIPT_OUTPUT_DIR
+    if not SAVE_POSTSCRIPT:
+        return
+    if not os.path.exists(POSTSCRIPT_OUTPUT_DIR):
+        os.mkdir(POSTSCRIPT_OUTPUT_DIR)
+    name = os.path.join(POSTSCRIPT_OUTPUT_DIR, 'frame_%08d.ps' % FRAME_NUMBER)
+    FRAME_NUMBER += 1
+    writePostscript(name)  # writes the current canvas
diff --git a/multiagent/graphicsUtils.py b/multiagent/graphicsUtils.py
new file mode 100644
index 0000000..a406fbc
--- /dev/null
+++ b/multiagent/graphicsUtils.py
@@ -0,0 +1,451 @@
+# graphicsUtils.py
+# ----------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+import sys
+import math
+import random
+import string
+import time
+import types
+import tkinter
+import os.path
+
+_Windows = sys.platform == 'win32'  # True if on Win95/98/NT
+
+_root_window = None      # The root window for graphics output
+_canvas = None      # The canvas which holds graphics
+_canvas_xs = None      # Size of canvas object
+_canvas_ys = None
+_canvas_x = None      # Current position on canvas
+_canvas_y = None
+_canvas_col = None      # Current colour (set to black below)
+_canvas_tsize = 12
+_canvas_tserifs = 0
+
+
+def formatColor(r, g, b):
+    return '#%02x%02x%02x' % (int(r * 255), int(g * 255), int(b * 255))
+
+
+def colorToVector(color):
+    return [int(x, 16) / 256.0 for x in [color[1:3], color[3:5], color[5:7]]]
+
+
+if _Windows:
+    _canvas_tfonts = ['times new roman', 'lucida console']
+else:
+    _canvas_tfonts = ['times', 'lucidasans-24']
+    pass  # XXX need defaults here
+
+
+def sleep(secs):
+    global _root_window
+    if _root_window == None:
+        time.sleep(secs)
+    else:
+        _root_window.update_idletasks()
+        _root_window.after(int(1000 * secs), _root_window.quit)
+        _root_window.mainloop()
+
+
+def begin_graphics(width=640, height=480, color=formatColor(0, 0, 0), title=None):
+
+    global _root_window, _canvas, _canvas_x, _canvas_y, _canvas_xs, _canvas_ys, _bg_color
+
+    # Check for duplicate call
+    if _root_window is not None:
+        # Lose the window.
+        _root_window.destroy()
+
+    # Save the canvas size parameters
+    _canvas_xs, _canvas_ys = width - 1, height - 1
+    _canvas_x, _canvas_y = 0, _canvas_ys
+    _bg_color = color
+
+    # Create the root window
+    _root_window = tkinter.Tk()
+    _root_window.protocol('WM_DELETE_WINDOW', _destroy_window)
+    _root_window.title(title or 'Graphics Window')
+    _root_window.resizable(0, 0)
+
+    # Create the canvas object
+    try:
+        _canvas = tkinter.Canvas(_root_window, width=width, height=height)
+        _canvas.pack()
+        draw_background()
+        _canvas.update()
+    except:
+        _root_window = None
+        raise
+
+    # Bind to key-down and key-up events
+    _root_window.bind("", _keypress)
+    _root_window.bind("", _keyrelease)
+    _root_window.bind("", _clear_keys)
+    _root_window.bind("", _clear_keys)
+    _root_window.bind("", _leftclick)
+    _root_window.bind("", _rightclick)
+    _root_window.bind("", _rightclick)
+    _root_window.bind("", _ctrl_leftclick)
+    _clear_keys()
+
+
+_leftclick_loc = None
+_rightclick_loc = None
+_ctrl_leftclick_loc = None
+
+
+def _leftclick(event):
+    global _leftclick_loc
+    _leftclick_loc = (event.x, event.y)
+
+
+def _rightclick(event):
+    global _rightclick_loc
+    _rightclick_loc = (event.x, event.y)
+
+
+def _ctrl_leftclick(event):
+    global _ctrl_leftclick_loc
+    _ctrl_leftclick_loc = (event.x, event.y)
+
+
+def wait_for_click():
+    while True:
+        global _leftclick_loc
+        global _rightclick_loc
+        global _ctrl_leftclick_loc
+        if _leftclick_loc != None:
+            val = _leftclick_loc
+            _leftclick_loc = None
+            return val, 'left'
+        if _rightclick_loc != None:
+            val = _rightclick_loc
+            _rightclick_loc = None
+            return val, 'right'
+        if _ctrl_leftclick_loc != None:
+            val = _ctrl_leftclick_loc
+            _ctrl_leftclick_loc = None
+            return val, 'ctrl_left'
+        sleep(0.05)
+
+
+def draw_background():
+    corners = [(0, 0), (0, _canvas_ys),
+               (_canvas_xs, _canvas_ys), (_canvas_xs, 0)]
+    polygon(corners, _bg_color, fillColor=_bg_color,
+            filled=True, smoothed=False)
+
+
+def _destroy_window(event=None):
+    sys.exit(0)
+#    global _root_window
+#    _root_window.destroy()
+#    _root_window = None
+    # print "DESTROY"
+
+
+def end_graphics():
+    global _root_window, _canvas, _mouse_enabled
+    try:
+        try:
+            sleep(1)
+            if _root_window != None:
+                _root_window.destroy()
+        except SystemExit as e:
+            print('Ending graphics raised an exception:', e)
+    finally:
+        _root_window = None
+        _canvas = None
+        _mouse_enabled = 0
+        _clear_keys()
+
+
+def clear_screen(background=None):
+    global _canvas_x, _canvas_y
+    _canvas.delete('all')
+    draw_background()
+    _canvas_x, _canvas_y = 0, _canvas_ys
+
+
+def polygon(coords, outlineColor, fillColor=None, filled=1, smoothed=1, behind=0, width=1):
+    c = []
+    for coord in coords:
+        c.append(coord[0])
+        c.append(coord[1])
+    if fillColor == None:
+        fillColor = outlineColor
+    if filled == 0:
+        fillColor = ""
+    poly = _canvas.create_polygon(
+        c, outline=outlineColor, fill=fillColor, smooth=smoothed, width=width)
+    if behind > 0:
+        _canvas.tag_lower(poly, behind)  # Higher should be more visible
+    return poly
+
+
+def square(pos, r, color, filled=1, behind=0):
+    x, y = pos
+    coords = [(x - r, y - r), (x + r, y - r), (x + r, y + r), (x - r, y + r)]
+    return polygon(coords, color, color, filled, 0, behind=behind)
+
+
+def circle(pos, r, outlineColor, fillColor, endpoints=None, style='pieslice', width=2):
+    x, y = pos
+    x0, x1 = x - r - 1, x + r
+    y0, y1 = y - r - 1, y + r
+    if endpoints == None:
+        e = [0, 359]
+    else:
+        e = list(endpoints)
+    while e[0] > e[1]:
+        e[1] = e[1] + 360
+
+    return _canvas.create_arc(x0, y0, x1, y1, outline=outlineColor, fill=fillColor,
+                              extent=e[1] - e[0], start=e[0], style=style, width=width)
+
+
+def image(pos, file="../../blueghost.gif"):
+    x, y = pos
+    # img = PhotoImage(file=file)
+    return _canvas.create_image(x, y, image=tkinter.PhotoImage(file=file), anchor=tkinter.NW)
+
+
+def refresh():
+    _canvas.update_idletasks()
+
+
+def moveCircle(id, pos, r, endpoints=None):
+    global _canvas_x, _canvas_y
+
+    x, y = pos
+#    x0, x1 = x - r, x + r + 1
+#    y0, y1 = y - r, y + r + 1
+    x0, x1 = x - r - 1, x + r
+    y0, y1 = y - r - 1, y + r
+    if endpoints == None:
+        e = [0, 359]
+    else:
+        e = list(endpoints)
+    while e[0] > e[1]:
+        e[1] = e[1] + 360
+
+    if os.path.isfile('flag'):
+        edit(id, ('extent', e[1] - e[0]))
+    else:
+        edit(id, ('start', e[0]), ('extent', e[1] - e[0]))
+    move_to(id, x0, y0)
+
+
+def edit(id, *args):
+    _canvas.itemconfigure(id, **dict(args))
+
+
+def text(pos, color, contents, font='Helvetica', size=12, style='normal', anchor="nw"):
+    global _canvas_x, _canvas_y
+    x, y = pos
+    font = (font, str(size), style)
+    return _canvas.create_text(x, y, fill=color, text=contents, font=font, anchor=anchor)
+
+
+def changeText(id, newText, font=None, size=12, style='normal'):
+    _canvas.itemconfigure(id, text=newText)
+    if font != None:
+        _canvas.itemconfigure(id, font=(font, '-%d' % size, style))
+
+
+def changeColor(id, newColor):
+    _canvas.itemconfigure(id, fill=newColor)
+
+
+def line(here, there, color=formatColor(0, 0, 0), width=2):
+    x0, y0 = here[0], here[1]
+    x1, y1 = there[0], there[1]
+    return _canvas.create_line(x0, y0, x1, y1, fill=color, width=width)
+
+##############################################################################
+### Keypress handling ########################################################
+##############################################################################
+
+# We bind to key-down and key-up events.
+
+
+_keysdown = {}
+_keyswaiting = {}
+# This holds an unprocessed key release.  We delay key releases by up to
+# one call to keys_pressed() to get round a problem with auto repeat.
+_got_release = None
+
+
+def _keypress(event):
+    global _got_release
+    # remap_arrows(event)
+    _keysdown[event.keysym] = 1
+    _keyswaiting[event.keysym] = 1
+#    print event.char, event.keycode
+    _got_release = None
+
+
+def _keyrelease(event):
+    global _got_release
+    # remap_arrows(event)
+    try:
+        del _keysdown[event.keysym]
+    except:
+        pass
+    _got_release = 1
+
+
+def remap_arrows(event):
+    # TURN ARROW PRESSES INTO LETTERS (SHOULD BE IN KEYBOARD AGENT)
+    if event.char in ['a', 's', 'd', 'w']:
+        return
+    if event.keycode in [37, 101]:  # LEFT ARROW (win / x)
+        event.char = 'a'
+    if event.keycode in [38, 99]:  # UP ARROW
+        event.char = 'w'
+    if event.keycode in [39, 102]:  # RIGHT ARROW
+        event.char = 'd'
+    if event.keycode in [40, 104]:  # DOWN ARROW
+        event.char = 's'
+
+
+def _clear_keys(event=None):
+    global _keysdown, _got_release, _keyswaiting
+    _keysdown = {}
+    _keyswaiting = {}
+    _got_release = None
+
+
+def keys_pressed(d_o_e=lambda arg: _root_window.dooneevent(arg),
+                 d_w=tkinter._tkinter.DONT_WAIT):
+    d_o_e(d_w)
+    if _got_release:
+        d_o_e(d_w)
+    return list(_keysdown.keys())
+
+
+def keys_waiting():
+    global _keyswaiting
+    keys = list(_keyswaiting.keys())
+    _keyswaiting = {}
+    return keys
+
+# Block for a list of keys...
+
+
+def wait_for_keys():
+    keys = []
+    while keys == []:
+        keys = keys_pressed()
+        sleep(0.05)
+    return keys
+
+
+def remove_from_screen(x,
+                       d_o_e=lambda arg: _root_window.dooneevent(arg),
+                       d_w=tkinter._tkinter.DONT_WAIT):
+    _canvas.delete(x)
+    d_o_e(d_w)
+
+
+def _adjust_coords(coord_list, x, y):
+    for i in range(0, len(coord_list), 2):
+        coord_list[i] = coord_list[i] + x
+        coord_list[i + 1] = coord_list[i + 1] + y
+    return coord_list
+
+
+def move_to(object, x, y=None,
+            d_o_e=lambda arg: _root_window.dooneevent(arg),
+            d_w=tkinter._tkinter.DONT_WAIT):
+    if y is None:
+        try:
+            x, y = x
+        except:
+            raise Exception('incomprehensible coordinates')
+
+    horiz = True
+    newCoords = []
+    current_x, current_y = _canvas.coords(object)[0:2]  # first point
+    for coord in _canvas.coords(object):
+        if horiz:
+            inc = x - current_x
+        else:
+            inc = y - current_y
+        horiz = not horiz
+
+        newCoords.append(coord + inc)
+
+    _canvas.coords(object, *newCoords)
+    d_o_e(d_w)
+
+
+def move_by(object, x, y=None,
+            d_o_e=lambda arg: _root_window.dooneevent(arg),
+            d_w=tkinter._tkinter.DONT_WAIT, lift=False):
+    if y is None:
+        try:
+            x, y = x
+        except:
+            raise Exception('incomprehensible coordinates')
+
+    horiz = True
+    newCoords = []
+    for coord in _canvas.coords(object):
+        if horiz:
+            inc = x
+        else:
+            inc = y
+        horiz = not horiz
+
+        newCoords.append(coord + inc)
+
+    _canvas.coords(object, *newCoords)
+    d_o_e(d_w)
+    if lift:
+        _canvas.tag_raise(object)
+
+
+def writePostscript(filename):
+    "Writes the current canvas to a postscript file."
+    psfile = file(filename, 'w')
+    psfile.write(_canvas.postscript(pageanchor='sw',
+                                    y='0.c',
+                                    x='0.c'))
+    psfile.close()
+
+
+ghost_shape = [
+    (0, - 0.5),
+    (0.25, - 0.75),
+    (0.5, - 0.5),
+    (0.75, - 0.75),
+    (0.75, 0.5),
+    (0.5, 0.75),
+    (- 0.5, 0.75),
+    (- 0.75, 0.5),
+    (- 0.75, - 0.75),
+    (- 0.5, - 0.5),
+    (- 0.25, - 0.75)
+]
+
+if __name__ == '__main__':
+    begin_graphics()
+    clear_screen()
+    ghost_shape = [(x * 10 + 20, y * 10 + 20) for x, y in ghost_shape]
+    g = polygon(ghost_shape, formatColor(1, 1, 1))
+    move_to(g, (50, 50))
+    circle((150, 150), 20, formatColor(0.7, 0.3, 0.0), endpoints=[15, - 15])
+    sleep(2)
diff --git a/multiagent/keyboardAgents.py b/multiagent/keyboardAgents.py
new file mode 100644
index 0000000..7c6d530
--- /dev/null
+++ b/multiagent/keyboardAgents.py
@@ -0,0 +1,95 @@
+# keyboardAgents.py
+# -----------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+from game import Agent
+from game import Directions
+import random
+
+
+class KeyboardAgent(Agent):
+    """
+    An agent controlled by the keyboard.
+    """
+    # NOTE: Arrow keys also work.
+    WEST_KEY = 'a'
+    EAST_KEY = 'd'
+    NORTH_KEY = 'w'
+    SOUTH_KEY = 's'
+    STOP_KEY = 'q'
+
+    def __init__(self, index=0):
+
+        self.lastMove = Directions.STOP
+        self.index = index
+        self.keys = []
+
+    def getAction(self, state):
+        from graphicsUtils import keys_waiting
+        from graphicsUtils import keys_pressed
+        keys = keys_waiting() + keys_pressed()
+        if keys != []:
+            self.keys = keys
+
+        legal = state.getLegalActions(self.index)
+        move = self.getMove(legal)
+
+        if move == Directions.STOP:
+            # Try to move in the same direction as before
+            if self.lastMove in legal:
+                move = self.lastMove
+
+        if (self.STOP_KEY in self.keys) and Directions.STOP in legal:
+            move = Directions.STOP
+
+        if move not in legal:
+            move = random.choice(legal)
+
+        self.lastMove = move
+        return move
+
+    def getMove(self, legal):
+        move = Directions.STOP
+        if (self.WEST_KEY in self.keys or 'Left' in self.keys) and Directions.WEST in legal:
+            move = Directions.WEST
+        if (self.EAST_KEY in self.keys or 'Right' in self.keys) and Directions.EAST in legal:
+            move = Directions.EAST
+        if (self.NORTH_KEY in self.keys or 'Up' in self.keys) and Directions.NORTH in legal:
+            move = Directions.NORTH
+        if (self.SOUTH_KEY in self.keys or 'Down' in self.keys) and Directions.SOUTH in legal:
+            move = Directions.SOUTH
+        return move
+
+
+class KeyboardAgent2(KeyboardAgent):
+    """
+    A second agent controlled by the keyboard.
+    """
+    # NOTE: Arrow keys also work.
+    WEST_KEY = 'j'
+    EAST_KEY = "l"
+    NORTH_KEY = 'i'
+    SOUTH_KEY = 'k'
+    STOP_KEY = 'u'
+
+    def getMove(self, legal):
+        move = Directions.STOP
+        if (self.WEST_KEY in self.keys) and Directions.WEST in legal:
+            move = Directions.WEST
+        if (self.EAST_KEY in self.keys) and Directions.EAST in legal:
+            move = Directions.EAST
+        if (self.NORTH_KEY in self.keys) and Directions.NORTH in legal:
+            move = Directions.NORTH
+        if (self.SOUTH_KEY in self.keys) and Directions.SOUTH in legal:
+            move = Directions.SOUTH
+        return move
diff --git a/multiagent/layout.py b/multiagent/layout.py
new file mode 100644
index 0000000..f317852
--- /dev/null
+++ b/multiagent/layout.py
@@ -0,0 +1,164 @@
+# layout.py
+# ---------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+from util import manhattanDistance
+from game import Grid
+import os
+import random
+from functools import reduce
+
+VISIBILITY_MATRIX_CACHE = {}
+
+
+class Layout:
+    """
+    A Layout manages the static information about the game board.
+    """
+
+    def __init__(self, layoutText):
+        self.width = len(layoutText[0])
+        self.height = len(layoutText)
+        self.walls = Grid(self.width, self.height, False)
+        self.food = Grid(self.width, self.height, False)
+        self.capsules = []
+        self.agentPositions = []
+        self.numGhosts = 0
+        self.processLayoutText(layoutText)
+        self.layoutText = layoutText
+        self.totalFood = len(self.food.asList())
+        # self.initializeVisibilityMatrix()
+
+    def getNumGhosts(self):
+        return self.numGhosts
+
+    def initializeVisibilityMatrix(self):
+        global VISIBILITY_MATRIX_CACHE
+        if reduce(str.__add__, self.layoutText) not in VISIBILITY_MATRIX_CACHE:
+            from game import Directions
+            vecs = [(-0.5, 0), (0.5, 0), (0, -0.5), (0, 0.5)]
+            dirs = [Directions.NORTH, Directions.SOUTH,
+                    Directions.WEST, Directions.EAST]
+            vis = Grid(self.width, self.height, {Directions.NORTH: set(), Directions.SOUTH: set(
+            ), Directions.EAST: set(), Directions.WEST: set(), Directions.STOP: set()})
+            for x in range(self.width):
+                for y in range(self.height):
+                    if self.walls[x][y] == False:
+                        for vec, direction in zip(vecs, dirs):
+                            dx, dy = vec
+                            nextx, nexty = x + dx, y + dy
+                            while (nextx + nexty) != int(nextx) + int(nexty) or not self.walls[int(nextx)][int(nexty)]:
+                                vis[x][y][direction].add((nextx, nexty))
+                                nextx, nexty = x + dx, y + dy
+            self.visibility = vis
+            VISIBILITY_MATRIX_CACHE[reduce(str.__add__, self.layoutText)] = vis
+        else:
+            self.visibility = VISIBILITY_MATRIX_CACHE[reduce(
+                str.__add__, self.layoutText)]
+
+    def isWall(self, pos):
+        x, col = pos
+        return self.walls[x][col]
+
+    def getRandomLegalPosition(self):
+        x = random.choice(list(range(self.width)))
+        y = random.choice(list(range(self.height)))
+        while self.isWall((x, y)):
+            x = random.choice(list(range(self.width)))
+            y = random.choice(list(range(self.height)))
+        return (x, y)
+
+    def getRandomCorner(self):
+        poses = [(1, 1), (1, self.height - 2), (self.width - 2, 1),
+                 (self.width - 2, self.height - 2)]
+        return random.choice(poses)
+
+    def getFurthestCorner(self, pacPos):
+        poses = [(1, 1), (1, self.height - 2), (self.width - 2, 1),
+                 (self.width - 2, self.height - 2)]
+        dist, pos = max([(manhattanDistance(p, pacPos), p) for p in poses])
+        return pos
+
+    def isVisibleFrom(self, ghostPos, pacPos, pacDirection):
+        row, col = [int(x) for x in pacPos]
+        return ghostPos in self.visibility[row][col][pacDirection]
+
+    def __str__(self):
+        return "\n".join(self.layoutText)
+
+    def deepCopy(self):
+        return Layout(self.layoutText[:])
+
+    def processLayoutText(self, layoutText):
+        """
+        Coordinates are flipped from the input format to the (x,y) convention here
+
+        The shape of the maze.  Each character
+        represents a different type of object.
+         % - Wall
+         . - Food
+         o - Capsule
+         G - Ghost
+         P - Pacman
+        Other characters are ignored.
+        """
+        maxY = self.height - 1
+        for y in range(self.height):
+            for x in range(self.width):
+                layoutChar = layoutText[maxY - y][x]
+                self.processLayoutChar(x, y, layoutChar)
+        self.agentPositions.sort()
+        self.agentPositions = [(i == 0, pos) for i, pos in self.agentPositions]
+
+    def processLayoutChar(self, x, y, layoutChar):
+        if layoutChar == '%':
+            self.walls[x][y] = True
+        elif layoutChar == '.':
+            self.food[x][y] = True
+        elif layoutChar == 'o':
+            self.capsules.append((x, y))
+        elif layoutChar == 'P':
+            self.agentPositions.append((0, (x, y)))
+        elif layoutChar in ['G']:
+            self.agentPositions.append((1, (x, y)))
+            self.numGhosts += 1
+        elif layoutChar in ['1', '2', '3', '4']:
+            self.agentPositions.append((int(layoutChar), (x, y)))
+            self.numGhosts += 1
+
+
+def getLayout(name, back=2):
+    if name.endswith('.lay'):
+        layout = tryToLoad('layouts/' + name)
+        if layout == None:
+            layout = tryToLoad(name)
+    else:
+        layout = tryToLoad('layouts/' + name + '.lay')
+        if layout == None:
+            layout = tryToLoad(name + '.lay')
+    if layout == None and back >= 0:
+        curdir = os.path.abspath('.')
+        os.chdir('..')
+        layout = getLayout(name, back - 1)
+        os.chdir(curdir)
+    return layout
+
+
+def tryToLoad(fullname):
+    if(not os.path.exists(fullname)):
+        return None
+    f = open(fullname)
+    try:
+        return Layout([line.strip() for line in f])
+    finally:
+        f.close()
diff --git a/multiagent/layouts/capsuleClassic.lay b/multiagent/layouts/capsuleClassic.lay
new file mode 100644
index 0000000..83e75f4
--- /dev/null
+++ b/multiagent/layouts/capsuleClassic.lay
@@ -0,0 +1,7 @@
+%%%%%%%%%%%%%%%%%%%
+%G.       G   ....%
+%.% % %%%%%% %.%%.%
+%.%o% %   o% %.o%.%
+%.%%%.%  %%% %..%.%
+%.....  P    %..%G%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/multiagent/layouts/contestClassic.lay b/multiagent/layouts/contestClassic.lay
new file mode 100644
index 0000000..0d6195e
--- /dev/null
+++ b/multiagent/layouts/contestClassic.lay
@@ -0,0 +1,9 @@
+%%%%%%%%%%%%%%%%%%%%
+%o...%........%...o%
+%.%%.%.%%..%%.%.%%.%
+%...... G GG%......%
+%.%.%%.%% %%%.%%.%.%
+%.%....% ooo%.%..%.%
+%.%.%%.% %% %.%.%%.%
+%o%......P....%....%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/multiagent/layouts/mediumClassic.lay b/multiagent/layouts/mediumClassic.lay
new file mode 100644
index 0000000..2ef1b3c
--- /dev/null
+++ b/multiagent/layouts/mediumClassic.lay
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%
+%o...%........%....%
+%.%%.%.%%%%%%.%.%%.%
+%.%..............%.%
+%.%.%%.%%  %%.%%.%.%
+%......%G  G%......%
+%.%.%%.%%%%%%.%%.%.%
+%.%..............%.%
+%.%%.%.%%%%%%.%.%%.%
+%....%...P....%...o%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/multiagent/layouts/minimaxClassic.lay b/multiagent/layouts/minimaxClassic.lay
new file mode 100644
index 0000000..202c335
--- /dev/null
+++ b/multiagent/layouts/minimaxClassic.lay
@@ -0,0 +1,5 @@
+%%%%%%%%%
+%.P    G% 
+% %.%G%%%  
+%G    %%% 
+%%%%%%%%%
diff --git a/multiagent/layouts/openClassic.lay b/multiagent/layouts/openClassic.lay
new file mode 100644
index 0000000..ec22729
--- /dev/null
+++ b/multiagent/layouts/openClassic.lay
@@ -0,0 +1,9 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%
+%.. P  ....      ....   %
+%..  ...  ...  ...  ... %
+%..  ...  ...  ...  ... %
+%..    ....      .... G %
+%..  ...  ...  ...  ... %
+%..  ...  ...  ...  ... %
+%..    ....      ....  o%
+%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/multiagent/layouts/originalClassic.lay b/multiagent/layouts/originalClassic.lay
new file mode 100644
index 0000000..8023758
--- /dev/null
+++ b/multiagent/layouts/originalClassic.lay
@@ -0,0 +1,27 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%............%%............%
+%.%%%%.%%%%%.%%.%%%%%.%%%%.%
+%o%%%%.%%%%%.%%.%%%%%.%%%%o%
+%.%%%%.%%%%%.%%.%%%%%.%%%%.%
+%..........................%
+%.%%%%.%%.%%%%%%%%.%%.%%%%.%
+%.%%%%.%%.%%%%%%%%.%%.%%%%.%
+%......%%....%%....%%......%
+%%%%%%.%%%%% %% %%%%%.%%%%%%
+%%%%%%.%%%%% %% %%%%%.%%%%%%
+%%%%%%.%            %.%%%%%%
+%%%%%%.% %%%%  %%%% %.%%%%%%
+%     .  %G  GG  G%  .     %
+%%%%%%.% %%%%%%%%%% %.%%%%%%
+%%%%%%.%            %.%%%%%%
+%%%%%%.% %%%%%%%%%% %.%%%%%%
+%............%%............%
+%.%%%%.%%%%%.%%.%%%%%.%%%%.%
+%.%%%%.%%%%%.%%.%%%%%.%%%%.%
+%o..%%.......  .......%%..o%
+%%%.%%.%%.%%%%%%%%.%%.%%.%%%
+%%%.%%.%%.%%%%%%%%.%%.%%.%%%
+%......%%....%%....%%......%
+%.%%%%%%%%%%.%%.%%%%%%%%%%.%
+%.............P............%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/multiagent/layouts/powerClassic.lay b/multiagent/layouts/powerClassic.lay
new file mode 100644
index 0000000..1b87623
--- /dev/null
+++ b/multiagent/layouts/powerClassic.lay
@@ -0,0 +1,7 @@
+%%%%%%%%%%%%%%%%%%%%
+%o....o%GGGG%o....o%
+%..%...%%  %%...%..%
+%.%o.%........%.o%.%
+%.o%.%.%%%%%%.%.%o.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/multiagent/layouts/smallClassic.lay b/multiagent/layouts/smallClassic.lay
new file mode 100644
index 0000000..5b704cb
--- /dev/null
+++ b/multiagent/layouts/smallClassic.lay
@@ -0,0 +1,7 @@
+%%%%%%%%%%%%%%%%%%%%
+%......%G  G%......%
+%.%%...%%  %%...%%.%
+%.%o.%........%.o%.%
+%.%%.%.%%%%%%.%.%%.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/multiagent/layouts/testClassic.lay b/multiagent/layouts/testClassic.lay
new file mode 100644
index 0000000..f050aca
--- /dev/null
+++ b/multiagent/layouts/testClassic.lay
@@ -0,0 +1,10 @@
+%%%%%
+% . %
+%.G.%
+% . %
+%. .%
+%   %
+%  .%
+%   %
+%P .%
+%%%%%
diff --git a/multiagent/layouts/trappedClassic.lay b/multiagent/layouts/trappedClassic.lay
new file mode 100644
index 0000000..6fdabd8
--- /dev/null
+++ b/multiagent/layouts/trappedClassic.lay
@@ -0,0 +1,5 @@
+%%%%%%%%
+%   P G%
+%G%%%%%%
+%....  %
+%%%%%%%%
diff --git a/multiagent/layouts/trickyClassic.lay b/multiagent/layouts/trickyClassic.lay
new file mode 100644
index 0000000..2a8bec1
--- /dev/null
+++ b/multiagent/layouts/trickyClassic.lay
@@ -0,0 +1,13 @@
+%%%%%%%%%%%%%%%%%%%%
+%o...%........%...o%
+%.%%.%.%%..%%.%.%%.%
+%.%.....%..%.....%.%
+%.%.%%.%%  %%.%%.%.%
+%...... GGGG%.%....%
+%.%....%%%%%%.%..%.%
+%.%....%  oo%.%..%.%
+%.%....% %%%%.%..%.%
+%.%...........%..%.%
+%.%%.%.%%%%%%.%.%%.%
+%o...%...P....%...o%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/multiagent/multiAgents.py b/multiagent/multiAgents.py
new file mode 100644
index 0000000..06a31a2
--- /dev/null
+++ b/multiagent/multiAgents.py
@@ -0,0 +1,179 @@
+# multiAgents.py
+# --------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+# 
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+from util import manhattanDistance
+from game import Directions
+import random, util
+
+from game import Agent
+from pacman import GameState
+
+class ReflexAgent(Agent):
+    """
+    A reflex agent chooses an action at each choice point by examining
+    its alternatives via a state evaluation function.
+
+    The code below is provided as a guide.  You are welcome to change
+    it in any way you see fit, so long as you don't touch our method
+    headers.
+    """
+
+
+    def getAction(self, gameState: GameState):
+        """
+        You do not need to change this method, but you're welcome to.
+
+        getAction chooses among the best options according to the evaluation function.
+
+        Just like in the previous project, getAction takes a GameState and returns
+        some Directions.X for some X in the set {NORTH, SOUTH, WEST, EAST, STOP}
+        """
+        # Collect legal moves and successor states
+        legalMoves = gameState.getLegalActions()
+
+        # Choose one of the best actions
+        scores = [self.evaluationFunction(gameState, action) for action in legalMoves]
+        bestScore = max(scores)
+        bestIndices = [index for index in range(len(scores)) if scores[index] == bestScore]
+        chosenIndex = random.choice(bestIndices) # Pick randomly among the best
+
+        "Add more of your code here if you want to"
+
+        return legalMoves[chosenIndex]
+
+    def evaluationFunction(self, currentGameState: GameState, action):
+        """
+        Design a better evaluation function here.
+
+        The evaluation function takes in the current and proposed successor
+        GameStates (pacman.py) and returns a number, where higher numbers are better.
+
+        The code below extracts some useful information from the state, like the
+        remaining food (newFood) and Pacman position after moving (newPos).
+        newScaredTimes holds the number of moves that each ghost will remain
+        scared because of Pacman having eaten a power pellet.
+
+        Print out these variables to see what you're getting, then combine them
+        to create a masterful evaluation function.
+        """
+        # Useful information you can extract from a GameState (pacman.py)
+        successorGameState = currentGameState.generatePacmanSuccessor(action)
+        newPos = successorGameState.getPacmanPosition()
+        newFood = successorGameState.getFood()
+        newGhostStates = successorGameState.getGhostStates()
+        newScaredTimes = [ghostState.scaredTimer for ghostState in newGhostStates]
+
+        "*** YOUR CODE HERE ***"
+        return successorGameState.getScore()
+
+def scoreEvaluationFunction(currentGameState: GameState):
+    """
+    This default evaluation function just returns the score of the state.
+    The score is the same one displayed in the Pacman GUI.
+
+    This evaluation function is meant for use with adversarial search agents
+    (not reflex agents).
+    """
+    return currentGameState.getScore()
+
+class MultiAgentSearchAgent(Agent):
+    """
+    This class provides some common elements to all of your
+    multi-agent searchers.  Any methods defined here will be available
+    to the MinimaxPacmanAgent, AlphaBetaPacmanAgent & ExpectimaxPacmanAgent.
+
+    You *do not* need to make any changes here, but you can if you want to
+    add functionality to all your adversarial search agents.  Please do not
+    remove anything, however.
+
+    Note: this is an abstract class: one that should not be instantiated.  It's
+    only partially specified, and designed to be extended.  Agent (game.py)
+    is another abstract class.
+    """
+
+    def __init__(self, evalFn = 'scoreEvaluationFunction', depth = '2'):
+        self.index = 0 # Pacman is always agent index 0
+        self.evaluationFunction = util.lookup(evalFn, globals())
+        self.depth = int(depth)
+
+class MinimaxAgent(MultiAgentSearchAgent):
+    """
+    Your minimax agent (question 2)
+    """
+
+    def getAction(self, gameState: GameState):
+        """
+        Returns the minimax action from the current gameState using self.depth
+        and self.evaluationFunction.
+
+        Here are some method calls that might be useful when implementing minimax.
+
+        gameState.getLegalActions(agentIndex):
+        Returns a list of legal actions for an agent
+        agentIndex=0 means Pacman, ghosts are >= 1
+
+        gameState.generateSuccessor(agentIndex, action):
+        Returns the successor game state after an agent takes an action
+
+        gameState.getNumAgents():
+        Returns the total number of agents in the game
+
+        gameState.isWin():
+        Returns whether or not the game state is a winning state
+
+        gameState.isLose():
+        Returns whether or not the game state is a losing state
+        """
+        "*** YOUR CODE HERE ***"
+        util.raiseNotDefined()
+
+class AlphaBetaAgent(MultiAgentSearchAgent):
+    """
+    Your minimax agent with alpha-beta pruning (question 3)
+    """
+
+    def getAction(self, gameState: GameState):
+        """
+        Returns the minimax action using self.depth and self.evaluationFunction
+        """
+        "*** YOUR CODE HERE ***"
+        util.raiseNotDefined()
+
+class ExpectimaxAgent(MultiAgentSearchAgent):
+    """
+      Your expectimax agent (question 4)
+    """
+
+    def getAction(self, gameState: GameState):
+        """
+        Returns the expectimax action using self.depth and self.evaluationFunction
+
+        All ghosts should be modeled as choosing uniformly at random from their
+        legal moves.
+        """
+        "*** YOUR CODE HERE ***"
+        util.raiseNotDefined()
+
+def betterEvaluationFunction(currentGameState: GameState):
+    """
+    Your extreme ghost-hunting, pellet-nabbing, food-gobbling, unstoppable
+    evaluation function (question 5).
+
+    DESCRIPTION: 
+    """
+    "*** YOUR CODE HERE ***"
+    util.raiseNotDefined()
+
+# Abbreviation
+better = betterEvaluationFunction
diff --git a/multiagent/multiagentTestClasses.py b/multiagent/multiagentTestClasses.py
new file mode 100644
index 0000000..4857f48
--- /dev/null
+++ b/multiagent/multiagentTestClasses.py
@@ -0,0 +1,578 @@
+# multiagentTestClasses.py
+# ------------------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+# A minimax tree which interfaces like gameState
+#     state.getNumAgents()
+#     state.isWin()
+#     state.isLose()
+#     state.generateSuccessor(agentIndex, action)
+#     state.getScore()
+#           used by multiAgents.scoreEvaluationFunction, which is the default
+#
+import testClasses
+import json
+
+from collections import defaultdict
+from pprint import PrettyPrinter
+pp = PrettyPrinter()
+
+from game import Agent
+from pacman import GameState
+from ghostAgents import RandomGhost, DirectionalGhost
+import random
+import math
+import traceback
+import sys
+import os
+import layout
+import pacman
+import autograder
+# import grading
+
+VERBOSE = False
+
+
+class MultiagentTreeState(object):
+    def __init__(self, problem, state):
+        self.problem = problem
+        self.state = state
+
+    def generateSuccessor(self, agentIndex, action):
+        if VERBOSE:
+            print("generateSuccessor(%s, %s, %s) -> %s" % (self.state, agentIndex,
+                                                           action, self.problem.stateToSuccessorMap[self.state][action]))
+        successor = self.problem.stateToSuccessorMap[self.state][action]
+        self.problem.generatedStates.add(successor)
+        return MultiagentTreeState(self.problem, successor)
+
+    def getScore(self):
+        if VERBOSE:
+            print("getScore(%s) -> %s" %
+                  (self.state, self.problem.evaluation[self.state]))
+        if self.state not in self.problem.evaluation:
+            raise Exception(
+                'getScore() called on non-terminal state or before maximum depth achieved.')
+        return float(self.problem.evaluation[self.state])
+
+    def getLegalActions(self, agentIndex=0):
+        if VERBOSE:
+            print("getLegalActions(%s) -> %s" %
+                  (self.state, self.problem.stateToActions[self.state]))
+        # if len(self.problem.stateToActions[self.state]) == 0:
+        #    print "WARNING: getLegalActions called on leaf state %s" % (self.state,)
+        return list(self.problem.stateToActions[self.state])
+
+    def isWin(self):
+        if VERBOSE:
+            print("isWin(%s) -> %s" %
+                  (self.state, self.state in self.problem.winStates))
+        return self.state in self.problem.winStates
+
+    def isLose(self):
+        if VERBOSE:
+            print("isLose(%s) -> %s" %
+                  (self.state, self.state in self.problem.loseStates))
+        return self.state in self.problem.loseStates
+
+    def getNumAgents(self):
+        if VERBOSE:
+            print("getNumAgents(%s) -> %s" %
+                  (self.state, self.problem.numAgents))
+        return self.problem.numAgents
+
+
+class MultiagentTreeProblem(object):
+    def __init__(self, numAgents, startState, winStates, loseStates, successors, evaluation):
+        self.startState = MultiagentTreeState(self, startState)
+
+        self.numAgents = numAgents
+        self.winStates = winStates
+        self.loseStates = loseStates
+        self.evaluation = evaluation
+        self.successors = successors
+
+        self.reset()
+
+        self.stateToSuccessorMap = defaultdict(dict)
+        self.stateToActions = defaultdict(list)
+        for state, action, nextState in successors:
+            self.stateToActions[state].append(action)
+            self.stateToSuccessorMap[state][action] = nextState
+
+    def reset(self):
+        self.generatedStates = set([self.startState.state])
+
+
+def parseTreeProblem(testDict):
+    numAgents = int(testDict["num_agents"])
+    startState = testDict["start_state"]
+    winStates = set(testDict["win_states"].split(" "))
+    loseStates = set(testDict["lose_states"].split(" "))
+    successors = []
+
+    evaluation = {}
+    for line in testDict["evaluation"].split('\n'):
+        tokens = line.split()
+        if len(tokens) == 2:
+            state, value = tokens
+            evaluation[state] = float(value)
+        else:
+            raise Exception("[parseTree] Bad evaluation line: |%s|" % (line,))
+
+    for line in testDict["successors"].split('\n'):
+        tokens = line.split()
+        if len(tokens) == 3:
+            state, action, nextState = tokens
+            successors.append((state, action, nextState))
+        else:
+            raise Exception("[parseTree] Bad successor line: |%s|" % (line,))
+
+    return MultiagentTreeProblem(numAgents, startState, winStates, loseStates, successors, evaluation)
+
+
+def run(lay, layName, pac, ghosts, disp, nGames=1, name='games'):
+    """
+    Runs a few games and outputs their statistics.
+    """
+    starttime = time.time()
+    print('*** Running %s on' % name, layName, '%d time(s).' % nGames)
+    games = pacman.runGames(lay, pac, ghosts, disp,
+                            nGames, False, catchExceptions=True, timeout=120)
+    print('*** Finished running %s on' % name, layName,
+          'after %d seconds.' % (time.time() - starttime))
+    stats = {'time': time.time() - starttime, 'wins': [g.state.isWin() for g in games].count(True), 'games': games, 'scores': [g.state.getScore() for g in games],
+             'timeouts': [g.agentTimeout for g in games].count(True), 'crashes': [g.agentCrashed for g in games].count(True)}
+    print('*** Won %d out of %d games. Average score: %f ***' %
+          (stats['wins'], len(games), sum(stats['scores']) * 1.0 / len(games)))
+    return stats
+
+
+class GradingAgent(Agent):
+    def __init__(self, seed, studentAgent, optimalActions, altDepthActions, partialPlyBugActions):
+        # save student agent and actions of refernce agents
+        self.studentAgent = studentAgent
+        self.optimalActions = optimalActions
+        self.altDepthActions = altDepthActions
+        self.partialPlyBugActions = partialPlyBugActions
+        # create fields for storing specific wrong actions
+        self.suboptimalMoves = []
+        self.wrongStatesExplored = -1
+        # boolean vectors represent types of implementation the student could have
+        self.actionsConsistentWithOptimal = [
+            True for i in range(len(optimalActions[0]))]
+        self.actionsConsistentWithAlternativeDepth = [
+            True for i in range(len(altDepthActions[0]))]
+        self.actionsConsistentWithPartialPlyBug = [
+            True for i in range(len(partialPlyBugActions[0]))]
+        # keep track of elapsed moves
+        self.stepCount = 0
+        self.seed = seed
+
+    def registerInitialState(self, state):
+        if 'registerInitialState' in dir(self.studentAgent):
+            self.studentAgent.registerInitialState(state)
+        random.seed(self.seed)
+
+    def getAction(self, state):
+        GameState.getAndResetExplored()
+        studentAction = (self.studentAgent.getAction(state),
+                         len(GameState.getAndResetExplored()))
+        optimalActions = self.optimalActions[self.stepCount]
+        altDepthActions = self.altDepthActions[self.stepCount]
+        partialPlyBugActions = self.partialPlyBugActions[self.stepCount]
+        studentOptimalAction = False
+        curRightStatesExplored = False
+        for i in range(len(optimalActions)):
+            if studentAction[0] in optimalActions[i][0]:
+                studentOptimalAction = True
+            else:
+                self.actionsConsistentWithOptimal[i] = False
+            if studentAction[1] == int(optimalActions[i][1]):
+                curRightStatesExplored = True
+        if not curRightStatesExplored and self.wrongStatesExplored < 0:
+            self.wrongStatesExplored = 1
+        for i in range(len(altDepthActions)):
+            if studentAction[0] not in altDepthActions[i]:
+                self.actionsConsistentWithAlternativeDepth[i] = False
+        for i in range(len(partialPlyBugActions)):
+            if studentAction[0] not in partialPlyBugActions[i]:
+                self.actionsConsistentWithPartialPlyBug[i] = False
+        if not studentOptimalAction:
+            self.suboptimalMoves.append(
+                (state, studentAction[0], optimalActions[0][0][0]))
+        self.stepCount += 1
+        random.seed(self.seed + self.stepCount)
+        return optimalActions[0][0][0]
+
+    def getSuboptimalMoves(self):
+        return self.suboptimalMoves
+
+    def getWrongStatesExplored(self):
+        return self.wrongStatesExplored
+
+    def checkFailure(self):
+        """
+        Return +n if have n suboptimal moves.
+        Return -1 if have only off by one depth moves.
+        Return 0 otherwise.
+        """
+        if self.wrongStatesExplored > 0:
+            return -3
+        if self.actionsConsistentWithOptimal.count(True) > 0:
+            return 0
+        elif self.actionsConsistentWithPartialPlyBug.count(True) > 0:
+            return -2
+        elif self.actionsConsistentWithAlternativeDepth.count(True) > 0:
+            return -1
+        else:
+            return len(self.suboptimalMoves)
+
+
+class PolyAgent(Agent):
+    def __init__(self, seed, multiAgents, ourPacOptions, depth):
+        # prepare our pacman agents
+        solutionAgents, alternativeDepthAgents, partialPlyBugAgents = self.construct_our_pacs(
+            multiAgents, ourPacOptions)
+        for p in solutionAgents:
+            p.depth = depth
+        for p in partialPlyBugAgents:
+            p.depth = depth
+        for p in alternativeDepthAgents[:2]:
+            p.depth = max(1, depth - 1)
+        for p in alternativeDepthAgents[2:]:
+            p.depth = depth + 1
+        self.solutionAgents = solutionAgents
+        self.alternativeDepthAgents = alternativeDepthAgents
+        self.partialPlyBugAgents = partialPlyBugAgents
+        # prepare fields for storing the results
+        self.optimalActionLists = []
+        self.alternativeDepthLists = []
+        self.partialPlyBugLists = []
+        self.seed = seed
+        self.stepCount = 0
+
+    def select(self, list, indices):
+        """
+        Return a sublist of elements given by indices in list.
+        """
+        return [list[i] for i in indices]
+
+    def construct_our_pacs(self, multiAgents, keyword_dict):
+        pacs_without_stop = [multiAgents.StaffMultiAgentSearchAgent(
+            **keyword_dict) for i in range(3)]
+        keyword_dict['keepStop'] = 'True'
+        pacs_with_stop = [multiAgents.StaffMultiAgentSearchAgent(
+            **keyword_dict) for i in range(3)]
+        keyword_dict['usePartialPlyBug'] = 'True'
+        partial_ply_bug_pacs = [
+            multiAgents.StaffMultiAgentSearchAgent(**keyword_dict)]
+        keyword_dict['keepStop'] = 'False'
+        partial_ply_bug_pacs = partial_ply_bug_pacs + \
+            [multiAgents.StaffMultiAgentSearchAgent(**keyword_dict)]
+        for pac in pacs_with_stop + pacs_without_stop + partial_ply_bug_pacs:
+            pac.verbose = False
+        ourpac = [pacs_with_stop[0], pacs_without_stop[0]]
+        alternative_depth_pacs = self.select(
+            pacs_with_stop + pacs_without_stop, [1, 4, 2, 5])
+        return (ourpac, alternative_depth_pacs, partial_ply_bug_pacs)
+
+    def registerInitialState(self, state):
+        for agent in self.solutionAgents + self.alternativeDepthAgents:
+            if 'registerInitialState' in dir(agent):
+                agent.registerInitialState(state)
+        random.seed(self.seed)
+
+    def getAction(self, state):
+        # survey agents
+        GameState.getAndResetExplored()
+        optimalActionLists = []
+        for agent in self.solutionAgents:
+            optimalActionLists.append((agent.getBestPacmanActions(
+                state)[0], len(GameState.getAndResetExplored())))
+        alternativeDepthLists = [agent.getBestPacmanActions(
+            state)[0] for agent in self.alternativeDepthAgents]
+        partialPlyBugLists = [agent.getBestPacmanActions(
+            state)[0] for agent in self.partialPlyBugAgents]
+        # record responses
+        self.optimalActionLists.append(optimalActionLists)
+        self.alternativeDepthLists.append(alternativeDepthLists)
+        self.partialPlyBugLists.append(partialPlyBugLists)
+        self.stepCount += 1
+        random.seed(self.seed + self.stepCount)
+        return optimalActionLists[0][0][0]
+
+    def getTraces(self):
+        # return traces from individual agents
+        return (self.optimalActionLists, self.alternativeDepthLists, self.partialPlyBugLists)
+
+
+class PacmanGameTreeTest(testClasses.TestCase):
+
+    def __init__(self, question, testDict):
+        super(PacmanGameTreeTest, self).__init__(question, testDict)
+        self.seed = int(self.testDict['seed'])
+        self.alg = self.testDict['alg']
+        self.layout_text = self.testDict['layout']
+        self.layout_name = self.testDict['layoutName']
+        self.depth = int(self.testDict['depth'])
+        self.max_points = int(self.testDict['max_points'])
+
+    def execute(self, grades, moduleDict, solutionDict):
+        # load student code and staff code solutions
+        multiAgents = moduleDict['multiAgents']
+        studentAgent = getattr(multiAgents, self.alg)(depth=self.depth)
+        allActions = [json.loads(x)
+                      for x in solutionDict['optimalActions'].split('\n')]
+        altDepthActions = [json.loads(
+            x) for x in solutionDict['altDepthActions'].split('\n')]
+        partialPlyBugActions = [json.loads(
+            x) for x in solutionDict['partialPlyBugActions'].split('\n')]
+        # set up game state and play a game
+        random.seed(self.seed)
+        lay = layout.Layout([l.strip() for l in self.layout_text.split('\n')])
+        pac = GradingAgent(self.seed, studentAgent, allActions,
+                           altDepthActions, partialPlyBugActions)
+        # check return codes and assign grades
+        disp = self.question.getDisplay()
+        stats = run(lay, self.layout_name, pac, [DirectionalGhost(
+            i + 1) for i in range(2)], disp, name=self.alg)
+        if stats['timeouts'] > 0:
+            self.addMessage('Agent timed out on smallClassic.  No credit')
+            return self.testFail(grades)
+        if stats['crashes'] > 0:
+            self.addMessage('Agent crashed on smallClassic.  No credit')
+            return self.testFail(grades)
+        code = pac.checkFailure()
+        if code == 0:
+            return self.testPass(grades)
+        elif code == -3:
+            if pac.getWrongStatesExplored() >= 0:
+                self.addMessage('Bug: Wrong number of states expanded.')
+                return self.testFail(grades)
+            else:
+                return self.testPass(grades)
+        elif code == -2:
+            self.addMessage('Bug: Partial Ply Bug')
+            return self.testFail(grades)
+        elif code == -1:
+            self.addMessage('Bug: Search depth off by 1')
+            return self.testFail(grades)
+        elif code > 0:
+            moves = pac.getSuboptimalMoves()
+            state, studentMove, optMove = random.choice(moves)
+            self.addMessage('Bug: Suboptimal moves')
+            self.addMessage('State:%s\nStudent Move:%s\nOptimal Move:%s' % (
+                state, studentMove, optMove))
+            return self.testFail(grades)
+
+    def writeList(self, handle, name, list):
+        handle.write('%s: """\n' % name)
+        for l in list:
+            handle.write('%s\n' % json.dumps(l))
+        handle.write('"""\n')
+
+    def writeSolution(self, moduleDict, filePath):
+        # load module, set seed, create ghosts and macman, run game
+        multiAgents = moduleDict['multiAgents']
+        random.seed(self.seed)
+        lay = layout.Layout([l.strip() for l in self.layout_text.split('\n')])
+        if self.alg == 'ExpectimaxAgent':
+            ourPacOptions = {'expectimax': 'True'}
+        elif self.alg == 'AlphaBetaAgent':
+            ourPacOptions = {'alphabeta': 'True'}
+        else:
+            ourPacOptions = {}
+        pac = PolyAgent(self.seed, multiAgents, ourPacOptions, self.depth)
+        disp = self.question.getDisplay()
+        run(lay, self.layout_name, pac, [DirectionalGhost(
+            i + 1) for i in range(2)], disp, name=self.alg)
+        (optimalActions, altDepthActions, partialPlyBugActions) = pac.getTraces()
+        # recover traces and record to file
+        handle = open(filePath, 'w')
+        self.writeList(handle, 'optimalActions', optimalActions)
+        self.writeList(handle, 'altDepthActions', altDepthActions)
+        self.writeList(handle, 'partialPlyBugActions', partialPlyBugActions)
+        handle.close()
+
+
+class GraphGameTreeTest(testClasses.TestCase):
+
+    def __init__(self, question, testDict):
+        super(GraphGameTreeTest, self).__init__(question, testDict)
+        self.problem = parseTreeProblem(testDict)
+        self.alg = self.testDict['alg']
+        self.diagram = self.testDict['diagram'].split('\n')
+        self.depth = int(self.testDict['depth'])
+
+    def solveProblem(self, multiAgents):
+        self.problem.reset()
+        studentAgent = getattr(multiAgents, self.alg)(depth=self.depth)
+        action = studentAgent.getAction(self.problem.startState)
+        generated = self.problem.generatedStates
+        return action, " ".join([str(s) for s in sorted(generated)])
+
+    def addDiagram(self):
+        self.addMessage('Tree:')
+        for line in self.diagram:
+            self.addMessage(line)
+
+    def execute(self, grades, moduleDict, solutionDict):
+        multiAgents = moduleDict['multiAgents']
+        goldAction = solutionDict['action']
+        goldGenerated = solutionDict['generated']
+        action, generated = self.solveProblem(multiAgents)
+
+        fail = False
+        if action != goldAction:
+            self.addMessage('Incorrect move for depth=%s' % (self.depth,))
+            self.addMessage(
+                '    Student move: %s\n    Optimal move: %s' % (action, goldAction))
+            fail = True
+
+        if generated != goldGenerated:
+            self.addMessage(
+                'Incorrect generated nodes for depth=%s' % (self.depth,))
+            self.addMessage('    Student generated nodes: %s\n    Correct generated nodes: %s' % (
+                generated, goldGenerated))
+            fail = True
+
+        if fail:
+            self.addDiagram()
+            return self.testFail(grades)
+        else:
+            return self.testPass(grades)
+
+    def writeSolution(self, moduleDict, filePath):
+        multiAgents = moduleDict['multiAgents']
+        action, generated = self.solveProblem(multiAgents)
+        with open(filePath, 'w') as handle:
+            handle.write('# This is the solution file for %s.\n' % self.path)
+            handle.write('action: "%s"\n' % (action,))
+            handle.write('generated: "%s"\n' % (generated,))
+        return True
+
+
+import time
+from util import TimeoutFunction
+
+
+class EvalAgentTest(testClasses.TestCase):
+
+    def __init__(self, question, testDict):
+        super(EvalAgentTest, self).__init__(question, testDict)
+        self.layoutName = testDict['layoutName']
+        self.agentName = testDict['agentName']
+        self.ghosts = eval(testDict['ghosts'])
+        self.maxTime = int(testDict['maxTime'])
+        self.seed = int(testDict['randomSeed'])
+        self.numGames = int(testDict['numGames'])
+
+        self.scoreMinimum = int(
+            testDict['scoreMinimum']) if 'scoreMinimum' in testDict else None
+        self.nonTimeoutMinimum = int(
+            testDict['nonTimeoutMinimum']) if 'nonTimeoutMinimum' in testDict else None
+        self.winsMinimum = int(
+            testDict['winsMinimum']) if 'winsMinimum' in testDict else None
+
+        self.scoreThresholds = [int(s) for s in testDict.get(
+            'scoreThresholds', '').split()]
+        self.nonTimeoutThresholds = [int(s) for s in testDict.get(
+            'nonTimeoutThresholds', '').split()]
+        self.winsThresholds = [int(s) for s in testDict.get(
+            'winsThresholds', '').split()]
+
+        self.maxPoints = sum([len(t) for t in [
+                             self.scoreThresholds, self.nonTimeoutThresholds, self.winsThresholds]])
+        self.agentArgs = testDict.get('agentArgs', '')
+
+    def execute(self, grades, moduleDict, solutionDict):
+        startTime = time.time()
+
+        agentType = getattr(moduleDict['multiAgents'], self.agentName)
+        agentOpts = pacman.parseAgentArgs(
+            self.agentArgs) if self.agentArgs != '' else {}
+        agent = agentType(**agentOpts)
+
+        lay = layout.getLayout(self.layoutName, 3)
+
+        disp = self.question.getDisplay()
+
+        random.seed(self.seed)
+        games = pacman.runGames(lay, agent, self.ghosts, disp, self.numGames,
+                                False, catchExceptions=True, timeout=self.maxTime)
+        totalTime = time.time() - startTime
+
+        stats = {'time': totalTime, 'wins': [g.state.isWin() for g in games].count(True),
+                 'games': games, 'scores': [g.state.getScore() for g in games],
+                 'timeouts': [g.agentTimeout for g in games].count(True), 'crashes': [g.agentCrashed for g in games].count(True)}
+
+        averageScore = sum(stats['scores']) / float(len(stats['scores']))
+        nonTimeouts = self.numGames - stats['timeouts']
+        wins = stats['wins']
+
+        def gradeThreshold(value, minimum, thresholds, name):
+            points = 0
+            passed = (minimum == None) or (value >= minimum)
+            if passed:
+                for t in thresholds:
+                    if value >= t:
+                        points += 1
+            return (passed, points, value, minimum, thresholds, name)
+
+        results = [gradeThreshold(averageScore, self.scoreMinimum, self.scoreThresholds, "average score"),
+                   gradeThreshold(nonTimeouts, self.nonTimeoutMinimum,
+                                  self.nonTimeoutThresholds, "games not timed out"),
+                   gradeThreshold(wins, self.winsMinimum, self.winsThresholds, "wins")]
+
+        totalPoints = 0
+        for passed, points, value, minimum, thresholds, name in results:
+            if minimum == None and len(thresholds) == 0:
+                continue
+
+            # print passed, points, value, minimum, thresholds, name
+            totalPoints += points
+            if not passed:
+                assert points == 0
+                self.addMessage(
+                    "%s %s (fail: below minimum value %s)" % (value, name, minimum))
+            else:
+                self.addMessage("%s %s (%s of %s points)" %
+                                (value, name, points, len(thresholds)))
+
+            if minimum != None:
+                self.addMessage("    Grading scheme:")
+                self.addMessage("     < %s:  fail" % (minimum,))
+                if len(thresholds) == 0 or minimum != thresholds[0]:
+                    self.addMessage("    >= %s:  0 points" % (minimum,))
+                for idx, threshold in enumerate(thresholds):
+                    self.addMessage("    >= %s:  %s points" %
+                                    (threshold, idx+1))
+            elif len(thresholds) > 0:
+                self.addMessage("    Grading scheme:")
+                self.addMessage("     < %s:  0 points" % (thresholds[0],))
+                for idx, threshold in enumerate(thresholds):
+                    self.addMessage("    >= %s:  %s points" %
+                                    (threshold, idx+1))
+
+        if any([not passed for passed, _, _, _, _, _ in results]):
+            totalPoints = 0
+
+        return self.testPartial(grades, totalPoints, self.maxPoints)
+
+    def writeSolution(self, moduleDict, filePath):
+        handle = open(filePath, 'w')
+        handle.write('# This is the solution file for %s.\n' % self.path)
+        handle.write('# File intentionally blank.\n')
+        handle.close()
+        return True
diff --git a/multiagent/pacman.py b/multiagent/pacman.py
new file mode 100644
index 0000000..37fe800
--- /dev/null
+++ b/multiagent/pacman.py
@@ -0,0 +1,738 @@
+# pacman.py
+# ---------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+"""
+Pacman.py holds the logic for the classic pacman game along with the main
+code to run a game.  This file is divided into three sections:
+
+  (i)  Your interface to the pacman world:
+          Pacman is a complex environment.  You probably don't want to
+          read through all of the code we wrote to make the game runs
+          correctly.  This section contains the parts of the code
+          that you will need to understand in order to complete the
+          project.  There is also some code in game.py that you should
+          understand.
+
+  (ii)  The hidden secrets of pacman:
+          This section contains all of the logic code that the pacman
+          environment uses to decide who can move where, who dies when
+          things collide, etc.  You shouldn't need to read this section
+          of code, but you can if you want.
+
+  (iii) Framework to start a game:
+          The final section contains the code for reading the command
+          you use to set up the game, then starting up a new game, along with
+          linking in all the external parts (agent functions, graphics).
+          Check this section out to see all the options available to you.
+
+To play your first game, type 'python pacman.py' from the command line.
+The keys are 'a', 's', 'd', and 'w' to move (or arrow keys).  Have fun!
+"""
+from game import GameStateData
+from game import Game
+from game import Directions
+from game import Actions
+from util import nearestPoint
+from util import manhattanDistance
+import util
+import layout
+import sys
+import types
+import time
+import random
+import os
+
+###################################################
+# YOUR INTERFACE TO THE PACMAN WORLD: A GameState #
+###################################################
+
+
+class GameState:
+    """
+    A GameState specifies the full game state, including the food, capsules,
+    agent configurations and score changes.
+
+    GameStates are used by the Game object to capture the actual state of the game and
+    can be used by agents to reason about the game.
+
+    Much of the information in a GameState is stored in a GameStateData object.  We
+    strongly suggest that you access that data via the accessor methods below rather
+    than referring to the GameStateData object directly.
+
+    Note that in classic Pacman, Pacman is always agent 0.
+    """
+
+    ####################################################
+    # Accessor methods: use these to access state data #
+    ####################################################
+
+    # static variable keeps track of which states have had getLegalActions called
+    explored = set()
+
+    def getAndResetExplored():
+        tmp = GameState.explored.copy()
+        GameState.explored = set()
+        return tmp
+    getAndResetExplored = staticmethod(getAndResetExplored)
+
+    def getLegalActions(self, agentIndex=0):
+        """
+        Returns the legal actions for the agent specified.
+        """
+#        GameState.explored.add(self)
+        if self.isWin() or self.isLose():
+            return []
+
+        if agentIndex == 0:  # Pacman is moving
+            return PacmanRules.getLegalActions(self)
+        else:
+            return GhostRules.getLegalActions(self, agentIndex)
+
+    def generateSuccessor(self, agentIndex, action):
+        """
+        Returns the successor state after the specified agent takes the action.
+        """
+        # Check that successors exist
+        if self.isWin() or self.isLose():
+            raise Exception('Can\'t generate a successor of a terminal state.')
+
+        # Copy current state
+        state = GameState(self)
+
+        # Let agent's logic deal with its action's effects on the board
+        if agentIndex == 0:  # Pacman is moving
+            state.data._eaten = [False for i in range(state.getNumAgents())]
+            PacmanRules.applyAction(state, action)
+        else:                # A ghost is moving
+            GhostRules.applyAction(state, action, agentIndex)
+
+        # Time passes
+        if agentIndex == 0:
+            state.data.scoreChange += -TIME_PENALTY  # Penalty for waiting around
+        else:
+            GhostRules.decrementTimer(state.data.agentStates[agentIndex])
+
+        # Resolve multi-agent effects
+        GhostRules.checkDeath(state, agentIndex)
+
+        # Book keeping
+        state.data._agentMoved = agentIndex
+        state.data.score += state.data.scoreChange
+        GameState.explored.add(self)
+        GameState.explored.add(state)
+        return state
+
+    def getLegalPacmanActions(self):
+        return self.getLegalActions(0)
+
+    def generatePacmanSuccessor(self, action):
+        """
+        Generates the successor state after the specified pacman move
+        """
+        return self.generateSuccessor(0, action)
+
+    def getPacmanState(self):
+        """
+        Returns an AgentState object for pacman (in game.py)
+
+        state.pos gives the current position
+        state.direction gives the travel vector
+        """
+        return self.data.agentStates[0].copy()
+
+    def getPacmanPosition(self):
+        return self.data.agentStates[0].getPosition()
+
+    def getGhostStates(self):
+        return self.data.agentStates[1:]
+
+    def getGhostState(self, agentIndex):
+        if agentIndex == 0 or agentIndex >= self.getNumAgents():
+            raise Exception("Invalid index passed to getGhostState")
+        return self.data.agentStates[agentIndex]
+
+    def getGhostPosition(self, agentIndex):
+        if agentIndex == 0:
+            raise Exception("Pacman's index passed to getGhostPosition")
+        return self.data.agentStates[agentIndex].getPosition()
+
+    def getGhostPositions(self):
+        return [s.getPosition() for s in self.getGhostStates()]
+
+    def getNumAgents(self):
+        return len(self.data.agentStates)
+
+    def getScore(self):
+        return float(self.data.score)
+
+    def getCapsules(self):
+        """
+        Returns a list of positions (x,y) of the remaining capsules.
+        """
+        return self.data.capsules
+
+    def getNumFood(self):
+        return self.data.food.count()
+
+    def getFood(self):
+        """
+        Returns a Grid of boolean food indicator variables.
+
+        Grids can be accessed via list notation, so to check
+        if there is food at (x,y), just call
+
+        currentFood = state.getFood()
+        if currentFood[x][y] == True: ...
+        """
+        return self.data.food
+
+    def getWalls(self):
+        """
+        Returns a Grid of boolean wall indicator variables.
+
+        Grids can be accessed via list notation, so to check
+        if there is a wall at (x,y), just call
+
+        walls = state.getWalls()
+        if walls[x][y] == True: ...
+        """
+        return self.data.layout.walls
+
+    def hasFood(self, x, y):
+        return self.data.food[x][y]
+
+    def hasWall(self, x, y):
+        return self.data.layout.walls[x][y]
+
+    def isLose(self):
+        return self.data._lose
+
+    def isWin(self):
+        return self.data._win
+
+    #############################################
+    #             Helper methods:               #
+    # You shouldn't need to call these directly #
+    #############################################
+
+    def __init__(self, prevState=None):
+        """
+        Generates a new state by copying information from its predecessor.
+        """
+        if prevState != None:  # Initial state
+            self.data = GameStateData(prevState.data)
+        else:
+            self.data = GameStateData()
+
+    def deepCopy(self):
+        state = GameState(self)
+        state.data = self.data.deepCopy()
+        return state
+
+    def __eq__(self, other):
+        """
+        Allows two states to be compared.
+        """
+        return hasattr(other, 'data') and self.data == other.data
+
+    def __hash__(self):
+        """
+        Allows states to be keys of dictionaries.
+        """
+        return hash(self.data)
+
+    def __str__(self):
+
+        return str(self.data)
+
+    def initialize(self, layout, numGhostAgents=1000):
+        """
+        Creates an initial game state from a layout array (see layout.py).
+        """
+        self.data.initialize(layout, numGhostAgents)
+
+############################################################################
+#                     THE HIDDEN SECRETS OF PACMAN                         #
+#                                                                          #
+# You shouldn't need to look through the code in this section of the file. #
+############################################################################
+
+
+SCARED_TIME = 40    # Moves ghosts are scared
+COLLISION_TOLERANCE = 0.7  # How close ghosts must be to Pacman to kill
+TIME_PENALTY = 1  # Number of points lost each round
+
+
+class ClassicGameRules:
+    """
+    These game rules manage the control flow of a game, deciding when
+    and how the game starts and ends.
+    """
+
+    def __init__(self, timeout=30):
+        self.timeout = timeout
+
+    def newGame(self, layout, pacmanAgent, ghostAgents, display, quiet=False, catchExceptions=False):
+        agents = [pacmanAgent] + ghostAgents[:layout.getNumGhosts()]
+        initState = GameState()
+        initState.initialize(layout, len(ghostAgents))
+        game = Game(agents, display, self, catchExceptions=catchExceptions)
+        game.state = initState
+        self.initialState = initState.deepCopy()
+        self.quiet = quiet
+        return game
+
+    def process(self, state, game):
+        """
+        Checks to see whether it is time to end the game.
+        """
+        if state.isWin():
+            self.win(state, game)
+        if state.isLose():
+            self.lose(state, game)
+
+    def win(self, state, game):
+        if not self.quiet:
+            print("Pacman emerges victorious! Score: %d" % state.data.score)
+        game.gameOver = True
+
+    def lose(self, state, game):
+        if not self.quiet:
+            print("Pacman died! Score: %d" % state.data.score)
+        game.gameOver = True
+
+    def getProgress(self, game):
+        return float(game.state.getNumFood()) / self.initialState.getNumFood()
+
+    def agentCrash(self, game, agentIndex):
+        if agentIndex == 0:
+            print("Pacman crashed")
+        else:
+            print("A ghost crashed")
+
+    def getMaxTotalTime(self, agentIndex):
+        return self.timeout
+
+    def getMaxStartupTime(self, agentIndex):
+        return self.timeout
+
+    def getMoveWarningTime(self, agentIndex):
+        return self.timeout
+
+    def getMoveTimeout(self, agentIndex):
+        return self.timeout
+
+    def getMaxTimeWarnings(self, agentIndex):
+        return 0
+
+
+class PacmanRules:
+    """
+    These functions govern how pacman interacts with his environment under
+    the classic game rules.
+    """
+    PACMAN_SPEED = 1
+
+    def getLegalActions(state):
+        """
+        Returns a list of possible actions.
+        """
+        return Actions.getPossibleActions(state.getPacmanState().configuration, state.data.layout.walls)
+    getLegalActions = staticmethod(getLegalActions)
+
+    def applyAction(state, action):
+        """
+        Edits the state to reflect the results of the action.
+        """
+        legal = PacmanRules.getLegalActions(state)
+        if action not in legal:
+            raise Exception("Illegal action " + str(action))
+
+        pacmanState = state.data.agentStates[0]
+
+        # Update Configuration
+        vector = Actions.directionToVector(action, PacmanRules.PACMAN_SPEED)
+        pacmanState.configuration = pacmanState.configuration.generateSuccessor(
+            vector)
+
+        # Eat
+        next = pacmanState.configuration.getPosition()
+        nearest = nearestPoint(next)
+        if manhattanDistance(nearest, next) <= 0.5:
+            # Remove food
+            PacmanRules.consume(nearest, state)
+    applyAction = staticmethod(applyAction)
+
+    def consume(position, state):
+        x, y = position
+        # Eat food
+        if state.data.food[x][y]:
+            state.data.scoreChange += 10
+            state.data.food = state.data.food.copy()
+            state.data.food[x][y] = False
+            state.data._foodEaten = position
+            # TODO: cache numFood?
+            numFood = state.getNumFood()
+            if numFood == 0 and not state.data._lose:
+                state.data.scoreChange += 500
+                state.data._win = True
+        # Eat capsule
+        if(position in state.getCapsules()):
+            state.data.capsules.remove(position)
+            state.data._capsuleEaten = position
+            # Reset all ghosts' scared timers
+            for index in range(1, len(state.data.agentStates)):
+                state.data.agentStates[index].scaredTimer = SCARED_TIME
+    consume = staticmethod(consume)
+
+
+class GhostRules:
+    """
+    These functions dictate how ghosts interact with their environment.
+    """
+    GHOST_SPEED = 1.0
+
+    def getLegalActions(state, ghostIndex):
+        """
+        Ghosts cannot stop, and cannot turn around unless they
+        reach a dead end, but can turn 90 degrees at intersections.
+        """
+        conf = state.getGhostState(ghostIndex).configuration
+        possibleActions = Actions.getPossibleActions(
+            conf, state.data.layout.walls)
+        reverse = Actions.reverseDirection(conf.direction)
+        if Directions.STOP in possibleActions:
+            possibleActions.remove(Directions.STOP)
+        if reverse in possibleActions and len(possibleActions) > 1:
+            possibleActions.remove(reverse)
+        return possibleActions
+    getLegalActions = staticmethod(getLegalActions)
+
+    def applyAction(state, action, ghostIndex):
+
+        legal = GhostRules.getLegalActions(state, ghostIndex)
+        if action not in legal:
+            raise Exception("Illegal ghost action " + str(action))
+
+        ghostState = state.data.agentStates[ghostIndex]
+        speed = GhostRules.GHOST_SPEED
+        if ghostState.scaredTimer > 0:
+            speed /= 2.0
+        vector = Actions.directionToVector(action, speed)
+        ghostState.configuration = ghostState.configuration.generateSuccessor(
+            vector)
+    applyAction = staticmethod(applyAction)
+
+    def decrementTimer(ghostState):
+        timer = ghostState.scaredTimer
+        if timer == 1:
+            ghostState.configuration.pos = nearestPoint(
+                ghostState.configuration.pos)
+        ghostState.scaredTimer = max(0, timer - 1)
+    decrementTimer = staticmethod(decrementTimer)
+
+    def checkDeath(state, agentIndex):
+        pacmanPosition = state.getPacmanPosition()
+        if agentIndex == 0:  # Pacman just moved; Anyone can kill him
+            for index in range(1, len(state.data.agentStates)):
+                ghostState = state.data.agentStates[index]
+                ghostPosition = ghostState.configuration.getPosition()
+                if GhostRules.canKill(pacmanPosition, ghostPosition):
+                    GhostRules.collide(state, ghostState, index)
+        else:
+            ghostState = state.data.agentStates[agentIndex]
+            ghostPosition = ghostState.configuration.getPosition()
+            if GhostRules.canKill(pacmanPosition, ghostPosition):
+                GhostRules.collide(state, ghostState, agentIndex)
+    checkDeath = staticmethod(checkDeath)
+
+    def collide(state, ghostState, agentIndex):
+        if ghostState.scaredTimer > 0:
+            state.data.scoreChange += 200
+            GhostRules.placeGhost(state, ghostState)
+            ghostState.scaredTimer = 0
+            # Added for first-person
+            state.data._eaten[agentIndex] = True
+        else:
+            if not state.data._win:
+                state.data.scoreChange -= 500
+                state.data._lose = True
+    collide = staticmethod(collide)
+
+    def canKill(pacmanPosition, ghostPosition):
+        return manhattanDistance(ghostPosition, pacmanPosition) <= COLLISION_TOLERANCE
+    canKill = staticmethod(canKill)
+
+    def placeGhost(state, ghostState):
+        ghostState.configuration = ghostState.start
+    placeGhost = staticmethod(placeGhost)
+
+#############################
+# FRAMEWORK TO START A GAME #
+#############################
+
+
+def default(str):
+    return str + ' [Default: %default]'
+
+
+def parseAgentArgs(str):
+    if str == None:
+        return {}
+    pieces = str.split(',')
+    opts = {}
+    for p in pieces:
+        if '=' in p:
+            key, val = p.split('=')
+        else:
+            key, val = p, 1
+        opts[key] = val
+    return opts
+
+
+def readCommand(argv):
+    """
+    Processes the command used to run pacman from the command line.
+    """
+    from optparse import OptionParser
+    usageStr = """
+    USAGE:      python pacman.py 
+    EXAMPLES:   (1) python pacman.py
+                    - starts an interactive game
+                (2) python pacman.py --layout smallClassic --zoom 2
+                OR  python pacman.py -l smallClassic -z 2
+                    - starts an interactive game on a smaller board, zoomed in
+    """
+    parser = OptionParser(usageStr)
+
+    parser.add_option('-n', '--numGames', dest='numGames', type='int',
+                      help=default('the number of GAMES to play'), metavar='GAMES', default=1)
+    parser.add_option('-l', '--layout', dest='layout',
+                      help=default(
+                          'the LAYOUT_FILE from which to load the map layout'),
+                      metavar='LAYOUT_FILE', default='mediumClassic')
+    parser.add_option('-p', '--pacman', dest='pacman',
+                      help=default(
+                          'the agent TYPE in the pacmanAgents module to use'),
+                      metavar='TYPE', default='KeyboardAgent')
+    parser.add_option('-t', '--textGraphics', action='store_true', dest='textGraphics',
+                      help='Display output as text only', default=False)
+    parser.add_option('-q', '--quietTextGraphics', action='store_true', dest='quietGraphics',
+                      help='Generate minimal output and no graphics', default=False)
+    parser.add_option('-g', '--ghosts', dest='ghost',
+                      help=default(
+                          'the ghost agent TYPE in the ghostAgents module to use'),
+                      metavar='TYPE', default='RandomGhost')
+    parser.add_option('-k', '--numghosts', type='int', dest='numGhosts',
+                      help=default('The maximum number of ghosts to use'), default=4)
+    parser.add_option('-z', '--zoom', type='float', dest='zoom',
+                      help=default('Zoom the size of the graphics window'), default=1.0)
+    parser.add_option('-f', '--fixRandomSeed', action='store_true', dest='fixRandomSeed',
+                      help='Fixes the random seed to always play the same game', default=False)
+    parser.add_option('-r', '--recordActions', action='store_true', dest='record',
+                      help='Writes game histories to a file (named by the time they were played)', default=False)
+    parser.add_option('--replay', dest='gameToReplay',
+                      help='A recorded game file (pickle) to replay', default=None)
+    parser.add_option('-a', '--agentArgs', dest='agentArgs',
+                      help='Comma separated values sent to agent. e.g. "opt1=val1,opt2,opt3=val3"')
+    parser.add_option('-x', '--numTraining', dest='numTraining', type='int',
+                      help=default('How many episodes are training (suppresses output)'), default=0)
+    parser.add_option('--frameTime', dest='frameTime', type='float',
+                      help=default('Time to delay between frames; <0 means keyboard'), default=0.1)
+    parser.add_option('-c', '--catchExceptions', action='store_true', dest='catchExceptions',
+                      help='Turns on exception handling and timeouts during games', default=False)
+    parser.add_option('--timeout', dest='timeout', type='int',
+                      help=default('Maximum length of time an agent can spend computing in a single game'), default=30)
+
+    options, otherjunk = parser.parse_args(argv)
+    if len(otherjunk) != 0:
+        raise Exception('Command line input not understood: ' + str(otherjunk))
+    args = dict()
+
+    # Fix the random seed
+    if options.fixRandomSeed:
+        random.seed('cs188')
+
+    # Choose a layout
+    args['layout'] = layout.getLayout(options.layout)
+    if args['layout'] == None:
+        raise Exception("The layout " + options.layout + " cannot be found")
+
+    # Choose a Pacman agent
+    noKeyboard = options.gameToReplay == None and (
+        options.textGraphics or options.quietGraphics)
+    pacmanType = loadAgent(options.pacman, noKeyboard)
+    agentOpts = parseAgentArgs(options.agentArgs)
+    if options.numTraining > 0:
+        args['numTraining'] = options.numTraining
+        if 'numTraining' not in agentOpts:
+            agentOpts['numTraining'] = options.numTraining
+    pacman = pacmanType(**agentOpts)  # Instantiate Pacman with agentArgs
+    args['pacman'] = pacman
+
+    # Don't display training games
+    if 'numTrain' in agentOpts:
+        options.numQuiet = int(agentOpts['numTrain'])
+        options.numIgnore = int(agentOpts['numTrain'])
+
+    # Choose a ghost agent
+    ghostType = loadAgent(options.ghost, noKeyboard)
+    args['ghosts'] = [ghostType(i+1) for i in range(options.numGhosts)]
+
+    # Choose a display format
+    if options.quietGraphics:
+        import textDisplay
+        args['display'] = textDisplay.NullGraphics()
+    elif options.textGraphics:
+        import textDisplay
+        textDisplay.SLEEP_TIME = options.frameTime
+        args['display'] = textDisplay.PacmanGraphics()
+    else:
+        import graphicsDisplay
+        args['display'] = graphicsDisplay.PacmanGraphics(
+            options.zoom, frameTime=options.frameTime)
+    args['numGames'] = options.numGames
+    args['record'] = options.record
+    args['catchExceptions'] = options.catchExceptions
+    args['timeout'] = options.timeout
+
+    # Special case: recorded games don't use the runGames method or args structure
+    if options.gameToReplay != None:
+        print('Replaying recorded game %s.' % options.gameToReplay)
+        import pickle
+        f = open(options.gameToReplay)
+        try:
+            recorded = pickle.load(f)
+        finally:
+            f.close()
+        recorded['display'] = args['display']
+        replayGame(**recorded)
+        sys.exit(0)
+
+    return args
+
+
+def loadAgent(pacman, nographics):
+    # Looks through all pythonPath Directories for the right module,
+    pythonPathStr = os.path.expandvars("$PYTHONPATH")
+    if pythonPathStr.find(';') == -1:
+        pythonPathDirs = pythonPathStr.split(':')
+    else:
+        pythonPathDirs = pythonPathStr.split(';')
+    pythonPathDirs.append('.')
+
+    for moduleDir in pythonPathDirs:
+        if not os.path.isdir(moduleDir):
+            continue
+        moduleNames = [f for f in os.listdir(
+            moduleDir) if f.endswith('gents.py')]
+        for modulename in moduleNames:
+            try:
+                module = __import__(modulename[:-3])
+            except ImportError:
+                continue
+            if pacman in dir(module):
+                if nographics and modulename == 'keyboardAgents.py':
+                    raise Exception(
+                        'Using the keyboard requires graphics (not text display)')
+                return getattr(module, pacman)
+    raise Exception('The agent ' + pacman +
+                    ' is not specified in any *Agents.py.')
+
+
+def replayGame(layout, actions, display):
+    import pacmanAgents
+    import ghostAgents
+    rules = ClassicGameRules()
+    agents = [pacmanAgents.GreedyAgent()] + [ghostAgents.RandomGhost(i+1)
+                                             for i in range(layout.getNumGhosts())]
+    game = rules.newGame(layout, agents[0], agents[1:], display)
+    state = game.state
+    display.initialize(state.data)
+
+    for action in actions:
+            # Execute the action
+        state = state.generateSuccessor(*action)
+        # Change the display
+        display.update(state.data)
+        # Allow for game specific conditions (winning, losing, etc.)
+        rules.process(state, game)
+
+    display.finish()
+
+
+def runGames(layout, pacman, ghosts, display, numGames, record, numTraining=0, catchExceptions=False, timeout=30):
+    import __main__
+    __main__.__dict__['_display'] = display
+
+    rules = ClassicGameRules(timeout)
+    games = []
+
+    for i in range(numGames):
+        beQuiet = i < numTraining
+        if beQuiet:
+                # Suppress output and graphics
+            import textDisplay
+            gameDisplay = textDisplay.NullGraphics()
+            rules.quiet = True
+        else:
+            gameDisplay = display
+            rules.quiet = False
+        game = rules.newGame(layout, pacman, ghosts,
+                             gameDisplay, beQuiet, catchExceptions)
+        game.run()
+        if not beQuiet:
+            games.append(game)
+
+        if record:
+            import time
+            import pickle
+            fname = ('recorded-game-%d' % (i + 1)) + \
+                '-'.join([str(t) for t in time.localtime()[1:6]])
+            f = file(fname, 'w')
+            components = {'layout': layout, 'actions': game.moveHistory}
+            pickle.dump(components, f)
+            f.close()
+
+    if (numGames-numTraining) > 0:
+        scores = [game.state.getScore() for game in games]
+        wins = [game.state.isWin() for game in games]
+        winRate = wins.count(True) / float(len(wins))
+        print('Average Score:', sum(scores) / float(len(scores)))
+        print('Scores:       ', ', '.join([str(score) for score in scores]))
+        print('Win Rate:      %d/%d (%.2f)' %
+              (wins.count(True), len(wins), winRate))
+        print('Record:       ', ', '.join(
+            [['Loss', 'Win'][int(w)] for w in wins]))
+
+    return games
+
+
+if __name__ == '__main__':
+    """
+    The main function called when pacman.py is run
+    from the command line:
+
+    > python pacman.py
+
+    See the usage string for more details.
+
+    > python pacman.py --help
+    """
+    args = readCommand(sys.argv[1:])  # Get game components based on input
+    runGames(**args)
+
+    # import cProfile
+    # cProfile.run("runGames( **args )")
+    pass
diff --git a/multiagent/pacmanAgents.py b/multiagent/pacmanAgents.py
new file mode 100644
index 0000000..30e24ec
--- /dev/null
+++ b/multiagent/pacmanAgents.py
@@ -0,0 +1,63 @@
+# pacmanAgents.py
+# ---------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+from pacman import Directions
+from game import Agent
+import random
+import game
+import util
+
+
+class LeftTurnAgent(game.Agent):
+    "An agent that turns left at every opportunity"
+
+    def getAction(self, state):
+        legal = state.getLegalPacmanActions()
+        current = state.getPacmanState().configuration.direction
+        if current == Directions.STOP:
+            current = Directions.NORTH
+        left = Directions.LEFT[current]
+        if left in legal:
+            return left
+        if current in legal:
+            return current
+        if Directions.RIGHT[current] in legal:
+            return Directions.RIGHT[current]
+        if Directions.LEFT[left] in legal:
+            return Directions.LEFT[left]
+        return Directions.STOP
+
+
+class GreedyAgent(Agent):
+    def __init__(self, evalFn="scoreEvaluation"):
+        self.evaluationFunction = util.lookup(evalFn, globals())
+        assert self.evaluationFunction != None
+
+    def getAction(self, state):
+        # Generate candidate actions
+        legal = state.getLegalPacmanActions()
+        if Directions.STOP in legal:
+            legal.remove(Directions.STOP)
+
+        successors = [(state.generateSuccessor(0, action), action)
+                      for action in legal]
+        scored = [(self.evaluationFunction(state), action)
+                  for state, action in successors]
+        bestScore = max(scored)[0]
+        bestActions = [pair[1] for pair in scored if pair[0] == bestScore]
+        return random.choice(bestActions)
+
+
+def scoreEvaluation(state):
+    return state.getScore()
diff --git a/multiagent/projectParams.py b/multiagent/projectParams.py
new file mode 100644
index 0000000..468632c
--- /dev/null
+++ b/multiagent/projectParams.py
@@ -0,0 +1,18 @@
+# projectParams.py
+# ----------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+STUDENT_CODE_DEFAULT = 'multiAgents.py'
+PROJECT_TEST_CLASSES = 'multiagentTestClasses.py'
+PROJECT_NAME = 'Project 2: Multiagent search'
+BONUS_PIC = False
diff --git a/multiagent/testClasses.py b/multiagent/testClasses.py
new file mode 100644
index 0000000..22cb5ad
--- /dev/null
+++ b/multiagent/testClasses.py
@@ -0,0 +1,212 @@
+# testClasses.py
+# --------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+# import modules from python standard library
+import inspect
+import re
+import sys
+import time
+
+# Class which models a question in a project.  Note that questions have a
+# maximum number of points they are worth, and are composed of a series of
+# test cases
+class Question(object):
+
+    def raiseNotDefined(self):
+        print('Method not implemented: %s' % inspect.stack()[1][3])
+        sys.exit(1)
+
+    def __init__(self, questionDict, display):
+        self.maxPoints = int(questionDict['max_points'])
+        self.testCases = []
+        self.display = display
+
+    def getDisplay(self):
+        return self.display
+
+    def getMaxPoints(self):
+        return self.maxPoints
+
+    # Note that 'thunk' must be a function which accepts a single argument,
+    # namely a 'grading' object
+    def addTestCase(self, testCase, thunk):
+        self.testCases.append((testCase, thunk))
+
+    def execute(self, grades):
+        self.raiseNotDefined()
+
+# Question in which all test cases must be passed in order to receive credit
+class PassAllTestsQuestion(Question):
+
+    def execute(self, grades):
+        # TODO: is this the right way to use grades?  The autograder doesn't seem to use it.
+        testsFailed = False
+        grades.assignZeroCredit()
+        for _, f in self.testCases:
+            start = time.time()
+            if not f(grades):
+                testsFailed = True
+            end = time.time()
+            if end-start > 60:
+                print("WARNING: this question took over 60 seconds to run. This may end up timing out the gradescope autograder")
+        if testsFailed:
+            grades.fail("Tests failed.")
+        else:
+            grades.assignFullCredit()
+
+
+class ExtraCreditPassAllTestsQuestion(Question):
+    def __init__(self, questionDict, display):
+        Question.__init__(self, questionDict, display)
+        self.extraPoints = int(questionDict['extra_points'])
+
+    def execute(self, grades):
+        # TODO: is this the right way to use grades?  The autograder doesn't seem to use it.
+        testsFailed = False
+        grades.assignZeroCredit()
+        for _, f in self.testCases:
+            if not f(grades):
+                testsFailed = True
+        if testsFailed:
+            grades.fail("Tests failed.")
+        else:
+            grades.assignFullCredit()
+            grades.addPoints(self.extraPoints)
+
+# Question in which predict credit is given for test cases with a ``points'' property.
+# All other tests are mandatory and must be passed.
+class HackedPartialCreditQuestion(Question):
+
+    def execute(self, grades):
+        # TODO: is this the right way to use grades?  The autograder doesn't seem to use it.
+        grades.assignZeroCredit()
+
+        points = 0
+        passed = True
+        for testCase, f in self.testCases:
+            testResult = f(grades)
+            if "points" in testCase.testDict:
+                if testResult:
+                    points += float(testCase.testDict["points"])
+            else:
+                passed = passed and testResult
+
+        # FIXME: Below terrible hack to match q3's logic
+        if int(points) == self.maxPoints and not passed:
+            grades.assignZeroCredit()
+        else:
+            grades.addPoints(int(points))
+
+
+class Q6PartialCreditQuestion(Question):
+    """Fails any test which returns False, otherwise doesn't effect the grades object.
+    Partial credit tests will add the required points."""
+
+    def execute(self, grades):
+        grades.assignZeroCredit()
+
+        results = []
+        for _, f in self.testCases:
+            results.append(f(grades))
+        if False in results:
+            grades.assignZeroCredit()
+
+
+class PartialCreditQuestion(Question):
+    """Fails any test which returns False, otherwise doesn't effect the grades object.
+    Partial credit tests will add the required points."""
+
+    def execute(self, grades):
+        grades.assignZeroCredit()
+
+        for _, f in self.testCases:
+            start = time.time()
+            if not f(grades):
+                grades.assignZeroCredit()
+                grades.fail("Tests failed.")
+                return False
+            end = time.time()
+        if end-start > 300:
+            print("WARNING: this question took over 5 minutes to run. This may end up timing out the gradescope autograder")
+
+
+class NumberPassedQuestion(Question):
+    """Grade is the number of test cases passed."""
+
+    def execute(self, grades):
+        grades.addPoints([f(grades) for _, f in self.testCases].count(True))
+
+
+# Template modeling a generic test case
+class TestCase(object):
+
+    def raiseNotDefined(self):
+        print('Method not implemented: %s' % inspect.stack()[1][3])
+        sys.exit(1)
+
+    def getPath(self):
+        return self.path
+
+    def __init__(self, question, testDict):
+        self.question = question
+        self.testDict = testDict
+        self.path = testDict['path']
+        self.messages = []
+
+    def __str__(self):
+        self.raiseNotDefined()
+
+    def execute(self, grades, moduleDict, solutionDict):
+        self.raiseNotDefined()
+
+    def writeSolution(self, moduleDict, filePath):
+        self.raiseNotDefined()
+        return True
+
+    # Tests should call the following messages for grading
+    # to ensure a uniform format for test output.
+    #
+    # TODO: this is hairy, but we need to fix grading.py's interface
+    # to get a nice hierarchical project - question - test structure,
+    # then these should be moved into Question proper.
+    def testPass(self, grades):
+        grades.addMessage('PASS: %s' % (self.path,))
+        for line in self.messages:
+            grades.addMessage('    %s' % (line,))
+        return True
+
+    def testFail(self, grades):
+        grades.addMessage('FAIL: %s' % (self.path,))
+        for line in self.messages:
+            grades.addMessage('    %s' % (line,))
+        return False
+
+    # This should really be question level?
+    def testPartial(self, grades, points, maxPoints):
+        grades.addPoints(points)
+        extraCredit = max(0, points - maxPoints)
+        regularCredit = points - extraCredit
+
+        grades.addMessage('%s: %s (%s of %s points)' % (
+            "PASS" if points >= maxPoints else "FAIL", self.path, regularCredit, maxPoints))
+        if extraCredit > 0:
+            grades.addMessage('EXTRA CREDIT: %s points' % (extraCredit,))
+
+        for line in self.messages:
+            grades.addMessage('    %s' % (line,))
+
+        return True
+
+    def addMessage(self, message):
+        self.messages.extend(message.split('\n'))
diff --git a/multiagent/testParser.py b/multiagent/testParser.py
new file mode 100644
index 0000000..1d720e7
--- /dev/null
+++ b/multiagent/testParser.py
@@ -0,0 +1,86 @@
+# testParser.py
+# -------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+import re
+import sys
+
+
+class TestParser(object):
+
+    def __init__(self, path):
+        # save the path to the test file
+        self.path = path
+
+    def removeComments(self, rawlines):
+        # remove any portion of a line following a '#' symbol
+        fixed_lines = []
+        for l in rawlines:
+            idx = l.find('#')
+            if idx == -1:
+                fixed_lines.append(l)
+            else:
+                fixed_lines.append(l[0:idx])
+        return '\n'.join(fixed_lines)
+
+    def parse(self):
+        # read in the test case and remove comments
+        test = {}
+        with open(self.path) as handle:
+            raw_lines = handle.read().split('\n')
+
+        test_text = self.removeComments(raw_lines)
+        test['__raw_lines__'] = raw_lines
+        test['path'] = self.path
+        test['__emit__'] = []
+        lines = test_text.split('\n')
+        i = 0
+        # read a property in each loop cycle
+        while(i < len(lines)):
+            # skip blank lines
+            if re.match(r'\A\s*\Z', lines[i]):
+                test['__emit__'].append(("raw", raw_lines[i]))
+                i += 1
+                continue
+            m = re.match(r'\A([^"]*?):\s*"([^"]*)"\s*\Z', lines[i])
+            if m:
+                test[m.group(1)] = m.group(2)
+                test['__emit__'].append(("oneline", m.group(1)))
+                i += 1
+                continue
+            m = re.match(r'\A([^"]*?):\s*"""\s*\Z', lines[i])
+            if m:
+                msg = []
+                i += 1
+                while(not re.match(r'\A\s*"""\s*\Z', lines[i])):
+                    msg.append(raw_lines[i])
+                    i += 1
+                test[m.group(1)] = '\n'.join(msg)
+                test['__emit__'].append(("multiline", m.group(1)))
+                i += 1
+                continue
+            print('error parsing test file: %s' % self.path)
+            sys.exit(1)
+        return test
+
+
+def emitTestDict(testDict, handle):
+    for kind, data in testDict['__emit__']:
+        if kind == "raw":
+            handle.write(data + "\n")
+        elif kind == "oneline":
+            handle.write('%s: "%s"\n' % (data, testDict[data]))
+        elif kind == "multiline":
+            handle.write('%s: """\n%s\n"""\n' % (data, testDict[data]))
+        else:
+            raise Exception("Bad __emit__")
diff --git a/multiagent/test_cases/CONFIG b/multiagent/test_cases/CONFIG
new file mode 100644
index 0000000..dc6ad04
--- /dev/null
+++ b/multiagent/test_cases/CONFIG
@@ -0,0 +1 @@
+order: "q1 q2 q3 q4 q5"
diff --git a/multiagent/test_cases/extra/CONFIG b/multiagent/test_cases/extra/CONFIG
new file mode 100644
index 0000000..76c89af
--- /dev/null
+++ b/multiagent/test_cases/extra/CONFIG
@@ -0,0 +1,2 @@
+max_points: "0"
+class: "PartialCreditQuestion"
diff --git a/multiagent/test_cases/extra/grade-agent.test b/multiagent/test_cases/extra/grade-agent.test
new file mode 100644
index 0000000..3d8f123
--- /dev/null
+++ b/multiagent/test_cases/extra/grade-agent.test
@@ -0,0 +1,11 @@
+class: "EvalAgentTest"
+
+agentName: "ContestAgent"
+layoutName: "contestClassic"
+maxTime: "180"
+numGames: "5"
+
+scoreThresholds: "2500 2900"
+
+randomSeed: "0"
+ghosts: "[DirectionalGhost(1), DirectionalGhost(2), DirectionalGhost(3)]"
diff --git a/multiagent/test_cases/q1/CONFIG b/multiagent/test_cases/q1/CONFIG
new file mode 100644
index 0000000..506820a
--- /dev/null
+++ b/multiagent/test_cases/q1/CONFIG
@@ -0,0 +1,2 @@
+max_points: "4"
+class: "PartialCreditQuestion"
diff --git a/multiagent/test_cases/q1/grade-agent.solution b/multiagent/test_cases/q1/grade-agent.solution
new file mode 100644
index 0000000..c5b1889
--- /dev/null
+++ b/multiagent/test_cases/q1/grade-agent.solution
@@ -0,0 +1,2 @@
+# This is the solution file for test_cases/q1/grade-agent.test.
+# File intentionally blank.
diff --git a/multiagent/test_cases/q1/grade-agent.test b/multiagent/test_cases/q1/grade-agent.test
new file mode 100644
index 0000000..bdd7fe4
--- /dev/null
+++ b/multiagent/test_cases/q1/grade-agent.test
@@ -0,0 +1,18 @@
+class: "EvalAgentTest"
+
+agentName: "ReflexAgent"
+layoutName: "openClassic"
+maxTime: "120"
+numGames: "10"
+
+
+nonTimeoutMinimum: "10"
+
+scoreThresholds: "500 1000"
+
+winsMinimum: "1"
+winsThresholds: "5 10"
+
+
+randomSeed: "0"
+ghosts: "[RandomGhost(1)]"
diff --git a/multiagent/test_cases/q2/0-eval-function-lose-states-1.solution b/multiagent/test_cases/q2/0-eval-function-lose-states-1.solution
new file mode 100644
index 0000000..f0088bb
--- /dev/null
+++ b/multiagent/test_cases/q2/0-eval-function-lose-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-eval-function-lose-states-1.test.
+action: "Left"
+generated: "lose1 lose2 root"
diff --git a/multiagent/test_cases/q2/0-eval-function-lose-states-1.test b/multiagent/test_cases/q2/0-eval-function-lose-states-1.test
new file mode 100644
index 0000000..974f0cc
--- /dev/null
+++ b/multiagent/test_cases/q2/0-eval-function-lose-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+successors: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 1.0
+lose2 0.0
+"""
+
diff --git a/multiagent/test_cases/q2/0-eval-function-lose-states-2.solution b/multiagent/test_cases/q2/0-eval-function-lose-states-2.solution
new file mode 100644
index 0000000..e0a44f7
--- /dev/null
+++ b/multiagent/test_cases/q2/0-eval-function-lose-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-eval-function-lose-states-2.test.
+action: "Right"
+generated: "lose1 lose2 root"
diff --git a/multiagent/test_cases/q2/0-eval-function-lose-states-2.test b/multiagent/test_cases/q2/0-eval-function-lose-states-2.test
new file mode 100644
index 0000000..b608129
--- /dev/null
+++ b/multiagent/test_cases/q2/0-eval-function-lose-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      0       1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+successors: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 0.0
+lose2 1.0
+"""
+
diff --git a/multiagent/test_cases/q2/0-eval-function-win-states-1.solution b/multiagent/test_cases/q2/0-eval-function-win-states-1.solution
new file mode 100644
index 0000000..e731cbb
--- /dev/null
+++ b/multiagent/test_cases/q2/0-eval-function-win-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-eval-function-win-states-1.test.
+action: "Left"
+generated: "root win1 win2"
diff --git a/multiagent/test_cases/q2/0-eval-function-win-states-1.test b/multiagent/test_cases/q2/0-eval-function-win-states-1.test
new file mode 100644
index 0000000..0fd3c23
--- /dev/null
+++ b/multiagent/test_cases/q2/0-eval-function-win-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1     win2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+successors: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 1.0
+win2 0.0
+"""
+
diff --git a/multiagent/test_cases/q2/0-eval-function-win-states-2.solution b/multiagent/test_cases/q2/0-eval-function-win-states-2.solution
new file mode 100644
index 0000000..1dbcd4c
--- /dev/null
+++ b/multiagent/test_cases/q2/0-eval-function-win-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-eval-function-win-states-2.test.
+action: "Right"
+generated: "root win1 win2"
diff --git a/multiagent/test_cases/q2/0-eval-function-win-states-2.test b/multiagent/test_cases/q2/0-eval-function-win-states-2.test
new file mode 100644
index 0000000..4f8369c
--- /dev/null
+++ b/multiagent/test_cases/q2/0-eval-function-win-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1    win2
+      0      1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+successors: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 0.0
+win2 1.0
+"""
+
diff --git a/multiagent/test_cases/q2/0-lecture-6-tree.solution b/multiagent/test_cases/q2/0-lecture-6-tree.solution
new file mode 100644
index 0000000..1e0834d
--- /dev/null
+++ b/multiagent/test_cases/q2/0-lecture-6-tree.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-lecture-6-tree.test.
+action: "Center"
+generated: "A B C D E F G H I max min1 min2 min3"
diff --git a/multiagent/test_cases/q2/0-lecture-6-tree.test b/multiagent/test_cases/q2/0-lecture-6-tree.test
new file mode 100644
index 0000000..6d516a0
--- /dev/null
+++ b/multiagent/test_cases/q2/0-lecture-6-tree.test
@@ -0,0 +1,50 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+#  Tree from lecture 6 slides
+diagram: """
+           max
+      /-/   |   \--\
+     /      |       \
+    /       |        \
+ min1      min2      min3
+  /|\      /|\       /|\ 
+ / | \    / | \     / | \
+A  B  C  D  E  F   G  H  I  
+3 12  8  5  4  6  14  1  11
+"""
+
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B C D E F G H I"
+lose_states: ""
+
+successors: """
+max Left min1
+max Center min2
+max Right min3
+min1 Left A
+min1 Center B
+min1 Right C
+min2 Left D
+min2 Center E
+min2 Right F
+min3 Left G
+min3 Center H
+min3 Right I
+"""
+
+
+evaluation: """
+A 3.0
+B 12.0
+C 8.0
+D 5.0
+E 4.0
+F 6.0
+G 14.0
+H 1.0
+I 11.0
+"""
diff --git a/multiagent/test_cases/q2/0-small-tree.solution b/multiagent/test_cases/q2/0-small-tree.solution
new file mode 100644
index 0000000..275257d
--- /dev/null
+++ b/multiagent/test_cases/q2/0-small-tree.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-small-tree.test.
+action: "pacLeft"
+generated: "A B C D deeper minLeft minRight root"
diff --git a/multiagent/test_cases/q2/0-small-tree.test b/multiagent/test_cases/q2/0-small-tree.test
new file mode 100644
index 0000000..5ab2926
--- /dev/null
+++ b/multiagent/test_cases/q2/0-small-tree.test
@@ -0,0 +1,36 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+        root
+       /    \
+ minLeft  minRight
+  / \       /    \
+ A   B     C   deeper
+ 4   3     2     |
+                 D
+               1000
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "A C"
+lose_states: "B D"
+
+successors: """
+root pacLeft minLeft
+root pacRight minRight
+minLeft gLeft A
+minLeft gRight B
+minRight gLeft C
+minRight gRight deeper
+deeper pacLeft D
+"""
+
+evaluation: """
+A 4.0
+B 3.0
+C 2.0
+D 1000.0
+"""
diff --git a/multiagent/test_cases/q2/1-1-minmax.solution b/multiagent/test_cases/q2/1-1-minmax.solution
new file mode 100644
index 0000000..92838e9
--- /dev/null
+++ b/multiagent/test_cases/q2/1-1-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-1-minmax.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/multiagent/test_cases/q2/1-1-minmax.test b/multiagent/test_cases/q2/1-1-minmax.test
new file mode 100644
index 0000000..2f7c288
--- /dev/null
+++ b/multiagent/test_cases/q2/1-1-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+   c1        c2             cx
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.01
+"""
diff --git a/multiagent/test_cases/q2/1-2-minmax.solution b/multiagent/test_cases/q2/1-2-minmax.solution
new file mode 100644
index 0000000..166571a
--- /dev/null
+++ b/multiagent/test_cases/q2/1-2-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-2-minmax.test.
+action: "Right"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/multiagent/test_cases/q2/1-2-minmax.test b/multiagent/test_cases/q2/1-2-minmax.test
new file mode 100644
index 0000000..67afad8
--- /dev/null
+++ b/multiagent/test_cases/q2/1-2-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+   c1        c2             cx
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -2.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -2.99
+"""
diff --git a/multiagent/test_cases/q2/1-3-minmax.solution b/multiagent/test_cases/q2/1-3-minmax.solution
new file mode 100644
index 0000000..0de3ad3
--- /dev/null
+++ b/multiagent/test_cases/q2/1-3-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-3-minmax.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/multiagent/test_cases/q2/1-3-minmax.test b/multiagent/test_cases/q2/1-3-minmax.test
new file mode 100644
index 0000000..85aa14c
--- /dev/null
+++ b/multiagent/test_cases/q2/1-3-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+        cx             c3        c4
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b2 is 4.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.01
+"""
diff --git a/multiagent/test_cases/q2/1-4-minmax.solution b/multiagent/test_cases/q2/1-4-minmax.solution
new file mode 100644
index 0000000..03ccec4
--- /dev/null
+++ b/multiagent/test_cases/q2/1-4-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-4-minmax.test.
+action: "Right"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/multiagent/test_cases/q2/1-4-minmax.test b/multiagent/test_cases/q2/1-4-minmax.test
new file mode 100644
index 0000000..16cbeee
--- /dev/null
+++ b/multiagent/test_cases/q2/1-4-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+        cx             c3        c4
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       3.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b2 is 4.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 3.99
+"""
diff --git a/multiagent/test_cases/q2/1-5-minmax.solution b/multiagent/test_cases/q2/1-5-minmax.solution
new file mode 100644
index 0000000..cdb2622
--- /dev/null
+++ b/multiagent/test_cases/q2/1-5-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-5-minmax.test.
+action: "Right"
+generated: "A B C D E F G H Z a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/multiagent/test_cases/q2/1-5-minmax.test b/multiagent/test_cases/q2/1-5-minmax.test
new file mode 100644
index 0000000..e9785a0
--- /dev/null
+++ b/multiagent/test_cases/q2/1-5-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+             /-----a------\
+            /              \
+           /                \
+         b1                  b2
+       /    \                |
+    c1        c2             cx
+   /  \      /  \            |
+  d1   d2  d3   d4           dx
+ / \  / \  / \  / \          |
+ A B  C D  E F  G H          Z
+-3 13 5 9 10 3 -6 8        3.01
+
+a - max
+b - min
+c - max
+d - min
+
+Note the minimax value of b1 is 3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+A -3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 3.0
+G -6.0
+H 8.0
+Z 3.01
+"""
diff --git a/multiagent/test_cases/q2/1-6-minmax.solution b/multiagent/test_cases/q2/1-6-minmax.solution
new file mode 100644
index 0000000..77e6960
--- /dev/null
+++ b/multiagent/test_cases/q2/1-6-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-6-minmax.test.
+action: "Left"
+generated: "A B C D E F G H Z a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/multiagent/test_cases/q2/1-6-minmax.test b/multiagent/test_cases/q2/1-6-minmax.test
new file mode 100644
index 0000000..2d25946
--- /dev/null
+++ b/multiagent/test_cases/q2/1-6-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+             /-----a------\
+            /              \
+           /                \
+         b1                  b2
+       /    \                |
+    c1        c2             cx
+   /  \      /  \            |
+  d1   d2  d3   d4           dx
+ / \  / \  / \  / \          |
+ A B  C D  E F  G H          Z
+-3 13 5 9 10 3 -6 8        2.99
+
+a - max
+b - min
+c - max
+d - min
+
+Note the minimax value of b1 is 3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+A -3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 3.0
+G -6.0
+H 8.0
+Z 2.99
+"""
diff --git a/multiagent/test_cases/q2/1-7-minmax.solution b/multiagent/test_cases/q2/1-7-minmax.solution
new file mode 100644
index 0000000..e47628d
--- /dev/null
+++ b/multiagent/test_cases/q2/1-7-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-7-minmax.test.
+action: "Left"
+generated: "I J K L M N O P Z a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/multiagent/test_cases/q2/1-7-minmax.test b/multiagent/test_cases/q2/1-7-minmax.test
new file mode 100644
index 0000000..7f402b7
--- /dev/null
+++ b/multiagent/test_cases/q2/1-7-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+        |                 /    \
+        cx             c3        c4
+        |             /   \     /   \
+        dx           d5   d6   d7   d8
+        |           / \  / \  / \  / \ 
+        Z           I J  K L  M N  O P
+     -1.99        -1 -9  4 7  2 5 -3 -2
+
+a - max
+b - min
+c - min
+d - max
+
+Note that the minimax value of b2 is -2
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+I -1.0
+J -9.0
+K 4.0
+L 7.0
+M 2.0
+N 5.0
+O -3.0
+P -2.0
+Z -1.99
+"""
diff --git a/multiagent/test_cases/q2/1-8-minmax.solution b/multiagent/test_cases/q2/1-8-minmax.solution
new file mode 100644
index 0000000..e0357d4
--- /dev/null
+++ b/multiagent/test_cases/q2/1-8-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-8-minmax.test.
+action: "Right"
+generated: "I J K L M N O P Z a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/multiagent/test_cases/q2/1-8-minmax.test b/multiagent/test_cases/q2/1-8-minmax.test
new file mode 100644
index 0000000..d3eb8e6
--- /dev/null
+++ b/multiagent/test_cases/q2/1-8-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+        |                 /    \
+        cx             c3        c4
+        |             /   \     /   \
+        dx           d5   d6   d7   d8 
+        |           / \  / \  / \  / \ 
+        Z           I J  K L  M N  O P
+     -2.01        -1 -9  4 7  2 5 -3 -2
+
+a - max
+b - min
+c - min
+d - max
+
+Note that the minimax value of b2 is -2.01
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+I -1.0
+J -9.0
+K 4.0
+L 7.0
+M 2.0
+N 5.0
+O -3.0
+P -2.0
+Z -2.01
+"""
diff --git a/multiagent/test_cases/q2/2-1a-vary-depth.solution b/multiagent/test_cases/q2/2-1a-vary-depth.solution
new file mode 100644
index 0000000..ef813a0
--- /dev/null
+++ b/multiagent/test_cases/q2/2-1a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-1a-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx"
diff --git a/multiagent/test_cases/q2/2-1a-vary-depth.test b/multiagent/test_cases/q2/2-1a-vary-depth.test
new file mode 100644
index 0000000..5265ae1
--- /dev/null
+++ b/multiagent/test_cases/q2/2-1a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -4.01
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -4.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -4.01
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -4.01
+"""
diff --git a/multiagent/test_cases/q2/2-1b-vary-depth.solution b/multiagent/test_cases/q2/2-1b-vary-depth.solution
new file mode 100644
index 0000000..b9636df
--- /dev/null
+++ b/multiagent/test_cases/q2/2-1b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-1b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/multiagent/test_cases/q2/2-1b-vary-depth.test b/multiagent/test_cases/q2/2-1b-vary-depth.test
new file mode 100644
index 0000000..8d0434e
--- /dev/null
+++ b/multiagent/test_cases/q2/2-1b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -4.01
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -4.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -4.01
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -4.01
+"""
diff --git a/multiagent/test_cases/q2/2-2a-vary-depth.solution b/multiagent/test_cases/q2/2-2a-vary-depth.solution
new file mode 100644
index 0000000..75eab88
--- /dev/null
+++ b/multiagent/test_cases/q2/2-2a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-2a-vary-depth.test.
+action: "Right"
+generated: "a b1 b2 c1 c2 cx"
diff --git a/multiagent/test_cases/q2/2-2a-vary-depth.test b/multiagent/test_cases/q2/2-2a-vary-depth.test
new file mode 100644
index 0000000..c6ba62d
--- /dev/null
+++ b/multiagent/test_cases/q2/2-2a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -3.99
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -3.99
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.99
+"""
diff --git a/multiagent/test_cases/q2/2-2b-vary-depth.solution b/multiagent/test_cases/q2/2-2b-vary-depth.solution
new file mode 100644
index 0000000..831182c
--- /dev/null
+++ b/multiagent/test_cases/q2/2-2b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-2b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/multiagent/test_cases/q2/2-2b-vary-depth.test b/multiagent/test_cases/q2/2-2b-vary-depth.test
new file mode 100644
index 0000000..ea58c39
--- /dev/null
+++ b/multiagent/test_cases/q2/2-2b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -3.99
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -3.99
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.99
+"""
diff --git a/multiagent/test_cases/q2/2-3a-vary-depth.solution b/multiagent/test_cases/q2/2-3a-vary-depth.solution
new file mode 100644
index 0000000..bbf705c
--- /dev/null
+++ b/multiagent/test_cases/q2/2-3a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-3a-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx"
diff --git a/multiagent/test_cases/q2/2-3a-vary-depth.test b/multiagent/test_cases/q2/2-3a-vary-depth.test
new file mode 100644
index 0000000..362cbbc
--- /dev/null
+++ b/multiagent/test_cases/q2/2-3a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 5.01   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       5.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 5.01
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 5.01
+"""
diff --git a/multiagent/test_cases/q2/2-3b-vary-depth.solution b/multiagent/test_cases/q2/2-3b-vary-depth.solution
new file mode 100644
index 0000000..936bb80
--- /dev/null
+++ b/multiagent/test_cases/q2/2-3b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-3b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/multiagent/test_cases/q2/2-3b-vary-depth.test b/multiagent/test_cases/q2/2-3b-vary-depth.test
new file mode 100644
index 0000000..e532bc7
--- /dev/null
+++ b/multiagent/test_cases/q2/2-3b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 5.01   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       5.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 5.01
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 5.01
+"""
diff --git a/multiagent/test_cases/q2/2-4a-vary-depth.solution b/multiagent/test_cases/q2/2-4a-vary-depth.solution
new file mode 100644
index 0000000..1161dfc
--- /dev/null
+++ b/multiagent/test_cases/q2/2-4a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-4a-vary-depth.test.
+action: "Right"
+generated: "a b1 b2 c3 c4 cx"
diff --git a/multiagent/test_cases/q2/2-4a-vary-depth.test b/multiagent/test_cases/q2/2-4a-vary-depth.test
new file mode 100644
index 0000000..534631c
--- /dev/null
+++ b/multiagent/test_cases/q2/2-4a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 4.99   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 4.99
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.99
+"""
diff --git a/multiagent/test_cases/q2/2-4b-vary-depth.solution b/multiagent/test_cases/q2/2-4b-vary-depth.solution
new file mode 100644
index 0000000..c5d91d7
--- /dev/null
+++ b/multiagent/test_cases/q2/2-4b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-4b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/multiagent/test_cases/q2/2-4b-vary-depth.test b/multiagent/test_cases/q2/2-4b-vary-depth.test
new file mode 100644
index 0000000..c884af4
--- /dev/null
+++ b/multiagent/test_cases/q2/2-4b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 4.99   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 4.99
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.99
+"""
diff --git a/multiagent/test_cases/q2/2-one-ghost-3level.solution b/multiagent/test_cases/q2/2-one-ghost-3level.solution
new file mode 100644
index 0000000..5d87269
--- /dev/null
+++ b/multiagent/test_cases/q2/2-one-ghost-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-one-ghost-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/multiagent/test_cases/q2/2-one-ghost-3level.test b/multiagent/test_cases/q2/2-one-ghost-3level.test
new file mode 100644
index 0000000..37fc5c6
--- /dev/null
+++ b/multiagent/test_cases/q2/2-one-ghost-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /    \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - min
+c - max
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/multiagent/test_cases/q2/3-one-ghost-4level.solution b/multiagent/test_cases/q2/3-one-ghost-4level.solution
new file mode 100644
index 0000000..b4af8a5
--- /dev/null
+++ b/multiagent/test_cases/q2/3-one-ghost-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/3-one-ghost-4level.test.
+action: "Left"
+generated: "A B C D E F G H I J K L M N O P a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/multiagent/test_cases/q2/3-one-ghost-4level.test b/multiagent/test_cases/q2/3-one-ghost-4level.test
new file mode 100644
index 0000000..a487e4c
--- /dev/null
+++ b/multiagent/test_cases/q2/3-one-ghost-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /    \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - min
+c - max
+d - min
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/multiagent/test_cases/q2/4-two-ghosts-3level.solution b/multiagent/test_cases/q2/4-two-ghosts-3level.solution
new file mode 100644
index 0000000..45000cd
--- /dev/null
+++ b/multiagent/test_cases/q2/4-two-ghosts-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/4-two-ghosts-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/multiagent/test_cases/q2/4-two-ghosts-3level.test b/multiagent/test_cases/q2/4-two-ghosts-3level.test
new file mode 100644
index 0000000..712ff27
--- /dev/null
+++ b/multiagent/test_cases/q2/4-two-ghosts-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /    \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - min
+c - min
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/multiagent/test_cases/q2/5-two-ghosts-4level.solution b/multiagent/test_cases/q2/5-two-ghosts-4level.solution
new file mode 100644
index 0000000..12c0a9b
--- /dev/null
+++ b/multiagent/test_cases/q2/5-two-ghosts-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/5-two-ghosts-4level.test.
+action: "Left"
+generated: "A B C D E F G H I J K L M N O P a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/multiagent/test_cases/q2/5-two-ghosts-4level.test b/multiagent/test_cases/q2/5-two-ghosts-4level.test
new file mode 100644
index 0000000..d1badd2
--- /dev/null
+++ b/multiagent/test_cases/q2/5-two-ghosts-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /    \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - min
+c - min
+d - max
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/multiagent/test_cases/q2/6-tied-root.solution b/multiagent/test_cases/q2/6-tied-root.solution
new file mode 100644
index 0000000..b93d188
--- /dev/null
+++ b/multiagent/test_cases/q2/6-tied-root.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/6-tied-root.test.
+action: "Left"
+generated: "A B C max min1 min2"
diff --git a/multiagent/test_cases/q2/6-tied-root.test b/multiagent/test_cases/q2/6-tied-root.test
new file mode 100644
index 0000000..2bd0cbe
--- /dev/null
+++ b/multiagent/test_cases/q2/6-tied-root.test
@@ -0,0 +1,31 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+    max
+   /   \
+min1    min2
+ |      /  \
+ A      B   C
+10     10   0
+"""
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B"
+lose_states: "C"
+
+successors: """
+max Left min1
+max Right min2
+min1 Down A
+min2 Left B
+min2 Right C
+"""
+
+evaluation: """
+A 10.0
+B 10.0
+C 0.0
+"""
diff --git a/multiagent/test_cases/q2/7-1a-check-depth-one-ghost.solution b/multiagent/test_cases/q2/7-1a-check-depth-one-ghost.solution
new file mode 100644
index 0000000..51149f9
--- /dev/null
+++ b/multiagent/test_cases/q2/7-1a-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-1a-check-depth-one-ghost.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3"
diff --git a/multiagent/test_cases/q2/7-1a-check-depth-one-ghost.test b/multiagent/test_cases/q2/7-1a-check-depth-one-ghost.test
new file mode 100644
index 0000000..627e66b
--- /dev/null
+++ b/multiagent/test_cases/q2/7-1a-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 1, the evaluation function is called at level c,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q2/7-1b-check-depth-one-ghost.solution b/multiagent/test_cases/q2/7-1b-check-depth-one-ghost.solution
new file mode 100644
index 0000000..994371e
--- /dev/null
+++ b/multiagent/test_cases/q2/7-1b-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-1b-check-depth-one-ghost.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3"
diff --git a/multiagent/test_cases/q2/7-1b-check-depth-one-ghost.test b/multiagent/test_cases/q2/7-1b-check-depth-one-ghost.test
new file mode 100644
index 0000000..3c3e3ea
--- /dev/null
+++ b/multiagent/test_cases/q2/7-1b-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 2, the evaluation function is called at level e,
+so Center should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q2/7-1c-check-depth-one-ghost.solution b/multiagent/test_cases/q2/7-1c-check-depth-one-ghost.solution
new file mode 100644
index 0000000..5027245
--- /dev/null
+++ b/multiagent/test_cases/q2/7-1c-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-1c-check-depth-one-ghost.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/multiagent/test_cases/q2/7-1c-check-depth-one-ghost.test b/multiagent/test_cases/q2/7-1c-check-depth-one-ghost.test
new file mode 100644
index 0000000..b7d6551
--- /dev/null
+++ b/multiagent/test_cases/q2/7-1c-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 3, the evaluation function is called at level g,
+so Right should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q2/7-2a-check-depth-two-ghosts.solution b/multiagent/test_cases/q2/7-2a-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..b3e0ed2
--- /dev/null
+++ b/multiagent/test_cases/q2/7-2a-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-2a-check-depth-two-ghosts.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3"
diff --git a/multiagent/test_cases/q2/7-2a-check-depth-two-ghosts.test b/multiagent/test_cases/q2/7-2a-check-depth-two-ghosts.test
new file mode 100644
index 0000000..94c966a
--- /dev/null
+++ b/multiagent/test_cases/q2/7-2a-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 1, the evaluation function is called at level d,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q2/7-2b-check-depth-two-ghosts.solution b/multiagent/test_cases/q2/7-2b-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..e737e05
--- /dev/null
+++ b/multiagent/test_cases/q2/7-2b-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-2b-check-depth-two-ghosts.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/multiagent/test_cases/q2/7-2b-check-depth-two-ghosts.test b/multiagent/test_cases/q2/7-2b-check-depth-two-ghosts.test
new file mode 100644
index 0000000..dbaab5a
--- /dev/null
+++ b/multiagent/test_cases/q2/7-2b-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 2, the evaluation function is called at level g,
+so Center should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q2/7-2c-check-depth-two-ghosts.solution b/multiagent/test_cases/q2/7-2c-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..6d42f5c
--- /dev/null
+++ b/multiagent/test_cases/q2/7-2c-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-2c-check-depth-two-ghosts.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3 h1 h2 h3 i1 i2 i3 j1 j2 j3"
diff --git a/multiagent/test_cases/q2/7-2c-check-depth-two-ghosts.test b/multiagent/test_cases/q2/7-2c-check-depth-two-ghosts.test
new file mode 100644
index 0000000..49612aa
--- /dev/null
+++ b/multiagent/test_cases/q2/7-2c-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 3, the evaluation function is called at level j,
+so Right should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q2/8-pacman-game.solution b/multiagent/test_cases/q2/8-pacman-game.solution
new file mode 100644
index 0000000..dcc1184
--- /dev/null
+++ b/multiagent/test_cases/q2/8-pacman-game.solution
@@ -0,0 +1,444 @@
+optimalActions: """
+[[["West", "East"], 59], [["West", "East"], 35]]
+[[["West"], 190], [["West"], 127]]
+[[["West"], 190], [["West"], 135]]
+[[["West", "North"], 120], [["West", "North"], 82]]
+[[["West"], 77], [["West"], 57]]
+[[["West", "North"], 143], [["West", "North"], 97]]
+[[["West"], 155], [["West"], 110]]
+[[["West"], 40], [["West"], 27]]
+[[["North"], 64], [["North"], 43]]
+[[["North"], 85], [["North"], 57]]
+[[["North"], 106], [["North"], 71]]
+[[["North"], 97], [["North"], 65]]
+[[["Stop", "East"], 154], [["East"], 103]]
+[[["East"], 156], [["East"], 101]]
+[[["West"], 30], [["West"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["North"], 29], [["North"], 18]]
+[[["North"], 50], [["North"], 31]]
+[[["West"], 55], [["West"], 36]]
+[[["East"], 29], [["East"], 16]]
+[[["North"], 89], [["North"], 61]]
+[[["East", "North"], 161], [["East", "North"], 121]]
+[[["East", "North"], 221], [["East", "North"], 166]]
+[[["North", "South"], 105], [["North", "South"], 77]]
+[[["West"], 69], [["West"], 51]]
+[[["West"], 94], [["West"], 69]]
+[[["West", "Stop"], 57], [["West"], 42]]
+[[["West", "Stop", "East"], 69], [["West", "East"], 49]]
+[[["West", "Stop", "East"], 61], [["West", "East"], 41]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 28], [["East", "South"], 19]]
+[[["Stop", "East", "South"], 34], [["East", "South"], 23]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 64], [["East", "South"], 43]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 102], [["East", "South"], 67]]
+[[["Stop", "South"], 23], [["South"], 13]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 29], [["East", "North"], 18]]
+[[["East"], 38], [["East"], 22]]
+[[["North"], 29], [["North"], 18]]
+[[["North"], 38], [["North"], 22]]
+[[["East"], 33], [["East"], 22]]
+[[["East"], 37], [["East"], 18]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 37], [["East"], 26]]
+[[["East"], 69], [["East"], 41]]
+[[["East"], 56], [["East"], 26]]
+[[["East"], 44], [["East"], 29]]
+[[["North", "South"], 83], [["North", "South"], 52]]
+[[["East", "North"], 121], [["East", "North"], 74]]
+[[["East", "North"], 97], [["East", "North"], 73]]
+[[["North", "South"], 173], [["North", "South"], 130]]
+[[["West", "East"], 90], [["West", "East"], 66]]
+[[["West", "Stop", "East"], 161], [["West", "East"], 118]]
+[[["Stop", "East", "South"], 58], [["East", "South"], 43]]
+[[["Stop", "East"], 120], [["South"], 85]]
+[[["East"], 78], [["East"], 45]]
+[[["West"], 77], [["West"], 42]]
+[[["South"], 83], [["South"], 48]]
+[[["South"], 49], [["South"], 37]]
+[[["South"], 185], [["South"], 104]]
+[[["South"], 68], [["South"], 41]]
+[[["West"], 30], [["West"], 18]]
+[[["West"], 56], [["West"], 29]]
+[[["West"], 14], [["West"], 10]]
+[[["West"], 20], [["West"], 14]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 16], [["West"], 12]]
+[[["West", "North"], 30], [["West", "North"], 20]]
+[[["West"], 38], [["West"], 23]]
+[[["West", "Stop", "East", "North"], 70], [["West", "East", "North"], 46]]
+[[["West", "Stop", "East"], 128], [["West", "East"], 89]]
+[[["West", "Stop", "East"], 31], [["West", "East"], 20]]
+[[["Stop", "East", "North"], 69], [["East", "North"], 45]]
+[[["Stop", "North"], 58], [["North"], 31]]
+[[["North"], 34], [["North"], 19]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 34], [["North"], 19]]
+[[["East"], 30], [["East"], 17]]
+[[["East"], 19], [["East"], 11]]
+[[["East"], 44], [["East"], 29]]
+[[["East", "South"], 87], [["East", "South"], 60]]
+[[["East", "South"], 108], [["East", "South"], 62]]
+[[["South"], 120], [["South"], 61]]
+[[["North", "South"], 209], [["North", "South"], 132]]
+[[["West"], 108], [["West"], 60]]
+[[["West", "Stop", "East", "South"], 83], [["West", "East", "South"], 61]]
+[[["West", "Stop", "East", "South"], 90], [["West", "East", "South"], 66]]
+[[["West", "Stop", "East"], 134], [["West", "East"], 95]]
+[[["West", "Stop", "East"], 82], [["West", "East"], 55]]
+[[["Stop", "East", "South"], 142], [["East", "South"], 95]]
+[[["Stop", "East", "South"], 98], [["East", "South"], 65]]
+[[["Stop", "East", "South"], 128], [["East", "South"], 86]]
+[[["Stop", "East", "South"], 82], [["East", "South"], 55]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 190], [["East", "South"], 127]]
+[[["Stop", "East", "South"], 158], [["East", "South"], 103]]
+[[["Stop", "South"], 50], [["South"], 27]]
+[[["South"], 30], [["South"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 29], [["East", "North"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 41], [["East", "North"], 24]]
+[[["East"], 59], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["East"], 26], [["East"], 15]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 29], [["East"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 41], [["East", "North"], 24]]
+[[["East"], 59], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["North"], 26], [["North"], 15]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 34], [["North"], 19]]
+[[["West"], 34], [["West"], 19]]
+[[["West"], 25], [["West"], 13]]
+[[["West", "Stop", "East"], 7], [["West", "East"], 3]]
+"""
+altDepthActions: """
+[["West", "East"], ["West", "East"], ["West", "East"], ["West", "East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["Stop", "North"], ["North"]]
+[["East"], ["East"], ["Stop", "East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["West"], ["West"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West", "Stop"], ["West"]]
+[["West"], ["West"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North", "South"], ["North", "South"], ["South"], ["South"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West", "East"], ["West", "East"], ["East"], ["East"]]
+[["West"], ["West"], ["East"], ["East"]]
+[["Stop", "East", "South"], ["East", "South"], ["East"], ["East"]]
+[["Stop", "East"], ["East"], ["Stop", "East"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["West", "East"], ["West", "East"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"], ["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"], ["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"], ["Stop", "North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["North", "South"], ["North", "South"], ["North", "South"], ["North", "South"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+"""
+partialPlyBugActions: """
+[["West", "East"], ["West", "East"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["Stop", "East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North", "South"], ["North", "South"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East"], ["East"]]
+[["East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"]]
+[["South"], ["South"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+"""
diff --git a/multiagent/test_cases/q2/8-pacman-game.test b/multiagent/test_cases/q2/8-pacman-game.test
new file mode 100644
index 0000000..de8df6f
--- /dev/null
+++ b/multiagent/test_cases/q2/8-pacman-game.test
@@ -0,0 +1,19 @@
+class: "PacmanGameTreeTest"
+alg: "MinimaxAgent"
+seed: "0"
+depth: "2"
+max_points: "4"
+
+# The following specifies the layout to be used 
+layoutName: "smallClassic"
+layout: """
+%%%%%%%%%%%%%%%%%%%%
+%......%G  G%......%
+%.%%...%%  %%...%%.%
+%.%o.%........%.o%.%
+%.%%.%.%%%%%%.%.%%.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
+"""
+
+
diff --git a/multiagent/test_cases/q2/CONFIG b/multiagent/test_cases/q2/CONFIG
new file mode 100644
index 0000000..2173a9f
--- /dev/null
+++ b/multiagent/test_cases/q2/CONFIG
@@ -0,0 +1,2 @@
+max_points: "5"
+class: "PassAllTestsQuestion"
diff --git a/multiagent/test_cases/q3/0-eval-function-lose-states-1.solution b/multiagent/test_cases/q3/0-eval-function-lose-states-1.solution
new file mode 100644
index 0000000..3a2bf0d
--- /dev/null
+++ b/multiagent/test_cases/q3/0-eval-function-lose-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-eval-function-lose-states-1.test.
+action: "Left"
+generated: "lose1 lose2 root"
diff --git a/multiagent/test_cases/q3/0-eval-function-lose-states-1.test b/multiagent/test_cases/q3/0-eval-function-lose-states-1.test
new file mode 100644
index 0000000..60d3424
--- /dev/null
+++ b/multiagent/test_cases/q3/0-eval-function-lose-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+successors: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 1.0
+lose2 0.0
+"""
+
diff --git a/multiagent/test_cases/q3/0-eval-function-lose-states-2.solution b/multiagent/test_cases/q3/0-eval-function-lose-states-2.solution
new file mode 100644
index 0000000..06e4e38
--- /dev/null
+++ b/multiagent/test_cases/q3/0-eval-function-lose-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-eval-function-lose-states-2.test.
+action: "Right"
+generated: "lose1 lose2 root"
diff --git a/multiagent/test_cases/q3/0-eval-function-lose-states-2.test b/multiagent/test_cases/q3/0-eval-function-lose-states-2.test
new file mode 100644
index 0000000..b6542df
--- /dev/null
+++ b/multiagent/test_cases/q3/0-eval-function-lose-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      0       1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+successors: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 0.0
+lose2 1.0
+"""
+
diff --git a/multiagent/test_cases/q3/0-eval-function-win-states-1.solution b/multiagent/test_cases/q3/0-eval-function-win-states-1.solution
new file mode 100644
index 0000000..422d322
--- /dev/null
+++ b/multiagent/test_cases/q3/0-eval-function-win-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-eval-function-win-states-1.test.
+action: "Left"
+generated: "root win1 win2"
diff --git a/multiagent/test_cases/q3/0-eval-function-win-states-1.test b/multiagent/test_cases/q3/0-eval-function-win-states-1.test
new file mode 100644
index 0000000..e23e977
--- /dev/null
+++ b/multiagent/test_cases/q3/0-eval-function-win-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1     win2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+successors: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 1.0
+win2 0.0
+"""
+
diff --git a/multiagent/test_cases/q3/0-eval-function-win-states-2.solution b/multiagent/test_cases/q3/0-eval-function-win-states-2.solution
new file mode 100644
index 0000000..7c56b64
--- /dev/null
+++ b/multiagent/test_cases/q3/0-eval-function-win-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-eval-function-win-states-2.test.
+action: "Right"
+generated: "root win1 win2"
diff --git a/multiagent/test_cases/q3/0-eval-function-win-states-2.test b/multiagent/test_cases/q3/0-eval-function-win-states-2.test
new file mode 100644
index 0000000..7d48572
--- /dev/null
+++ b/multiagent/test_cases/q3/0-eval-function-win-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1    win2
+      0      1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+successors: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 0.0
+win2 1.0
+"""
+
diff --git a/multiagent/test_cases/q3/0-lecture-6-tree.solution b/multiagent/test_cases/q3/0-lecture-6-tree.solution
new file mode 100644
index 0000000..c5778a9
--- /dev/null
+++ b/multiagent/test_cases/q3/0-lecture-6-tree.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-lecture-6-tree.test.
+action: "Center"
+generated: "A B C D E F G H max min1 min2 min3"
diff --git a/multiagent/test_cases/q3/0-lecture-6-tree.test b/multiagent/test_cases/q3/0-lecture-6-tree.test
new file mode 100644
index 0000000..73b12d3
--- /dev/null
+++ b/multiagent/test_cases/q3/0-lecture-6-tree.test
@@ -0,0 +1,50 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+#  Tree from lecture 6 slides
+diagram: """
+           max
+      /-/   |   \--\
+     /      |       \
+    /       |        \
+ min1      min2      min3
+  /|\      /|\       /|\ 
+ / | \    / | \     / | \
+A  B  C  D  E  F   G  H  I  
+3 12  8  5  4  6  14  1  11
+"""
+
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B C D E F G H I"
+lose_states: ""
+
+successors: """
+max Left min1
+max Center min2
+max Right min3
+min1 Left A
+min1 Center B
+min1 Right C
+min2 Left D
+min2 Center E
+min2 Right F
+min3 Left G
+min3 Center H
+min3 Right I
+"""
+
+
+evaluation: """
+A 3.0
+B 12.0
+C 8.0
+D 5.0
+E 4.0
+F 6.0
+G 14.0
+H 1.0
+I 11.0
+"""
diff --git a/multiagent/test_cases/q3/0-small-tree.solution b/multiagent/test_cases/q3/0-small-tree.solution
new file mode 100644
index 0000000..af8745b
--- /dev/null
+++ b/multiagent/test_cases/q3/0-small-tree.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-small-tree.test.
+action: "pacLeft"
+generated: "A B C minLeft minRight root"
diff --git a/multiagent/test_cases/q3/0-small-tree.test b/multiagent/test_cases/q3/0-small-tree.test
new file mode 100644
index 0000000..6e2accf
--- /dev/null
+++ b/multiagent/test_cases/q3/0-small-tree.test
@@ -0,0 +1,36 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+        root
+       /    \
+ minLeft  minRight
+  / \       /    \
+ A   B     C   deeper
+ 4   3     2     |
+                 D
+               1000
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "A C"
+lose_states: "B D"
+
+successors: """
+root pacLeft minLeft
+root pacRight minRight
+minLeft gLeft A
+minLeft gRight B
+minRight gLeft C
+minRight gRight deeper
+deeper pacLeft D
+"""
+
+evaluation: """
+A 4.0
+B 3.0
+C 2.0
+D 1000.0
+"""
diff --git a/multiagent/test_cases/q3/1-1-minmax.solution b/multiagent/test_cases/q3/1-1-minmax.solution
new file mode 100644
index 0000000..dd9a115
--- /dev/null
+++ b/multiagent/test_cases/q3/1-1-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-1-minmax.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 dx"
diff --git a/multiagent/test_cases/q3/1-1-minmax.test b/multiagent/test_cases/q3/1-1-minmax.test
new file mode 100644
index 0000000..dca9cc3
--- /dev/null
+++ b/multiagent/test_cases/q3/1-1-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+   c1        c2             cx
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.01
+"""
diff --git a/multiagent/test_cases/q3/1-2-minmax.solution b/multiagent/test_cases/q3/1-2-minmax.solution
new file mode 100644
index 0000000..92f7548
--- /dev/null
+++ b/multiagent/test_cases/q3/1-2-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-2-minmax.test.
+action: "Right"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 dx"
diff --git a/multiagent/test_cases/q3/1-2-minmax.test b/multiagent/test_cases/q3/1-2-minmax.test
new file mode 100644
index 0000000..fba18ca
--- /dev/null
+++ b/multiagent/test_cases/q3/1-2-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+   c1        c2             cx
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -2.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -2.99
+"""
diff --git a/multiagent/test_cases/q3/1-3-minmax.solution b/multiagent/test_cases/q3/1-3-minmax.solution
new file mode 100644
index 0000000..2ddbcbd
--- /dev/null
+++ b/multiagent/test_cases/q3/1-3-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-3-minmax.test.
+action: "Left"
+generated: "a b1 b2 c3 cx d5 d6 dx"
diff --git a/multiagent/test_cases/q3/1-3-minmax.test b/multiagent/test_cases/q3/1-3-minmax.test
new file mode 100644
index 0000000..90f6f74
--- /dev/null
+++ b/multiagent/test_cases/q3/1-3-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+        cx             c3        c4
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b2 is 4.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.01
+"""
diff --git a/multiagent/test_cases/q3/1-4-minmax.solution b/multiagent/test_cases/q3/1-4-minmax.solution
new file mode 100644
index 0000000..bdeab5d
--- /dev/null
+++ b/multiagent/test_cases/q3/1-4-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-4-minmax.test.
+action: "Right"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/multiagent/test_cases/q3/1-4-minmax.test b/multiagent/test_cases/q3/1-4-minmax.test
new file mode 100644
index 0000000..3d9434d
--- /dev/null
+++ b/multiagent/test_cases/q3/1-4-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+        cx             c3        c4
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       3.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b2 is 4.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 3.99
+"""
diff --git a/multiagent/test_cases/q3/1-5-minmax.solution b/multiagent/test_cases/q3/1-5-minmax.solution
new file mode 100644
index 0000000..3fa97d4
--- /dev/null
+++ b/multiagent/test_cases/q3/1-5-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-5-minmax.test.
+action: "Right"
+generated: "A B C D E F G Z a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/multiagent/test_cases/q3/1-5-minmax.test b/multiagent/test_cases/q3/1-5-minmax.test
new file mode 100644
index 0000000..c850e0f
--- /dev/null
+++ b/multiagent/test_cases/q3/1-5-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+             /-----a------\
+            /              \
+           /                \
+         b1                  b2
+       /    \                |
+    c1        c2             cx
+   /  \      /  \            |
+  d1   d2  d3   d4           dx
+ / \  / \  / \  / \          |
+ A B  C D  E F  G H          Z
+-3 13 5 9 10 3 -6 8        3.01
+
+a - max
+b - min
+c - max
+d - min
+
+Note the minimax value of b1 is 3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+A -3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 3.0
+G -6.0
+H 8.0
+Z 3.01
+"""
diff --git a/multiagent/test_cases/q3/1-6-minmax.solution b/multiagent/test_cases/q3/1-6-minmax.solution
new file mode 100644
index 0000000..9608b22
--- /dev/null
+++ b/multiagent/test_cases/q3/1-6-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-6-minmax.test.
+action: "Left"
+generated: "A B C D E F G Z a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/multiagent/test_cases/q3/1-6-minmax.test b/multiagent/test_cases/q3/1-6-minmax.test
new file mode 100644
index 0000000..361fdaf
--- /dev/null
+++ b/multiagent/test_cases/q3/1-6-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+             /-----a------\
+            /              \
+           /                \
+         b1                  b2
+       /    \                |
+    c1        c2             cx
+   /  \      /  \            |
+  d1   d2  d3   d4           dx
+ / \  / \  / \  / \          |
+ A B  C D  E F  G H          Z
+-3 13 5 9 10 3 -6 8        2.99
+
+a - max
+b - min
+c - max
+d - min
+
+Note the minimax value of b1 is 3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+A -3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 3.0
+G -6.0
+H 8.0
+Z 2.99
+"""
diff --git a/multiagent/test_cases/q3/1-7-minmax.solution b/multiagent/test_cases/q3/1-7-minmax.solution
new file mode 100644
index 0000000..fb8c1ca
--- /dev/null
+++ b/multiagent/test_cases/q3/1-7-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-7-minmax.test.
+action: "Left"
+generated: "I J K M O P Z a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/multiagent/test_cases/q3/1-7-minmax.test b/multiagent/test_cases/q3/1-7-minmax.test
new file mode 100644
index 0000000..ed9970f
--- /dev/null
+++ b/multiagent/test_cases/q3/1-7-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+        |                 /    \
+        cx             c3        c4
+        |             /   \     /   \
+        dx           d5   d6   d7   d8
+        |           / \  / \  / \  / \ 
+        Z           I J  K L  M N  O P
+     -1.99        -1 -9  4 7  2 5 -3 -2
+
+a - max
+b - min
+c - min
+d - max
+
+Note that the minimax value of b2 is -2
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+I -1.0
+J -9.0
+K 4.0
+L 7.0
+M 2.0
+N 5.0
+O -3.0
+P -2.0
+Z -1.99
+"""
diff --git a/multiagent/test_cases/q3/1-8-minmax.solution b/multiagent/test_cases/q3/1-8-minmax.solution
new file mode 100644
index 0000000..f6f86ba
--- /dev/null
+++ b/multiagent/test_cases/q3/1-8-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-8-minmax.test.
+action: "Right"
+generated: "I J K M O P Z a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/multiagent/test_cases/q3/1-8-minmax.test b/multiagent/test_cases/q3/1-8-minmax.test
new file mode 100644
index 0000000..32c15da
--- /dev/null
+++ b/multiagent/test_cases/q3/1-8-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+        |                 /    \
+        cx             c3        c4
+        |             /   \     /   \
+        dx           d5   d6   d7   d8 
+        |           / \  / \  / \  / \ 
+        Z           I J  K L  M N  O P
+     -2.01        -1 -9  4 7  2 5 -3 -2
+
+a - max
+b - min
+c - min
+d - max
+
+Note that the minimax value of b2 is -2.01
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+I -1.0
+J -9.0
+K 4.0
+L 7.0
+M 2.0
+N 5.0
+O -3.0
+P -2.0
+Z -2.01
+"""
diff --git a/multiagent/test_cases/q3/2-1a-vary-depth.solution b/multiagent/test_cases/q3/2-1a-vary-depth.solution
new file mode 100644
index 0000000..892546f
--- /dev/null
+++ b/multiagent/test_cases/q3/2-1a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-1a-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx"
diff --git a/multiagent/test_cases/q3/2-1a-vary-depth.test b/multiagent/test_cases/q3/2-1a-vary-depth.test
new file mode 100644
index 0000000..392ae13
--- /dev/null
+++ b/multiagent/test_cases/q3/2-1a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -4.01
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -4.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -4.01
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -4.01
+"""
diff --git a/multiagent/test_cases/q3/2-1b-vary-depth.solution b/multiagent/test_cases/q3/2-1b-vary-depth.solution
new file mode 100644
index 0000000..66f3a6d
--- /dev/null
+++ b/multiagent/test_cases/q3/2-1b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-1b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 dx"
diff --git a/multiagent/test_cases/q3/2-1b-vary-depth.test b/multiagent/test_cases/q3/2-1b-vary-depth.test
new file mode 100644
index 0000000..fd4e46c
--- /dev/null
+++ b/multiagent/test_cases/q3/2-1b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -4.01
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -4.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -4.01
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -4.01
+"""
diff --git a/multiagent/test_cases/q3/2-2a-vary-depth.solution b/multiagent/test_cases/q3/2-2a-vary-depth.solution
new file mode 100644
index 0000000..71213b5
--- /dev/null
+++ b/multiagent/test_cases/q3/2-2a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-2a-vary-depth.test.
+action: "Right"
+generated: "a b1 b2 c1 c2 cx"
diff --git a/multiagent/test_cases/q3/2-2a-vary-depth.test b/multiagent/test_cases/q3/2-2a-vary-depth.test
new file mode 100644
index 0000000..a51f580
--- /dev/null
+++ b/multiagent/test_cases/q3/2-2a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -3.99
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -3.99
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.99
+"""
diff --git a/multiagent/test_cases/q3/2-2b-vary-depth.solution b/multiagent/test_cases/q3/2-2b-vary-depth.solution
new file mode 100644
index 0000000..073eab4
--- /dev/null
+++ b/multiagent/test_cases/q3/2-2b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-2b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 dx"
diff --git a/multiagent/test_cases/q3/2-2b-vary-depth.test b/multiagent/test_cases/q3/2-2b-vary-depth.test
new file mode 100644
index 0000000..44dfb63
--- /dev/null
+++ b/multiagent/test_cases/q3/2-2b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -3.99
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -3.99
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.99
+"""
diff --git a/multiagent/test_cases/q3/2-3a-vary-depth.solution b/multiagent/test_cases/q3/2-3a-vary-depth.solution
new file mode 100644
index 0000000..6cb00a6
--- /dev/null
+++ b/multiagent/test_cases/q3/2-3a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-3a-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx"
diff --git a/multiagent/test_cases/q3/2-3a-vary-depth.test b/multiagent/test_cases/q3/2-3a-vary-depth.test
new file mode 100644
index 0000000..61a4ce5
--- /dev/null
+++ b/multiagent/test_cases/q3/2-3a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 5.01   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       5.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 5.01
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 5.01
+"""
diff --git a/multiagent/test_cases/q3/2-3b-vary-depth.solution b/multiagent/test_cases/q3/2-3b-vary-depth.solution
new file mode 100644
index 0000000..4ee5c53
--- /dev/null
+++ b/multiagent/test_cases/q3/2-3b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-3b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 cx d5 d6 dx"
diff --git a/multiagent/test_cases/q3/2-3b-vary-depth.test b/multiagent/test_cases/q3/2-3b-vary-depth.test
new file mode 100644
index 0000000..c5dd181
--- /dev/null
+++ b/multiagent/test_cases/q3/2-3b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 5.01   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       5.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 5.01
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 5.01
+"""
diff --git a/multiagent/test_cases/q3/2-4a-vary-depth.solution b/multiagent/test_cases/q3/2-4a-vary-depth.solution
new file mode 100644
index 0000000..fa44304
--- /dev/null
+++ b/multiagent/test_cases/q3/2-4a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-4a-vary-depth.test.
+action: "Right"
+generated: "a b1 b2 c3 c4 cx"
diff --git a/multiagent/test_cases/q3/2-4a-vary-depth.test b/multiagent/test_cases/q3/2-4a-vary-depth.test
new file mode 100644
index 0000000..8f81995
--- /dev/null
+++ b/multiagent/test_cases/q3/2-4a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 4.99   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 4.99
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.99
+"""
diff --git a/multiagent/test_cases/q3/2-4b-vary-depth.solution b/multiagent/test_cases/q3/2-4b-vary-depth.solution
new file mode 100644
index 0000000..284c12d
--- /dev/null
+++ b/multiagent/test_cases/q3/2-4b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-4b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 cx d5 d6 dx"
diff --git a/multiagent/test_cases/q3/2-4b-vary-depth.test b/multiagent/test_cases/q3/2-4b-vary-depth.test
new file mode 100644
index 0000000..819ed51
--- /dev/null
+++ b/multiagent/test_cases/q3/2-4b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 4.99   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 4.99
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.99
+"""
diff --git a/multiagent/test_cases/q3/2-one-ghost-3level.solution b/multiagent/test_cases/q3/2-one-ghost-3level.solution
new file mode 100644
index 0000000..77e669a
--- /dev/null
+++ b/multiagent/test_cases/q3/2-one-ghost-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-one-ghost-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 d1 d2 d3 d5 d6"
diff --git a/multiagent/test_cases/q3/2-one-ghost-3level.test b/multiagent/test_cases/q3/2-one-ghost-3level.test
new file mode 100644
index 0000000..99aa2fb
--- /dev/null
+++ b/multiagent/test_cases/q3/2-one-ghost-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - min
+c - max
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/multiagent/test_cases/q3/3-one-ghost-4level.solution b/multiagent/test_cases/q3/3-one-ghost-4level.solution
new file mode 100644
index 0000000..34dd2ce
--- /dev/null
+++ b/multiagent/test_cases/q3/3-one-ghost-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/3-one-ghost-4level.test.
+action: "Left"
+generated: "A B C D E F I K a b1 b2 c1 c2 c3 d1 d2 d3 d5 d6"
diff --git a/multiagent/test_cases/q3/3-one-ghost-4level.test b/multiagent/test_cases/q3/3-one-ghost-4level.test
new file mode 100644
index 0000000..7035a84
--- /dev/null
+++ b/multiagent/test_cases/q3/3-one-ghost-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - min
+c - max
+d - min
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/multiagent/test_cases/q3/4-two-ghosts-3level.solution b/multiagent/test_cases/q3/4-two-ghosts-3level.solution
new file mode 100644
index 0000000..102f443
--- /dev/null
+++ b/multiagent/test_cases/q3/4-two-ghosts-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/4-two-ghosts-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7"
diff --git a/multiagent/test_cases/q3/4-two-ghosts-3level.test b/multiagent/test_cases/q3/4-two-ghosts-3level.test
new file mode 100644
index 0000000..d20ba31
--- /dev/null
+++ b/multiagent/test_cases/q3/4-two-ghosts-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - min
+c - min
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/multiagent/test_cases/q3/5-two-ghosts-4level.solution b/multiagent/test_cases/q3/5-two-ghosts-4level.solution
new file mode 100644
index 0000000..614a8b4
--- /dev/null
+++ b/multiagent/test_cases/q3/5-two-ghosts-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/5-two-ghosts-4level.test.
+action: "Left"
+generated: "A B C D E G H I J a b1 b2 c1 c2 c3 d1 d2 d3 d4 d5"
diff --git a/multiagent/test_cases/q3/5-two-ghosts-4level.test b/multiagent/test_cases/q3/5-two-ghosts-4level.test
new file mode 100644
index 0000000..343665b
--- /dev/null
+++ b/multiagent/test_cases/q3/5-two-ghosts-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - min
+c - min
+d - max
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/multiagent/test_cases/q3/6-tied-root.solution b/multiagent/test_cases/q3/6-tied-root.solution
new file mode 100644
index 0000000..36f3c1d
--- /dev/null
+++ b/multiagent/test_cases/q3/6-tied-root.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/6-tied-root.test.
+action: "Left"
+generated: "A B C max min1 min2"
diff --git a/multiagent/test_cases/q3/6-tied-root.test b/multiagent/test_cases/q3/6-tied-root.test
new file mode 100644
index 0000000..b0ba81c
--- /dev/null
+++ b/multiagent/test_cases/q3/6-tied-root.test
@@ -0,0 +1,31 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+    max
+   /   \
+min1    min2
+ |      /  \
+ A      B   C
+10     10   0
+"""
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B"
+lose_states: "C"
+
+successors: """
+max Left min1
+max Right min2
+min1 Down A
+min2 Left B
+min2 Right C
+"""
+
+evaluation: """
+A 10.0
+B 10.0
+C 0.0
+"""
diff --git a/multiagent/test_cases/q3/7-1a-check-depth-one-ghost.solution b/multiagent/test_cases/q3/7-1a-check-depth-one-ghost.solution
new file mode 100644
index 0000000..d03bfc1
--- /dev/null
+++ b/multiagent/test_cases/q3/7-1a-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-1a-check-depth-one-ghost.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3"
diff --git a/multiagent/test_cases/q3/7-1a-check-depth-one-ghost.test b/multiagent/test_cases/q3/7-1a-check-depth-one-ghost.test
new file mode 100644
index 0000000..da5b428
--- /dev/null
+++ b/multiagent/test_cases/q3/7-1a-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 1, the evaluation function is called at level c,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q3/7-1b-check-depth-one-ghost.solution b/multiagent/test_cases/q3/7-1b-check-depth-one-ghost.solution
new file mode 100644
index 0000000..f68218d
--- /dev/null
+++ b/multiagent/test_cases/q3/7-1b-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-1b-check-depth-one-ghost.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3"
diff --git a/multiagent/test_cases/q3/7-1b-check-depth-one-ghost.test b/multiagent/test_cases/q3/7-1b-check-depth-one-ghost.test
new file mode 100644
index 0000000..ee3e750
--- /dev/null
+++ b/multiagent/test_cases/q3/7-1b-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 2, the evaluation function is called at level e,
+so Center should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q3/7-1c-check-depth-one-ghost.solution b/multiagent/test_cases/q3/7-1c-check-depth-one-ghost.solution
new file mode 100644
index 0000000..3d5c062
--- /dev/null
+++ b/multiagent/test_cases/q3/7-1c-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-1c-check-depth-one-ghost.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/multiagent/test_cases/q3/7-1c-check-depth-one-ghost.test b/multiagent/test_cases/q3/7-1c-check-depth-one-ghost.test
new file mode 100644
index 0000000..1e342bf
--- /dev/null
+++ b/multiagent/test_cases/q3/7-1c-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 3, the evaluation function is called at level g,
+so Right should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q3/7-2a-check-depth-two-ghosts.solution b/multiagent/test_cases/q3/7-2a-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..98246da
--- /dev/null
+++ b/multiagent/test_cases/q3/7-2a-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-2a-check-depth-two-ghosts.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3"
diff --git a/multiagent/test_cases/q3/7-2a-check-depth-two-ghosts.test b/multiagent/test_cases/q3/7-2a-check-depth-two-ghosts.test
new file mode 100644
index 0000000..d22beda
--- /dev/null
+++ b/multiagent/test_cases/q3/7-2a-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 1, the evaluation function is called at level d,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q3/7-2b-check-depth-two-ghosts.solution b/multiagent/test_cases/q3/7-2b-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..0920b08
--- /dev/null
+++ b/multiagent/test_cases/q3/7-2b-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-2b-check-depth-two-ghosts.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/multiagent/test_cases/q3/7-2b-check-depth-two-ghosts.test b/multiagent/test_cases/q3/7-2b-check-depth-two-ghosts.test
new file mode 100644
index 0000000..f0c4a4c
--- /dev/null
+++ b/multiagent/test_cases/q3/7-2b-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 2, the evaluation function is called at level g,
+so Center should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q3/7-2c-check-depth-two-ghosts.solution b/multiagent/test_cases/q3/7-2c-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..61f84f1
--- /dev/null
+++ b/multiagent/test_cases/q3/7-2c-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-2c-check-depth-two-ghosts.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3 h1 h2 h3 i1 i2 i3 j1 j2 j3"
diff --git a/multiagent/test_cases/q3/7-2c-check-depth-two-ghosts.test b/multiagent/test_cases/q3/7-2c-check-depth-two-ghosts.test
new file mode 100644
index 0000000..c8df42c
--- /dev/null
+++ b/multiagent/test_cases/q3/7-2c-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 3, the evaluation function is called at level j,
+so Right should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q3/8-pacman-game.solution b/multiagent/test_cases/q3/8-pacman-game.solution
new file mode 100644
index 0000000..faa6a40
--- /dev/null
+++ b/multiagent/test_cases/q3/8-pacman-game.solution
@@ -0,0 +1,444 @@
+optimalActions: """
+[[["West", "East"], 39], [["West", "East"], 27]]
+[[["West"], 75], [["West"], 57]]
+[[["West"], 95], [["West"], 77]]
+[[["West", "North"], 72], [["West", "North"], 54]]
+[[["West"], 51], [["West"], 39]]
+[[["West", "North"], 76], [["West", "North"], 58]]
+[[["West"], 69], [["West"], 51]]
+[[["West"], 34], [["West"], 23]]
+[[["North"], 55], [["North"], 41]]
+[[["North"], 63], [["North"], 32]]
+[[["North"], 87], [["North"], 43]]
+[[["North"], 69], [["North"], 34]]
+[[["Stop", "East"], 116], [["East"], 56]]
+[[["East"], 110], [["East"], 52]]
+[[["West"], 28], [["West"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["North"], 28], [["North"], 18]]
+[[["North"], 47], [["North"], 30]]
+[[["West"], 35], [["West"], 23]]
+[[["East"], 28], [["East"], 15]]
+[[["North"], 74], [["North"], 48]]
+[[["East", "North"], 130], [["East", "North"], 87]]
+[[["East", "North"], 213], [["East", "North"], 158]]
+[[["North", "South"], 101], [["North", "South"], 73]]
+[[["West"], 48], [["West"], 36]]
+[[["West"], 60], [["West"], 45]]
+[[["West", "Stop"], 49], [["West"], 36]]
+[[["West", "Stop", "East"], 69], [["West", "East"], 49]]
+[[["West", "Stop", "East"], 61], [["West", "East"], 41]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 28], [["East", "South"], 19]]
+[[["Stop", "East", "South"], 34], [["East", "South"], 23]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 81], [["East", "South"], 53]]
+[[["Stop", "East", "South"], 64], [["East", "South"], 43]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 81], [["East", "South"], 53]]
+[[["Stop", "East", "South"], 102], [["East", "South"], 67]]
+[[["Stop", "South"], 23], [["South"], 13]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 28], [["East", "North"], 18]]
+[[["East"], 35], [["East"], 22]]
+[[["North"], 28], [["North"], 18]]
+[[["North"], 38], [["North"], 22]]
+[[["East"], 30], [["East"], 20]]
+[[["East"], 33], [["East"], 18]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 33], [["East"], 23]]
+[[["East"], 48], [["East"], 29]]
+[[["East"], 49], [["East"], 26]]
+[[["East"], 44], [["East"], 29]]
+[[["North", "South"], 75], [["North", "South"], 52]]
+[[["East", "North"], 113], [["East", "North"], 74]]
+[[["East", "North"], 89], [["East", "North"], 65]]
+[[["North", "South"], 173], [["North", "South"], 130]]
+[[["West", "East"], 54], [["West", "East"], 42]]
+[[["West", "Stop", "East"], 130], [["West", "East"], 87]]
+[[["Stop", "East", "South"], 58], [["East", "South"], 43]]
+[[["Stop", "East"], 110], [["South"], 82]]
+[[["East"], 71], [["East"], 45]]
+[[["West"], 66], [["West"], 42]]
+[[["South"], 70], [["South"], 48]]
+[[["South"], 48], [["South"], 37]]
+[[["South"], 179], [["South"], 104]]
+[[["South"], 68], [["South"], 41]]
+[[["West"], 25], [["West"], 18]]
+[[["West"], 41], [["West"], 29]]
+[[["West"], 14], [["West"], 10]]
+[[["West"], 20], [["West"], 14]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 16], [["West"], 12]]
+[[["West", "North"], 28], [["West", "North"], 20]]
+[[["West"], 30], [["West"], 23]]
+[[["West", "Stop", "East", "North"], 66], [["West", "East", "North"], 46]]
+[[["West", "Stop", "East"], 126], [["West", "East"], 89]]
+[[["West", "Stop", "East"], 30], [["West", "East"], 20]]
+[[["Stop", "East", "North"], 67], [["East", "North"], 45]]
+[[["Stop", "North"], 52], [["North"], 27]]
+[[["North"], 30], [["North"], 19]]
+[[["North"], 28], [["North"], 17]]
+[[["North"], 17], [["North"], 11]]
+[[["North"], 30], [["North"], 19]]
+[[["East"], 28], [["East"], 17]]
+[[["East"], 17], [["East"], 11]]
+[[["East"], 40], [["East"], 29]]
+[[["East", "South"], 79], [["East", "South"], 60]]
+[[["East", "South"], 90], [["East", "South"], 62]]
+[[["South"], 96], [["South"], 61]]
+[[["North", "South"], 195], [["North", "South"], 132]]
+[[["West"], 80], [["West"], 60]]
+[[["West", "Stop", "East", "South"], 83], [["West", "East", "South"], 61]]
+[[["West", "Stop", "East", "South"], 90], [["West", "East", "South"], 66]]
+[[["West", "Stop", "East"], 134], [["West", "East"], 95]]
+[[["West", "Stop", "East"], 82], [["West", "East"], 55]]
+[[["Stop", "East", "South"], 142], [["East", "South"], 95]]
+[[["Stop", "East", "South"], 95], [["East", "South"], 62]]
+[[["Stop", "East", "South"], 128], [["East", "South"], 86]]
+[[["Stop", "East", "South"], 82], [["East", "South"], 55]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 182], [["East", "South"], 119]]
+[[["Stop", "East", "South"], 154], [["East", "South"], 103]]
+[[["Stop", "South"], 46], [["South"], 25]]
+[[["South"], 28], [["South"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 28], [["East", "North"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 34], [["East", "North"], 24]]
+[[["East"], 56], [["East"], 29]]
+[[["East"], 17], [["East"], 11]]
+[[["East"], 26], [["East"], 15]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 27], [["East"], 17]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 37], [["East", "North"], 24]]
+[[["East"], 56], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["North"], 26], [["North"], 15]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 30], [["North"], 19]]
+[[["West"], 28], [["West"], 19]]
+[[["West"], 23], [["West"], 13]]
+[[["West", "Stop", "East"], 7], [["West", "East"], 3]]
+"""
+altDepthActions: """
+[["West", "East"], ["West", "East"], ["West", "East"], ["West", "East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["Stop", "North"], ["North"]]
+[["East"], ["East"], ["Stop", "East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["West"], ["West"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West", "Stop"], ["West"]]
+[["West"], ["West"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North", "South"], ["North", "South"], ["South"], ["South"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West", "East"], ["West", "East"], ["East"], ["East"]]
+[["West"], ["West"], ["East"], ["East"]]
+[["Stop", "East", "South"], ["East", "South"], ["East"], ["East"]]
+[["Stop", "East"], ["East"], ["Stop", "East"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["West", "East"], ["West", "East"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"], ["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"], ["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"], ["Stop", "North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["North", "South"], ["North", "South"], ["North", "South"], ["North", "South"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+"""
+partialPlyBugActions: """
+[["West", "East"], ["West", "East"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["Stop", "East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North", "South"], ["North", "South"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East"], ["East"]]
+[["East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"]]
+[["South"], ["South"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+"""
diff --git a/multiagent/test_cases/q3/8-pacman-game.test b/multiagent/test_cases/q3/8-pacman-game.test
new file mode 100644
index 0000000..8439209
--- /dev/null
+++ b/multiagent/test_cases/q3/8-pacman-game.test
@@ -0,0 +1,19 @@
+class: "PacmanGameTreeTest"
+alg: "AlphaBetaAgent"
+seed: "0"
+depth: "2"
+max_points: "4"
+
+# The following specifies the layout to be used 
+layoutName: "smallClassic"
+layout: """
+%%%%%%%%%%%%%%%%%%%%
+%......%G  G%......%
+%.%%...%%  %%...%%.%
+%.%o.%........%.o%.%
+%.%%.%.%%%%%%.%.%%.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
+"""
+
+
diff --git a/multiagent/test_cases/q3/CONFIG b/multiagent/test_cases/q3/CONFIG
new file mode 100644
index 0000000..2173a9f
--- /dev/null
+++ b/multiagent/test_cases/q3/CONFIG
@@ -0,0 +1,2 @@
+max_points: "5"
+class: "PassAllTestsQuestion"
diff --git a/multiagent/test_cases/q4/0-eval-function-lose-states-1.solution b/multiagent/test_cases/q4/0-eval-function-lose-states-1.solution
new file mode 100644
index 0000000..416fcee
--- /dev/null
+++ b/multiagent/test_cases/q4/0-eval-function-lose-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-eval-function-lose-states-1.test.
+action: "Left"
+generated: "lose1 lose2 root"
diff --git a/multiagent/test_cases/q4/0-eval-function-lose-states-1.test b/multiagent/test_cases/q4/0-eval-function-lose-states-1.test
new file mode 100644
index 0000000..8682a60
--- /dev/null
+++ b/multiagent/test_cases/q4/0-eval-function-lose-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+successors: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 1.0
+lose2 0.0
+"""
+
diff --git a/multiagent/test_cases/q4/0-eval-function-lose-states-2.solution b/multiagent/test_cases/q4/0-eval-function-lose-states-2.solution
new file mode 100644
index 0000000..e8d5b38
--- /dev/null
+++ b/multiagent/test_cases/q4/0-eval-function-lose-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-eval-function-lose-states-2.test.
+action: "Right"
+generated: "lose1 lose2 root"
diff --git a/multiagent/test_cases/q4/0-eval-function-lose-states-2.test b/multiagent/test_cases/q4/0-eval-function-lose-states-2.test
new file mode 100644
index 0000000..3f07534
--- /dev/null
+++ b/multiagent/test_cases/q4/0-eval-function-lose-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      0       1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+successors: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 0.0
+lose2 1.0
+"""
+
diff --git a/multiagent/test_cases/q4/0-eval-function-win-states-1.solution b/multiagent/test_cases/q4/0-eval-function-win-states-1.solution
new file mode 100644
index 0000000..ce5d2f2
--- /dev/null
+++ b/multiagent/test_cases/q4/0-eval-function-win-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-eval-function-win-states-1.test.
+action: "Left"
+generated: "root win1 win2"
diff --git a/multiagent/test_cases/q4/0-eval-function-win-states-1.test b/multiagent/test_cases/q4/0-eval-function-win-states-1.test
new file mode 100644
index 0000000..654af6c
--- /dev/null
+++ b/multiagent/test_cases/q4/0-eval-function-win-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1     win2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+successors: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 1.0
+win2 0.0
+"""
+
diff --git a/multiagent/test_cases/q4/0-eval-function-win-states-2.solution b/multiagent/test_cases/q4/0-eval-function-win-states-2.solution
new file mode 100644
index 0000000..3c65760
--- /dev/null
+++ b/multiagent/test_cases/q4/0-eval-function-win-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-eval-function-win-states-2.test.
+action: "Right"
+generated: "root win1 win2"
diff --git a/multiagent/test_cases/q4/0-eval-function-win-states-2.test b/multiagent/test_cases/q4/0-eval-function-win-states-2.test
new file mode 100644
index 0000000..93fac73
--- /dev/null
+++ b/multiagent/test_cases/q4/0-eval-function-win-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1    win2
+      0      1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+successors: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 0.0
+win2 1.0
+"""
+
diff --git a/multiagent/test_cases/q4/0-expectimax1.solution b/multiagent/test_cases/q4/0-expectimax1.solution
new file mode 100644
index 0000000..a870247
--- /dev/null
+++ b/multiagent/test_cases/q4/0-expectimax1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-expectimax1.test.
+action: "Left"
+generated: "A B C D E F G H I exp1 exp2 exp3 max"
diff --git a/multiagent/test_cases/q4/0-expectimax1.test b/multiagent/test_cases/q4/0-expectimax1.test
new file mode 100644
index 0000000..d0421be
--- /dev/null
+++ b/multiagent/test_cases/q4/0-expectimax1.test
@@ -0,0 +1,48 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+#  Tree adapted from lecture 6 slides
+diagram: """
+           max
+      /-/   |   \--\
+     /      |       \
+    /       |        \
+ exp1      exp2      exp3
+  /|\      /|\       /|\ 
+ / | \    / | \     / | \
+A  B  C  D  E  F   G  H  I  
+3 12  8  2  4  6  14  5  2
+"""
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B C D E F G H I"
+lose_states: ""
+
+successors: """
+max Left exp1
+max Center exp2
+max Right exp3
+exp1 Left A
+exp1 Center B
+exp1 Right C
+exp2 Left D
+exp2 Center E
+exp2 Right F
+exp3 Left G
+exp3 Center H
+exp3 Right I
+"""
+
+evaluation: """
+A 3.0
+B 12.0
+C 8.0
+D 2.0
+E 4.0
+F 6.0
+G 14.0
+H 5.0
+I 2.0
+"""
diff --git a/multiagent/test_cases/q4/1-expectimax2.solution b/multiagent/test_cases/q4/1-expectimax2.solution
new file mode 100644
index 0000000..926e035
--- /dev/null
+++ b/multiagent/test_cases/q4/1-expectimax2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/1-expectimax2.test.
+action: "Left"
+generated: "A B C D E F G H I exp1 exp2 exp3 max"
diff --git a/multiagent/test_cases/q4/1-expectimax2.test b/multiagent/test_cases/q4/1-expectimax2.test
new file mode 100644
index 0000000..b4f7858
--- /dev/null
+++ b/multiagent/test_cases/q4/1-expectimax2.test
@@ -0,0 +1,48 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+#  Tree from lecture 7 slides
+diagram: """
+           max
+      /-/   |   \--\
+     /      |       \
+    /       |        \
+ exp1      exp2      exp3
+  /|\      /|\       /|\ 
+ / | \    / | \     / | \
+A  B  C  D  E  F   G  H  I  
+3 12  9  2  4  6  15  6  0
+"""
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B C D E F G H I"
+lose_states: ""
+
+successors: """
+max Left exp1
+max Center exp2
+max Right exp3
+exp1 Left A
+exp1 Center B
+exp1 Right C
+exp2 Left D
+exp2 Center E
+exp2 Right F
+exp3 Left G
+exp3 Center H
+exp3 Right I
+"""
+
+evaluation: """
+A 3.0
+B 12.0
+C 9.0
+D 2.0
+E 4.0
+F 6.0
+G 15.0
+H 6.0
+I 0.0
+"""
diff --git a/multiagent/test_cases/q4/2-one-ghost-3level.solution b/multiagent/test_cases/q4/2-one-ghost-3level.solution
new file mode 100644
index 0000000..17bfb04
--- /dev/null
+++ b/multiagent/test_cases/q4/2-one-ghost-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/2-one-ghost-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/multiagent/test_cases/q4/2-one-ghost-3level.test b/multiagent/test_cases/q4/2-one-ghost-3level.test
new file mode 100644
index 0000000..3d206e8
--- /dev/null
+++ b/multiagent/test_cases/q4/2-one-ghost-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - exp
+c - max
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/multiagent/test_cases/q4/3-one-ghost-4level.solution b/multiagent/test_cases/q4/3-one-ghost-4level.solution
new file mode 100644
index 0000000..d31415b
--- /dev/null
+++ b/multiagent/test_cases/q4/3-one-ghost-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/3-one-ghost-4level.test.
+action: "Right"
+generated: "A B C D E F G H I J K L M N O P a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/multiagent/test_cases/q4/3-one-ghost-4level.test b/multiagent/test_cases/q4/3-one-ghost-4level.test
new file mode 100644
index 0000000..b928139
--- /dev/null
+++ b/multiagent/test_cases/q4/3-one-ghost-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - exp
+c - max
+d - exp
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/multiagent/test_cases/q4/4-two-ghosts-3level.solution b/multiagent/test_cases/q4/4-two-ghosts-3level.solution
new file mode 100644
index 0000000..4dae117
--- /dev/null
+++ b/multiagent/test_cases/q4/4-two-ghosts-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/4-two-ghosts-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/multiagent/test_cases/q4/4-two-ghosts-3level.test b/multiagent/test_cases/q4/4-two-ghosts-3level.test
new file mode 100644
index 0000000..0e58b52
--- /dev/null
+++ b/multiagent/test_cases/q4/4-two-ghosts-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - exp
+c - exp
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/multiagent/test_cases/q4/5-two-ghosts-4level.solution b/multiagent/test_cases/q4/5-two-ghosts-4level.solution
new file mode 100644
index 0000000..8453f7a
--- /dev/null
+++ b/multiagent/test_cases/q4/5-two-ghosts-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/5-two-ghosts-4level.test.
+action: "Left"
+generated: "A B C D E F G H I J K L M N O P a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/multiagent/test_cases/q4/5-two-ghosts-4level.test b/multiagent/test_cases/q4/5-two-ghosts-4level.test
new file mode 100644
index 0000000..b8b74a1
--- /dev/null
+++ b/multiagent/test_cases/q4/5-two-ghosts-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - exp
+c - exp
+d - max
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+successors: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/multiagent/test_cases/q4/6-1a-check-depth-one-ghost.solution b/multiagent/test_cases/q4/6-1a-check-depth-one-ghost.solution
new file mode 100644
index 0000000..65223dc
--- /dev/null
+++ b/multiagent/test_cases/q4/6-1a-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-1a-check-depth-one-ghost.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3"
diff --git a/multiagent/test_cases/q4/6-1a-check-depth-one-ghost.test b/multiagent/test_cases/q4/6-1a-check-depth-one-ghost.test
new file mode 100644
index 0000000..e43289d
--- /dev/null
+++ b/multiagent/test_cases/q4/6-1a-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 1, the evaluation function is called at level c,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q4/6-1b-check-depth-one-ghost.solution b/multiagent/test_cases/q4/6-1b-check-depth-one-ghost.solution
new file mode 100644
index 0000000..ed57c6d
--- /dev/null
+++ b/multiagent/test_cases/q4/6-1b-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-1b-check-depth-one-ghost.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3"
diff --git a/multiagent/test_cases/q4/6-1b-check-depth-one-ghost.test b/multiagent/test_cases/q4/6-1b-check-depth-one-ghost.test
new file mode 100644
index 0000000..8ae747f
--- /dev/null
+++ b/multiagent/test_cases/q4/6-1b-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 2, the evaluation function is called at level e,
+so Center should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q4/6-1c-check-depth-one-ghost.solution b/multiagent/test_cases/q4/6-1c-check-depth-one-ghost.solution
new file mode 100644
index 0000000..f5b16c4
--- /dev/null
+++ b/multiagent/test_cases/q4/6-1c-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-1c-check-depth-one-ghost.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/multiagent/test_cases/q4/6-1c-check-depth-one-ghost.test b/multiagent/test_cases/q4/6-1c-check-depth-one-ghost.test
new file mode 100644
index 0000000..bf5779a
--- /dev/null
+++ b/multiagent/test_cases/q4/6-1c-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 3, the evaluation function is called at level g,
+so Right should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q4/6-2a-check-depth-two-ghosts.solution b/multiagent/test_cases/q4/6-2a-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..57a4290
--- /dev/null
+++ b/multiagent/test_cases/q4/6-2a-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-2a-check-depth-two-ghosts.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3"
diff --git a/multiagent/test_cases/q4/6-2a-check-depth-two-ghosts.test b/multiagent/test_cases/q4/6-2a-check-depth-two-ghosts.test
new file mode 100644
index 0000000..1465fb2
--- /dev/null
+++ b/multiagent/test_cases/q4/6-2a-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 1, the evaluation function is called at level d,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q4/6-2b-check-depth-two-ghosts.solution b/multiagent/test_cases/q4/6-2b-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..65a48d5
--- /dev/null
+++ b/multiagent/test_cases/q4/6-2b-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-2b-check-depth-two-ghosts.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/multiagent/test_cases/q4/6-2b-check-depth-two-ghosts.test b/multiagent/test_cases/q4/6-2b-check-depth-two-ghosts.test
new file mode 100644
index 0000000..4585e5a
--- /dev/null
+++ b/multiagent/test_cases/q4/6-2b-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 2, the evaluation function is called at level g,
+so Center should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q4/6-2c-check-depth-two-ghosts.solution b/multiagent/test_cases/q4/6-2c-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..2047966
--- /dev/null
+++ b/multiagent/test_cases/q4/6-2c-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-2c-check-depth-two-ghosts.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3 h1 h2 h3 i1 i2 i3 j1 j2 j3"
diff --git a/multiagent/test_cases/q4/6-2c-check-depth-two-ghosts.test b/multiagent/test_cases/q4/6-2c-check-depth-two-ghosts.test
new file mode 100644
index 0000000..1b10950
--- /dev/null
+++ b/multiagent/test_cases/q4/6-2c-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 3, the evaluation function is called at level j,
+so Right should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+successors: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/multiagent/test_cases/q4/7-pacman-game.solution b/multiagent/test_cases/q4/7-pacman-game.solution
new file mode 100644
index 0000000..7c611c8
--- /dev/null
+++ b/multiagent/test_cases/q4/7-pacman-game.solution
@@ -0,0 +1,444 @@
+optimalActions: """
+[[["West", "East"], 59], [["West", "East"], 35]]
+[[["West"], 190], [["West"], 127]]
+[[["West"], 190], [["West"], 135]]
+[[["West", "North"], 120], [["West", "North"], 82]]
+[[["West"], 77], [["West"], 57]]
+[[["West", "North"], 143], [["West", "North"], 97]]
+[[["West"], 155], [["West"], 110]]
+[[["West"], 40], [["West"], 27]]
+[[["North"], 64], [["North"], 43]]
+[[["North"], 85], [["North"], 57]]
+[[["North"], 106], [["North"], 71]]
+[[["North"], 97], [["North"], 65]]
+[[["East"], 154], [["East"], 103]]
+[[["Stop"], 130], [["West"], 85]]
+[[["West"], 30], [["West"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["North"], 29], [["North"], 18]]
+[[["North"], 50], [["North"], 31]]
+[[["West"], 55], [["West"], 36]]
+[[["East"], 29], [["East"], 16]]
+[[["North"], 89], [["North"], 61]]
+[[["East", "North"], 161], [["East", "North"], 121]]
+[[["East", "North"], 221], [["East", "North"], 166]]
+[[["North", "South"], 105], [["North", "South"], 77]]
+[[["West"], 69], [["West"], 51]]
+[[["West"], 94], [["West"], 69]]
+[[["West", "Stop"], 57], [["West"], 42]]
+[[["West", "Stop", "East"], 69], [["West", "East"], 49]]
+[[["West", "Stop", "East"], 61], [["West", "East"], 41]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 28], [["East", "South"], 19]]
+[[["Stop", "East", "South"], 34], [["East", "South"], 23]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 64], [["East", "South"], 43]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 102], [["East", "South"], 67]]
+[[["Stop", "South"], 23], [["South"], 13]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 29], [["East", "North"], 18]]
+[[["East"], 38], [["East"], 22]]
+[[["North"], 29], [["North"], 18]]
+[[["North"], 38], [["North"], 22]]
+[[["East"], 33], [["East"], 22]]
+[[["East"], 37], [["East"], 18]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 37], [["East"], 26]]
+[[["East"], 69], [["East"], 41]]
+[[["East"], 56], [["East"], 26]]
+[[["East"], 44], [["East"], 29]]
+[[["North", "South"], 83], [["North", "South"], 52]]
+[[["East", "North"], 121], [["East", "North"], 74]]
+[[["East", "North"], 97], [["East", "North"], 73]]
+[[["North", "South"], 173], [["North", "South"], 130]]
+[[["West", "East"], 90], [["West", "East"], 66]]
+[[["West", "Stop", "East"], 161], [["West", "East"], 118]]
+[[["Stop", "East", "South"], 58], [["East", "South"], 43]]
+[[["Stop", "East"], 120], [["East"], 85]]
+[[["East"], 78], [["East"], 45]]
+[[["West"], 77], [["West"], 42]]
+[[["South"], 83], [["South"], 48]]
+[[["South"], 49], [["South"], 37]]
+[[["South"], 185], [["South"], 104]]
+[[["South"], 68], [["South"], 41]]
+[[["West"], 30], [["West"], 18]]
+[[["West"], 56], [["West"], 29]]
+[[["West"], 14], [["West"], 10]]
+[[["West"], 20], [["West"], 14]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 16], [["West"], 12]]
+[[["West", "North"], 30], [["West", "North"], 20]]
+[[["West"], 38], [["West"], 23]]
+[[["West", "Stop", "East", "North"], 70], [["West", "East", "North"], 46]]
+[[["West", "Stop", "East"], 128], [["West", "East"], 89]]
+[[["West", "Stop", "East"], 31], [["West", "East"], 20]]
+[[["Stop", "East", "North"], 69], [["East", "North"], 45]]
+[[["Stop", "North"], 58], [["North"], 31]]
+[[["North"], 34], [["North"], 19]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 34], [["North"], 19]]
+[[["East"], 30], [["East"], 17]]
+[[["East"], 19], [["East"], 11]]
+[[["East"], 44], [["East"], 29]]
+[[["East", "South"], 87], [["East", "South"], 60]]
+[[["East", "South"], 108], [["East", "South"], 62]]
+[[["South"], 120], [["South"], 61]]
+[[["North", "South"], 209], [["North", "South"], 132]]
+[[["West"], 108], [["West"], 60]]
+[[["West", "Stop", "East", "South"], 83], [["West", "East", "South"], 61]]
+[[["West", "Stop", "East", "South"], 90], [["West", "East", "South"], 66]]
+[[["West", "Stop", "East"], 134], [["West", "East"], 95]]
+[[["West", "Stop", "East"], 82], [["West", "East"], 55]]
+[[["Stop", "East", "South"], 142], [["East", "South"], 95]]
+[[["Stop", "East", "South"], 98], [["East", "South"], 65]]
+[[["Stop", "East", "South"], 128], [["East", "South"], 86]]
+[[["Stop", "East", "South"], 82], [["East", "South"], 55]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 190], [["East", "South"], 127]]
+[[["Stop", "East", "South"], 158], [["East", "South"], 103]]
+[[["Stop", "South"], 50], [["South"], 27]]
+[[["South"], 30], [["South"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 29], [["East", "North"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 41], [["East", "North"], 24]]
+[[["East"], 59], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["East"], 26], [["East"], 15]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 29], [["East"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 41], [["East", "North"], 24]]
+[[["East"], 59], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["North"], 26], [["North"], 15]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 34], [["North"], 19]]
+[[["West"], 34], [["West"], 19]]
+[[["West"], 25], [["West"], 13]]
+[[["West", "Stop", "East"], 7], [["West", "East"], 3]]
+"""
+altDepthActions: """
+[["West", "East"], ["West", "East"], ["West", "East"], ["West", "East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West", "Stop"], ["West"], ["Stop"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["West"], ["West"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West", "Stop"], ["West"]]
+[["West"], ["West"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North", "South"], ["North", "South"], ["South"], ["South"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West", "East"], ["West", "East"], ["East"], ["East"]]
+[["West"], ["West"], ["East"], ["East"]]
+[["Stop", "East", "South"], ["East", "South"], ["East"], ["East"]]
+[["Stop", "East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["West", "East"], ["West", "East"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"], ["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"], ["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"], ["Stop", "North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["North", "South"], ["North", "South"], ["North", "South"], ["North", "South"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+"""
+partialPlyBugActions: """
+[["West", "East"], ["West", "East"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["Stop"], ["West"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North", "South"], ["North", "South"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East"], ["East"]]
+[["East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"]]
+[["South"], ["South"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+"""
diff --git a/multiagent/test_cases/q4/7-pacman-game.test b/multiagent/test_cases/q4/7-pacman-game.test
new file mode 100644
index 0000000..0df1615
--- /dev/null
+++ b/multiagent/test_cases/q4/7-pacman-game.test
@@ -0,0 +1,19 @@
+class: "PacmanGameTreeTest"
+alg: "ExpectimaxAgent"
+seed: "0"
+depth: "2"
+max_points: "4"
+
+# The following specifies the layout to be used 
+layoutName: "smallClassic"
+layout: """
+%%%%%%%%%%%%%%%%%%%%
+%......%G  G%......%
+%.%%...%%  %%...%%.%
+%.%o.%........%.o%.%
+%.%%.%.%%%%%%.%.%%.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
+"""
+
+
diff --git a/multiagent/test_cases/q4/CONFIG b/multiagent/test_cases/q4/CONFIG
new file mode 100644
index 0000000..2173a9f
--- /dev/null
+++ b/multiagent/test_cases/q4/CONFIG
@@ -0,0 +1,2 @@
+max_points: "5"
+class: "PassAllTestsQuestion"
diff --git a/multiagent/test_cases/q5/CONFIG b/multiagent/test_cases/q5/CONFIG
new file mode 100644
index 0000000..c127ab3
--- /dev/null
+++ b/multiagent/test_cases/q5/CONFIG
@@ -0,0 +1,2 @@
+max_points: "6"
+class: "PartialCreditQuestion"
diff --git a/multiagent/test_cases/q5/grade-agent.solution b/multiagent/test_cases/q5/grade-agent.solution
new file mode 100644
index 0000000..fe06fc0
--- /dev/null
+++ b/multiagent/test_cases/q5/grade-agent.solution
@@ -0,0 +1,2 @@
+# This is the solution file for test_cases/q5/grade-agent.test.
+# File intentionally blank.
diff --git a/multiagent/test_cases/q5/grade-agent.test b/multiagent/test_cases/q5/grade-agent.test
new file mode 100644
index 0000000..1e21bbf
--- /dev/null
+++ b/multiagent/test_cases/q5/grade-agent.test
@@ -0,0 +1,18 @@
+class: "EvalAgentTest"
+
+agentName: "ExpectimaxAgent"
+agentArgs: "evalFn=better"
+layoutName: "smallClassic"
+maxTime: "120"
+numGames: "10"
+
+nonTimeoutMinimum: "0"
+nonTimeoutThresholds: "10"
+
+scoreThresholds: "500 1000"
+
+winsMinimum: "1"
+winsThresholds: "1 5 10"
+
+randomSeed: "0"
+ghosts: "[RandomGhost(1)]"
diff --git a/multiagent/textDisplay.py b/multiagent/textDisplay.py
new file mode 100644
index 0000000..3a28080
--- /dev/null
+++ b/multiagent/textDisplay.py
@@ -0,0 +1,85 @@
+# textDisplay.py
+# --------------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+import time
+try:
+    import pacman
+except:
+    pass
+
+DRAW_EVERY = 1
+SLEEP_TIME = 0  # This can be overwritten by __init__
+DISPLAY_MOVES = False
+QUIET = False  # Supresses output
+
+
+class NullGraphics:
+    def initialize(self, state, isBlue=False):
+        pass
+
+    def update(self, state):
+        pass
+
+    def checkNullDisplay(self):
+        return True
+
+    def pause(self):
+        time.sleep(SLEEP_TIME)
+
+    def draw(self, state):
+        print(state)
+
+    def updateDistributions(self, dist):
+        pass
+
+    def finish(self):
+        pass
+
+
+class PacmanGraphics:
+    def __init__(self, speed=None):
+        if speed != None:
+            global SLEEP_TIME
+            SLEEP_TIME = speed
+
+    def initialize(self, state, isBlue=False):
+        self.draw(state)
+        self.pause()
+        self.turn = 0
+        self.agentCounter = 0
+
+    def update(self, state):
+        numAgents = len(state.agentStates)
+        self.agentCounter = (self.agentCounter + 1) % numAgents
+        if self.agentCounter == 0:
+            self.turn += 1
+            if DISPLAY_MOVES:
+                ghosts = [pacman.nearestPoint(
+                    state.getGhostPosition(i)) for i in range(1, numAgents)]
+                print("%4d) P: %-8s" % (self.turn, str(pacman.nearestPoint(state.getPacmanPosition()))),
+                      '| Score: %-5d' % state.score, '| Ghosts:', ghosts)
+            if self.turn % DRAW_EVERY == 0:
+                self.draw(state)
+                self.pause()
+        if state._win or state._lose:
+            self.draw(state)
+
+    def pause(self):
+        time.sleep(SLEEP_TIME)
+
+    def draw(self, state):
+        print(state)
+
+    def finish(self):
+        pass
diff --git a/multiagent/util.py b/multiagent/util.py
new file mode 100644
index 0000000..6799299
--- /dev/null
+++ b/multiagent/util.py
@@ -0,0 +1,717 @@
+# util.py
+# -------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+# util.py
+# -------
+# Licensing Information:  You are free to use or extend these projects for
+# educational purposes provided that (1) you do not distribute or publish
+# solutions, (2) you retain this notice, and (3) you provide clear
+# attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
+#
+# Attribution Information: The Pacman AI projects were developed at UC Berkeley.
+# The core projects and autograders were primarily created by John DeNero
+# (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
+# Student side autograding was added by Brad Miller, Nick Hay, and
+# Pieter Abbeel (pabbeel@cs.berkeley.edu).
+
+
+import sys
+import inspect
+import heapq
+import random
+import io
+
+
+class FixedRandom:
+    def __init__(self):
+        fixedState = (3, (2147483648, 507801126, 683453281, 310439348, 2597246090,
+                          2209084787, 2267831527, 979920060, 3098657677, 37650879, 807947081, 3974896263,
+                          881243242, 3100634921, 1334775171, 3965168385, 746264660, 4074750168, 500078808,
+                          776561771, 702988163, 1636311725, 2559226045, 157578202, 2498342920, 2794591496,
+                          4130598723, 496985844, 2944563015, 3731321600, 3514814613, 3362575829, 3038768745,
+                          2206497038, 1108748846, 1317460727, 3134077628, 988312410, 1674063516, 746456451,
+                          3958482413, 1857117812, 708750586, 1583423339, 3466495450, 1536929345, 1137240525,
+                          3875025632, 2466137587, 1235845595, 4214575620, 3792516855, 657994358, 1241843248,
+                          1695651859, 3678946666, 1929922113, 2351044952, 2317810202, 2039319015, 460787996,
+                          3654096216, 4068721415, 1814163703, 2904112444, 1386111013, 574629867, 2654529343,
+                          3833135042, 2725328455, 552431551, 4006991378, 1331562057, 3710134542, 303171486,
+                          1203231078, 2670768975, 54570816, 2679609001, 578983064, 1271454725, 3230871056,
+                          2496832891, 2944938195, 1608828728, 367886575, 2544708204, 103775539, 1912402393,
+                          1098482180, 2738577070, 3091646463, 1505274463, 2079416566, 659100352, 839995305,
+                          1696257633, 274389836, 3973303017, 671127655, 1061109122, 517486945, 1379749962,
+                          3421383928, 3116950429, 2165882425, 2346928266, 2892678711, 2936066049, 1316407868,
+                          2873411858, 4279682888, 2744351923, 3290373816, 1014377279, 955200944, 4220990860,
+                          2386098930, 1772997650, 3757346974, 1621616438, 2877097197, 442116595, 2010480266,
+                          2867861469, 2955352695, 605335967, 2222936009, 2067554933, 4129906358, 1519608541,
+                          1195006590, 1942991038, 2736562236, 279162408, 1415982909, 4099901426, 1732201505,
+                          2934657937, 860563237, 2479235483, 3081651097, 2244720867, 3112631622, 1636991639,
+                          3860393305, 2312061927, 48780114, 1149090394, 2643246550, 1764050647, 3836789087,
+                          3474859076, 4237194338, 1735191073, 2150369208, 92164394, 756974036, 2314453957,
+                          323969533, 4267621035, 283649842, 810004843, 727855536, 1757827251, 3334960421,
+                          3261035106, 38417393, 2660980472, 1256633965, 2184045390, 811213141, 2857482069,
+                          2237770878, 3891003138, 2787806886, 2435192790, 2249324662, 3507764896, 995388363,
+                          856944153, 619213904, 3233967826, 3703465555, 3286531781, 3863193356, 2992340714,
+                          413696855, 3865185632, 1704163171, 3043634452, 2225424707, 2199018022, 3506117517,
+                          3311559776, 3374443561, 1207829628, 668793165, 1822020716, 2082656160, 1160606415,
+                          3034757648, 741703672, 3094328738, 459332691, 2702383376, 1610239915, 4162939394,
+                          557861574, 3805706338, 3832520705, 1248934879, 3250424034, 892335058, 74323433,
+                          3209751608, 3213220797, 3444035873, 3743886725, 1783837251, 610968664, 580745246,
+                          4041979504, 201684874, 2673219253, 1377283008, 3497299167, 2344209394, 2304982920,
+                          3081403782, 2599256854, 3184475235, 3373055826, 695186388, 2423332338, 222864327,
+                          1258227992, 3627871647, 3487724980, 4027953808, 3053320360, 533627073, 3026232514,
+                          2340271949, 867277230, 868513116, 2158535651, 2487822909, 3428235761, 3067196046,
+                          3435119657, 1908441839, 788668797, 3367703138, 3317763187, 908264443, 2252100381,
+                          764223334, 4127108988, 384641349, 3377374722, 1263833251, 1958694944, 3847832657,
+                          1253909612, 1096494446, 555725445, 2277045895, 3340096504, 1383318686, 4234428127,
+                          1072582179, 94169494, 1064509968, 2681151917, 2681864920, 734708852, 1338914021,
+                          1270409500, 1789469116, 4191988204, 1716329784, 2213764829, 3712538840, 919910444,
+                          1318414447, 3383806712, 3054941722, 3378649942, 1205735655, 1268136494, 2214009444,
+                          2532395133, 3232230447, 230294038, 342599089, 772808141, 4096882234, 3146662953,
+                          2784264306, 1860954704, 2675279609, 2984212876, 2466966981, 2627986059, 2985545332,
+                          2578042598, 1458940786, 2944243755, 3959506256, 1509151382, 325761900, 942251521,
+                          4184289782, 2756231555, 3297811774, 1169708099, 3280524138, 3805245319, 3227360276,
+                          3199632491, 2235795585, 2865407118, 36763651, 2441503575, 3314890374, 1755526087,
+                          17915536, 1196948233, 949343045, 3815841867, 489007833, 2654997597, 2834744136,
+                          417688687, 2843220846, 85621843, 747339336, 2043645709, 3520444394, 1825470818,
+                          647778910, 275904777, 1249389189, 3640887431, 4200779599, 323384601, 3446088641,
+                          4049835786, 1718989062, 3563787136, 44099190, 3281263107, 22910812, 1826109246,
+                          745118154, 3392171319, 1571490704, 354891067, 815955642, 1453450421, 940015623,
+                          796817754, 1260148619, 3898237757, 176670141, 1870249326, 3317738680, 448918002,
+                          4059166594, 2003827551, 987091377, 224855998, 3520570137, 789522610, 2604445123,
+                          454472869, 475688926, 2990723466, 523362238, 3897608102, 806637149, 2642229586,
+                          2928614432, 1564415411, 1691381054, 3816907227, 4082581003, 1895544448, 3728217394,
+                          3214813157, 4054301607, 1882632454, 2873728645, 3694943071, 1297991732, 2101682438,
+                          3952579552, 678650400, 1391722293, 478833748, 2976468591, 158586606, 2576499787,
+                          662690848, 3799889765, 3328894692, 2474578497, 2383901391, 1718193504, 3003184595,
+                          3630561213, 1929441113, 3848238627, 1594310094, 3040359840, 3051803867, 2462788790,
+                          954409915, 802581771, 681703307, 545982392, 2738993819, 8025358, 2827719383,
+                          770471093, 3484895980, 3111306320, 3900000891, 2116916652, 397746721, 2087689510,
+                          721433935, 1396088885, 2751612384, 1998988613, 2135074843, 2521131298, 707009172,
+                          2398321482, 688041159, 2264560137, 482388305, 207864885, 3735036991, 3490348331,
+                          1963642811, 3260224305, 3493564223, 1939428454, 1128799656, 1366012432, 2858822447,
+                          1428147157, 2261125391, 1611208390, 1134826333, 2374102525, 3833625209, 2266397263,
+                          3189115077, 770080230, 2674657172, 4280146640, 3604531615, 4235071805, 3436987249,
+                          509704467, 2582695198, 4256268040, 3391197562, 1460642842, 1617931012, 457825497,
+                          1031452907, 1330422862, 4125947620, 2280712485, 431892090, 2387410588, 2061126784,
+                          896457479, 3480499461, 2488196663, 4021103792, 1877063114, 2744470201, 1046140599,
+                          2129952955, 3583049218, 4217723693, 2720341743, 820661843, 1079873609, 3360954200,
+                          3652304997, 3335838575, 2178810636, 1908053374, 4026721976, 1793145418, 476541615,
+                          973420250, 515553040, 919292001, 2601786155, 1685119450, 3030170809, 1590676150,
+                          1665099167, 651151584, 2077190587, 957892642, 646336572, 2743719258, 866169074,
+                          851118829, 4225766285, 963748226, 799549420, 1955032629, 799460000, 2425744063,
+                          2441291571, 1928963772, 528930629, 2591962884, 3495142819, 1896021824, 901320159,
+                          3181820243, 843061941, 3338628510, 3782438992, 9515330, 1705797226, 953535929,
+                          764833876, 3202464965, 2970244591, 519154982, 3390617541, 566616744, 3438031503,
+                          1853838297, 170608755, 1393728434, 676900116, 3184965776, 1843100290, 78995357,
+                          2227939888, 3460264600, 1745705055, 1474086965, 572796246, 4081303004, 882828851,
+                          1295445825, 137639900, 3304579600, 2722437017, 4093422709, 273203373, 2666507854,
+                          3998836510, 493829981, 1623949669, 3482036755, 3390023939, 833233937, 1639668730,
+                          1499455075, 249728260, 1210694006, 3836497489, 1551488720, 3253074267, 3388238003,
+                          2372035079, 3945715164, 2029501215, 3362012634, 2007375355, 4074709820, 631485888,
+                          3135015769, 4273087084, 3648076204, 2739943601, 1374020358, 1760722448, 3773939706,
+                          1313027823, 1895251226, 4224465911, 421382535, 1141067370, 3660034846, 3393185650,
+                          1850995280, 1451917312, 3841455409, 3926840308, 1397397252, 2572864479, 2500171350,
+                          3119920613, 531400869, 1626487579, 1099320497, 407414753, 2438623324, 99073255,
+                          3175491512, 656431560, 1153671785, 236307875, 2824738046, 2320621382, 892174056,
+                          230984053, 719791226, 2718891946, 624), None)
+        self.random = random.Random()
+        self.random.setstate(fixedState)
+
+
+"""
+ Data structures useful for implementing SearchAgents
+"""
+
+
+class Stack:
+    "A container with a last-in-first-out (LIFO) queuing policy."
+
+    def __init__(self):
+        self.list = []
+
+    def push(self, item):
+        "Push 'item' onto the stack"
+        self.list.append(item)
+
+    def pop(self):
+        "Pop the most recently pushed item from the stack"
+        return self.list.pop()
+
+    def isEmpty(self):
+        "Returns true if the stack is empty"
+        return len(self.list) == 0
+
+
+class Queue:
+    "A container with a first-in-first-out (FIFO) queuing policy."
+
+    def __init__(self):
+        self.list = []
+
+    def push(self, item):
+        "Enqueue the 'item' into the queue"
+        self.list.insert(0, item)
+
+    def pop(self):
+        """
+        Dequeue the earliest enqueued item still in the queue. This
+        operation removes the item from the queue.
+        """
+        return self.list.pop()
+
+    def isEmpty(self):
+        "Returns true if the queue is empty"
+        return len(self.list) == 0
+
+
+class PriorityQueue:
+    """
+    Implements a priority queue data structure. Each inserted item
+    has a priority associated with it and the client is usually interested
+    in quick retrieval of the lowest-priority item in the queue. This
+    data structure allows O(1) access to the lowest-priority item.
+    """
+
+    def __init__(self):
+        self.heap = []
+        self.count = 0
+
+    def push(self, item, priority):
+        entry = (priority, self.count, item)
+        heapq.heappush(self.heap, entry)
+        self.count += 1
+
+    def pop(self):
+        (_, _, item) = heapq.heappop(self.heap)
+        return item
+
+    def isEmpty(self):
+        return len(self.heap) == 0
+
+    def update(self, item, priority):
+        # If item already in priority queue with higher priority, update its priority and rebuild the heap.
+        # If item already in priority queue with equal or lower priority, do nothing.
+        # If item not in priority queue, do the same thing as self.push.
+        for index, (p, c, i) in enumerate(self.heap):
+            if i == item:
+                if p <= priority:
+                    break
+                del self.heap[index]
+                self.heap.append((priority, c, item))
+                heapq.heapify(self.heap)
+                break
+        else:
+            self.push(item, priority)
+
+
+class PriorityQueueWithFunction(PriorityQueue):
+    """
+    Implements a priority queue with the same push/pop signature of the
+    Queue and the Stack classes. This is designed for drop-in replacement for
+    those two classes. The caller has to provide a priority function, which
+    extracts each item's priority.
+    """
+
+    def __init__(self, priorityFunction):
+        "priorityFunction (item) -> priority"
+        self.priorityFunction = priorityFunction      # store the priority function
+        PriorityQueue.__init__(self)        # super-class initializer
+
+    def push(self, item):
+        "Adds an item to the queue with priority from the priority function"
+        PriorityQueue.push(self, item, self.priorityFunction(item))
+
+
+def manhattanDistance(xy1, xy2):
+    "Returns the Manhattan distance between points xy1 and xy2"
+    return abs(xy1[0] - xy2[0]) + abs(xy1[1] - xy2[1])
+
+
+"""
+Data structures and functions useful for various course projects
+
+The search project should not need anything below this line.
+"""
+
+
+class Counter(dict):
+    """
+    A counter keeps track of counts for a set of keys.
+
+    The counter class is an extension of the standard python
+    dictionary type.  It is specialized to have number values
+    (integers or floats), and includes a handful of additional
+    functions to ease the task of counting data.  In particular,
+    all keys are defaulted to have value 0.  Using a dictionary:
+
+    a = {}
+    print a['test']
+
+    would give an error, while the Counter class analogue:
+
+    >>> a = Counter()
+    >>> print a['test']
+    0
+
+    returns the default 0 value. Note that to reference a key
+    that you know is contained in the counter,
+    you can still use the dictionary syntax:
+
+    >>> a = Counter()
+    >>> a['test'] = 2
+    >>> print a['test']
+    2
+
+    This is very useful for counting things without initializing their counts,
+    see for example:
+
+    >>> a['blah'] += 1
+    >>> print a['blah']
+    1
+
+    The counter also includes additional functionality useful in implementing
+    the classifiers for this assignment.  Two counters can be added,
+    subtracted or multiplied together.  See below for details.  They can
+    also be normalized and their total count and arg max can be extracted.
+    """
+
+    def __getitem__(self, idx):
+        self.setdefault(idx, 0)
+        return dict.__getitem__(self, idx)
+
+    def incrementAll(self, keys, count):
+        """
+        Increments all elements of keys by the same count.
+
+        >>> a = Counter()
+        >>> a.incrementAll(['one','two', 'three'], 1)
+        >>> a['one']
+        1
+        >>> a['two']
+        1
+        """
+        for key in keys:
+            self[key] += count
+
+    def argMax(self):
+        """
+        Returns the key with the highest value.
+        """
+        if len(list(self.keys())) == 0:
+            return None
+        all = list(self.items())
+        values = [x[1] for x in all]
+        maxIndex = values.index(max(values))
+        return all[maxIndex][0]
+
+    def sortedKeys(self):
+        """
+        Returns a list of keys sorted by their values.  Keys
+        with the highest values will appear first.
+
+        >>> a = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> a['third'] = 1
+        >>> a.sortedKeys()
+        ['second', 'third', 'first']
+        """
+        sortedItems = list(self.items())
+
+        def compare(x, y): return sign(y[1] - x[1])
+        sortedItems.sort(cmp=compare)
+        return [x[0] for x in sortedItems]
+
+    def totalCount(self):
+        """
+        Returns the sum of counts for all keys.
+        """
+        return sum(self.values())
+
+    def normalize(self):
+        """
+        Edits the counter such that the total count of all
+        keys sums to 1.  The ratio of counts for all keys
+        will remain the same. Note that normalizing an empty
+        Counter will result in an error.
+        """
+        total = float(self.totalCount())
+        if total == 0:
+            return
+        for key in list(self.keys()):
+            self[key] = self[key] / total
+
+    def divideAll(self, divisor):
+        """
+        Divides all counts by divisor
+        """
+        divisor = float(divisor)
+        for key in self:
+            self[key] /= divisor
+
+    def copy(self):
+        """
+        Returns a copy of the counter
+        """
+        return Counter(dict.copy(self))
+
+    def __mul__(self, y):
+        """
+        Multiplying two counters gives the dot product of their vectors where
+        each unique label is a vector element.
+
+        >>> a = Counter()
+        >>> b = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> b['first'] = 3
+        >>> b['second'] = 5
+        >>> a['third'] = 1.5
+        >>> a['fourth'] = 2.5
+        >>> a * b
+        14
+        """
+        sum = 0
+        x = self
+        if len(x) > len(y):
+            x, y = y, x
+        for key in x:
+            if key not in y:
+                continue
+            sum += x[key] * y[key]
+        return sum
+
+    def __radd__(self, y):
+        """
+        Adding another counter to a counter increments the current counter
+        by the values stored in the second counter.
+
+        >>> a = Counter()
+        >>> b = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> b['first'] = 3
+        >>> b['third'] = 1
+        >>> a += b
+        >>> a['first']
+        1
+        """
+        for key, value in list(y.items()):
+            self[key] += value
+
+    def __add__(self, y):
+        """
+        Adding two counters gives a counter with the union of all keys and
+        counts of the second added to counts of the first.
+
+        >>> a = Counter()
+        >>> b = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> b['first'] = 3
+        >>> b['third'] = 1
+        >>> (a + b)['first']
+        1
+        """
+        addend = Counter()
+        for key in self:
+            if key in y:
+                addend[key] = self[key] + y[key]
+            else:
+                addend[key] = self[key]
+        for key in y:
+            if key in self:
+                continue
+            addend[key] = y[key]
+        return addend
+
+    def __sub__(self, y):
+        """
+        Subtracting a counter from another gives a counter with the union of all keys and
+        counts of the second subtracted from counts of the first.
+
+        >>> a = Counter()
+        >>> b = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> b['first'] = 3
+        >>> b['third'] = 1
+        >>> (a - b)['first']
+        -5
+        """
+        addend = Counter()
+        for key in self:
+            if key in y:
+                addend[key] = self[key] - y[key]
+            else:
+                addend[key] = self[key]
+        for key in y:
+            if key in self:
+                continue
+            addend[key] = -1 * y[key]
+        return addend
+
+
+def raiseNotDefined():
+    fileName = inspect.stack()[1][1]
+    line = inspect.stack()[1][2]
+    method = inspect.stack()[1][3]
+
+    print("*** Method not implemented: %s at line %s of %s" %
+          (method, line, fileName))
+    sys.exit(1)
+
+
+def normalize(vectorOrCounter):
+    """
+    Normalize a vector or counter by dividing each value by the sum of all values
+    """
+    normalizedCounter = Counter()
+    if type(vectorOrCounter) == type(normalizedCounter):
+        counter = vectorOrCounter
+        total = float(counter.totalCount())
+        if total == 0:
+            return counter
+        for key in list(counter.keys()):
+            value = counter[key]
+            normalizedCounter[key] = value / total
+        return normalizedCounter
+    else:
+        vector = vectorOrCounter
+        s = float(sum(vector))
+        if s == 0:
+            return vector
+        return [el / s for el in vector]
+
+
+def nSample(distribution, values, n):
+    if sum(distribution) != 1:
+        distribution = normalize(distribution)
+    rand = [random.random() for i in range(n)]
+    rand.sort()
+    samples = []
+    samplePos, distPos, cdf = 0, 0, distribution[0]
+    while samplePos < n:
+        if rand[samplePos] < cdf:
+            samplePos += 1
+            samples.append(values[distPos])
+        else:
+            distPos += 1
+            cdf += distribution[distPos]
+    return samples
+
+
+def sample(distribution, values=None):
+    if type(distribution) == Counter:
+        items = sorted(distribution.items())
+        distribution = [i[1] for i in items]
+        values = [i[0] for i in items]
+    if sum(distribution) != 1:
+        distribution = normalize(distribution)
+    choice = random.random()
+    i, total = 0, distribution[0]
+    while choice > total:
+        i += 1
+        total += distribution[i]
+    return values[i]
+
+
+def sampleFromCounter(ctr):
+    items = sorted(ctr.items())
+    return sample([v for k, v in items], [k for k, v in items])
+
+
+def getProbability(value, distribution, values):
+    """
+    Gives the probability of a value under a discrete distribution
+    defined by (distributions, values).
+    """
+    total = 0.0
+    for prob, val in zip(distribution, values):
+        if val == value:
+            total += prob
+    return total
+
+
+def flipCoin(p):
+    r = random.random()
+    return r < p
+
+
+def chooseFromDistribution(distribution):
+    "Takes either a counter or a list of (prob, key) pairs and samples"
+    if type(distribution) == dict or type(distribution) == Counter:
+        return sample(distribution)
+    r = random.random()
+    base = 0.0
+    for prob, element in distribution:
+        base += prob
+        if r <= base:
+            return element
+
+
+def nearestPoint(pos):
+    """
+    Finds the nearest grid point to a position (discretizes).
+    """
+    (current_row, current_col) = pos
+
+    grid_row = int(current_row + 0.5)
+    grid_col = int(current_col + 0.5)
+    return (grid_row, grid_col)
+
+
+def sign(x):
+    """
+    Returns 1 or -1 depending on the sign of x
+    """
+    if(x >= 0):
+        return 1
+    else:
+        return -1
+
+
+def arrayInvert(array):
+    """
+    Inverts a matrix stored as a list of lists.
+    """
+    result = [[] for i in array]
+    for outer in array:
+        for inner in range(len(outer)):
+            result[inner].append(outer[inner])
+    return result
+
+
+def matrixAsList(matrix, value=True):
+    """
+    Turns a matrix into a list of coordinates matching the specified value
+    """
+    rows, cols = len(matrix), len(matrix[0])
+    cells = []
+    for row in range(rows):
+        for col in range(cols):
+            if matrix[row][col] == value:
+                cells.append((row, col))
+    return cells
+
+
+def lookup(name, namespace):
+    """
+    Get a method or class from any imported module from its name.
+    Usage: lookup(functionName, globals())
+    """
+    dots = name.count('.')
+    if dots > 0:
+        moduleName, objName = '.'.join(
+            name.split('.')[:-1]), name.split('.')[-1]
+        module = __import__(moduleName)
+        return getattr(module, objName)
+    else:
+        modules = [obj for obj in list(namespace.values()) if str(
+            type(obj)) == ""]
+        options = [getattr(module, name)
+                   for module in modules if name in dir(module)]
+        options += [obj[1]
+                    for obj in list(namespace.items()) if obj[0] == name]
+        if len(options) == 1:
+            return options[0]
+        if len(options) > 1:
+            raise Exception('Name conflict for %s')
+        raise Exception('%s not found as a method or class' % name)
+
+
+def pause():
+    """
+    Pauses the output stream awaiting user feedback.
+    """
+    print("")
+    input()
+
+
+# code to handle timeouts
+#
+# FIXME
+# NOTE: TimeoutFuncton is NOT reentrant.  Later timeouts will silently
+# disable earlier timeouts.  Could be solved by maintaining a global list
+# of active time outs.  Currently, questions which have test cases calling
+# this have all student code so wrapped.
+#
+import signal
+import time
+
+
+class TimeoutFunctionException(Exception):
+    """Exception to raise on a timeout"""
+    pass
+
+
+class TimeoutFunction:
+    def __init__(self, function, timeout):
+        self.timeout = timeout
+        self.function = function
+
+    def handle_timeout(self, signum, frame):
+        raise TimeoutFunctionException()
+
+    def __call__(self, *args, **keyArgs):
+        # If we have SIGALRM signal, use it to cause an exception if and
+        # when this function runs too long.  Otherwise check the time taken
+        # after the method has returned, and throw an exception then.
+        if hasattr(signal, 'SIGALRM'):
+            old = signal.signal(signal.SIGALRM, self.handle_timeout)
+            signal.alarm(self.timeout)
+            try:
+                result = self.function(*args, **keyArgs)
+            finally:
+                signal.signal(signal.SIGALRM, old)
+            signal.alarm(0)
+        else:
+            startTime = time.time()
+            result = self.function(*args, **keyArgs)
+            timeElapsed = time.time() - startTime
+            if timeElapsed >= self.timeout:
+                self.handle_timeout(None, None)
+        return result
+
+
+_ORIGINAL_STDOUT = None
+_ORIGINAL_STDERR = None
+_MUTED = False
+
+
+class WritableNull:
+    def write(self, string):
+        pass
+
+
+def mutePrint():
+    global _ORIGINAL_STDOUT, _ORIGINAL_STDERR, _MUTED
+    if _MUTED:
+        return
+    _MUTED = True
+
+    _ORIGINAL_STDOUT = sys.stdout
+    #_ORIGINAL_STDERR = sys.stderr
+    sys.stdout = WritableNull()
+    #sys.stderr = WritableNull()
+
+
+def unmutePrint():
+    global _ORIGINAL_STDOUT, _ORIGINAL_STDERR, _MUTED
+    if not _MUTED:
+        return
+    _MUTED = False
+
+    sys.stdout = _ORIGINAL_STDOUT
+    #sys.stderr = _ORIGINAL_STDERR