From bd221efd212c4b2d78ffef321eca11fe216cae46 Mon Sep 17 00:00:00 2001 From: zsq259 <2530059525@qq.com> Date: Tue, 25 Jun 2024 09:59:02 +0800 Subject: [PATCH] fix: a* in docs --- docs/A*.md | 29 ++++++------------ docs/minmax.md | 18 ++++++++--- multiagent/__pycache__/game.cpython-312.pyc | Bin 0 -> 34624 bytes .../__pycache__/ghostAgents.cpython-312.pyc | Bin 0 -> 4266 bytes .../graphicsDisplay.cpython-312.pyc | Bin 0 -> 38395 bytes .../__pycache__/graphicsUtils.cpython-312.pyc | Bin 0 -> 16353 bytes .../keyboardAgents.cpython-312.pyc | Bin 0 -> 3915 bytes multiagent/__pycache__/layout.cpython-312.pyc | Bin 0 -> 9691 bytes .../__pycache__/multiAgents.cpython-312.pyc | Bin 0 -> 7492 bytes multiagent/__pycache__/pacman.cpython-312.pyc | Bin 0 -> 35144 bytes .../__pycache__/pacmanAgents.cpython-312.pyc | Bin 0 -> 2990 bytes .../__pycache__/textDisplay.cpython-312.pyc | Bin 0 -> 3834 bytes multiagent/__pycache__/util.cpython-312.pyc | Bin 0 -> 29134 bytes 13 files changed, 24 insertions(+), 23 deletions(-) create mode 100644 multiagent/__pycache__/game.cpython-312.pyc create mode 100644 multiagent/__pycache__/ghostAgents.cpython-312.pyc create mode 100644 multiagent/__pycache__/graphicsDisplay.cpython-312.pyc create mode 100644 multiagent/__pycache__/graphicsUtils.cpython-312.pyc create mode 100644 multiagent/__pycache__/keyboardAgents.cpython-312.pyc create mode 100644 multiagent/__pycache__/layout.cpython-312.pyc create mode 100644 multiagent/__pycache__/multiAgents.cpython-312.pyc create mode 100644 multiagent/__pycache__/pacman.cpython-312.pyc create mode 100644 multiagent/__pycache__/pacmanAgents.cpython-312.pyc create mode 100644 multiagent/__pycache__/textDisplay.cpython-312.pyc create mode 100644 multiagent/__pycache__/util.cpython-312.pyc diff --git a/docs/A*.md b/docs/A*.md index e8b8f75..f7040e3 100644 --- a/docs/A*.md +++ b/docs/A*.md @@ -14,27 +14,27 @@ 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。 + - 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:\(h(n) \leq c(n, m) + h(m)\)。 + - 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:\(h(n) = |x_1 - x_2| + |y_1 - y_2|\)。 + - 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:\(h(n) = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)。 + - 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 @@ -48,15 +48,14 @@ A*搜索是一种图搜索算法,它结合了Dijkstra算法和贪婪最佳优 - 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 @@ -67,26 +66,18 @@ function A*(start, goal) while openSet is not empty current := node in openSet with lowest fScore[current] if current == goal - return reconstruct_path(cameFrom, current) + return success openSet.remove(current) for each neighbor of current tentative_gScore := gScore[current] + d(current, neighbor) - if tentative_gScore < gScore[neighbor] - cameFrom[neighbor] := current + if tentative_gScore < gScore[neighbor] 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 diff --git a/docs/minmax.md b/docs/minmax.md index e3105c8..2e80eaf 100644 --- a/docs/minmax.md +++ b/docs/minmax.md @@ -43,7 +43,7 @@ Minimax 是一种用于两人对弈游戏的决策算法,如国际象棋、井 ``` X | O | X X | O | X X | O | X ----------- ----------- ----------- - O | X | X O | X | O | X | + O | X | X O | X | O | X | ----------- ----------- ----------- | | O X | | O X | | O ``` @@ -58,7 +58,7 @@ Minimax 是一种用于两人对弈游戏的决策算法,如国际象棋、井 ``` X | O | X X | O | X X | O | X ----------- ----------- ----------- - O | X | X O | X | O | X | + O | X | X O | X | O | X | ----------- ----------- ----------- | | O X | | O X | | O @@ -107,6 +107,16 @@ function minimax(node, depth, maximizingPlayer) 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。 +### Alpha-Beta 剪枝的基本思想 + +Alpha-Beta 剪枝的主要思想是:在某些情况下,可以提前停止对某些节点的评估,因为这些节点不会影响最终的决策。 + +- **Alpha 值**:当前节点在最大化玩家层面上可以得到的最高分数。 +- **Beta 值**:当前节点在最小化玩家层面上可以得到的最低分数。 + +如果在搜索过程中发现一个节点的评估值无法改进当前的 Alpha 或 Beta 值,就可以停止对该节点的进一步搜索。 + + ### 带 Alpha-Beta 剪枝的伪代码 ```pseudo @@ -120,7 +130,7 @@ function alphabeta(node, depth, α, β, maximizingPlayer) eval = alphabeta(child, depth - 1, α, β, false) maxEval = max(maxEval, eval) α = max(α, eval) - if β <= α + if β < α break return maxEval else @@ -129,7 +139,7 @@ function alphabeta(node, depth, α, β, maximizingPlayer) eval = alphabeta(child, depth - 1, α, β, true) minEval = min(minEval, eval) β = min(β, eval) - if β <= α + if β < α break return minEval ``` diff --git a/multiagent/__pycache__/game.cpython-312.pyc b/multiagent/__pycache__/game.cpython-312.pyc new file mode 100644 index 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