20240418

2024-04-18 18:38:55 +08:00
parent bfcbb1996a
commit 4f8f929242
20 changed files with 3408 additions and 0 deletions
--- a/ACMOJ-2148.cpp
+++ b/ACMOJ-2148.cpp
@ -0,0 +1,107 @@
+#include <cstdio>
+#include <cstring>
+#include <iostream>
+using namespace std;
+typedef long long LL;
+typedef long double LDB;
+const int kMaxN = 1e5 + 10;
+int N, S;
+LDB A[kMaxN], B[kMaxN], R[kMaxN];
+struct NodeType {
+  int rawid;
+  LDB a, b, r, f;
+};
+NodeType nodes[kMaxN];
+inline LDB GetX(const NodeType &node) {
+  return node.f * node.r / (node.a * node.r + node.b);
+}
+inline LDB GetY(const NodeType &node) {
+  return node.f / (node.a * node.r + node.b);
+}
+bool CmpX(const NodeType &na, const NodeType &nb) {
+  return GetX(na) < GetX(nb);
+}
+bool CmpId(const NodeType &na, const NodeType &nb) {
+  return na.rawid < nb.rawid;
+}
+bool CmpK(const NodeType &na, const NodeType &nb) {
+  return -na.a / na.b > -nb.a / nb.b;
+}
+int Q[kMaxN], QL, QR;
+typedef bool (*CmpType)(const NodeType &, const NodeType &);
+void MergeSort(NodeType *beg, NodeType *end, CmpType cmp) {
+  if (end - beg <= 1) return;
+  size_t len = end - beg;
+  NodeType *mid = beg + (len >> 1);
+  MergeSort(beg, mid, cmp);
+  MergeSort(mid, end, cmp);
+  NodeType *tmp = new NodeType[len];
+  NodeType *cur_tmp = tmp, *cur_L = beg, *cur_R = mid;
+  while ((cur_L < mid) && (cur_R < end)) {
+    if (cmp(*cur_L, *cur_R))
+      *(cur_tmp++) = *(cur_L++);
+    else
+      *(cur_tmp++) = *(cur_R++);
+  }
+  while (cur_L < mid) *(cur_tmp++) = *(cur_L++);
+  while (cur_R < end) *(cur_tmp++) = *(cur_R++);
+  cur_tmp = tmp;
+  NodeType *cur_dst = beg;
+  while (cur_dst < end) *(cur_dst++) = *(cur_tmp++);
+  delete[] tmp;
+}
+void CDQ(int L, int R) {
+  if (L == R) return;
+  int M = (L + R) >> 1;
+  CDQ(L, M);
+  MergeSort(nodes + L, nodes + M + 1, CmpX);
+  MergeSort(nodes + M + 1, nodes + R + 1, CmpK);
+  Q[QL = QR = 0] = L;
+  for (int i = L + 1; i <= M; i++) {
+    while (QR - QL + 1 >= 2 &&
+           (GetX(nodes[Q[QR]]) - GetX(nodes[Q[QR - 1]])) *
+                       (GetY(nodes[i]) - GetY(nodes[Q[QR - 1]])) -
+                   (GetY(nodes[Q[QR]]) - GetY(nodes[Q[QR - 1]])) *
+                       (GetX(nodes[i]) - GetX(nodes[Q[QR - 1]])) >=
+               0)
+      QR--;
+    Q[++QR] = i;
+  }
+  LDB base = 0;
+  for (int i = L; i <= M; i++) base = max(base, nodes[i].f);
+  for (int i = M + 1; i <= R; i++) {
+    while (QR - QL + 1 >= 2 &&
+           (GetY(nodes[Q[QL + 1]]) - GetY(nodes[Q[QL]])) /
+                   (GetX(nodes[Q[QL + 1]]) - GetX(nodes[Q[QL]])) >=
+               -nodes[i].a / nodes[i].b)
+      QL++;
+    nodes[i].f = max(nodes[i].f, base);
+    nodes[i].f = max(nodes[i].f, nodes[i].a * GetX(nodes[Q[QL]]) +
+                                     nodes[i].b * GetY(nodes[Q[QL]]));
+  }
+  MergeSort(nodes + M + 1, nodes + R + 1, CmpId);
+  CDQ(M + 1, R);
+}
+int main() {
+#ifdef local
+  freopen("pro.in", "r", stdin);
+#endif
+  scanf("%d%d", &N, &S);
+  for (int i = 1; i <= N; i++) {
+    scanf("%Lf%Lf%Lf", &A[i], &B[i], &R[i]);
+    nodes[i].rawid = i;
+    nodes[i].a = A[i];
+    nodes[i].b = B[i];
+    nodes[i].r = R[i];
+  }
+  nodes[1].f = S;
+  CDQ(1, N);
+  // for (int i = 1; i <= N; i++)
+  // printf("f(%d)=%.3Lf\n", nodes[i].rawid, nodes[i].f);
+  for (int i = 1; i <= N; i++)
+    if (nodes[i].rawid == N) {
+      printf("%.3Lf\n", nodes[i].f);
+      return 0;
+    }
+  return 0;
+}