题意:Freda控制着N座可以发射导弹的防御塔。每座塔都有足够数量的导弹,但是每座塔每次只能发射一枚。在发射导弹时,导弹需要T1秒才能从防御塔中射出,而在发射导弹后,发射这枚导弹的防御塔需要T2分钟来冷却。所有导弹都有相同的匀速飞行速度V,并且会沿着距离最短的路径去打击目标。计算防御塔到目标的距离Distance时,你只需要计算水平距离,而忽略导弹飞行的高度。导弹在空中飞行的时间就是 (Distance/V) 分钟,导弹到达目标后可以立即将它击毁。现在,给出N座导弹防御塔的坐标,M个入侵者的坐标,T1、T2和V,你需要求出至少要多少分钟才能击退所有的入侵者。
分析:抽象成导弹与入侵者的匹配问题,详见《算法竞赛进阶指南》P423。
代码:
#include <cmath>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#define pii pair<int, int>
#define x first
#define y second
using namespace std;
const int N = 56, M = 2506;
const double eps = 1e-8;
int n, m, t, t2, V, f[M];
double t1;
bool v[M];
pii a[N], b[N];
pair<int, double> c[M];
vector<int> e[N];inline double S(pii a, pii b) {int dx = a.x - b.x, dy = a.y - b.y;return sqrt(dx * dx + dy * dy);
}bool dfs(int x) {for (unsigned int i = 0; i < e[x].size(); i++) {int y = e[x][i];if (v[y]) continue;v[y] = 1;if (!f[y] || dfs(f[y])) {f[y] = x;return 1;}}return 0;
}inline bool pd(double mid) {memset(f, 0, sizeof(f));for (int i = 1; i <= m; i++) {e[i].clear();for (int j = 1; j <= t; j++)if (c[j].y + S(a[i], b[c[j].x]) / V <= mid)e[i].push_back(j);}for (int i = 1; i <= m; i++) {memset(v, 0, sizeof(v));if (!dfs(i)) return 0;}return 1;
}int main() {cin >> n >> m >> t1 >> t2 >> V;t = n * m;t1 /= 60;for (int i = 1; i <= m; i++)scanf("%d %d", &a[i].x, &a[i].y);for (int i = 1; i <= n; i++)scanf("%d %d", &b[i].x, &b[i].y);for (int i = 1; i <= m; i++)for (int j = 1; j <= n; j++) {int k = (i - 1) * n + j;c[k].x = j;c[k].y = (i - 1) * (t1 + t2) + t1;}double l = t1, r = 100000;while (l + eps < r) {double mid = (l + r) / 2;if (pd(mid)) r = mid;else l = mid;}printf("%.6f\n", l);return 0;
}