解题思路:
AC代码:
// Test1.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。
//
//二分答案 + 二分图多重匹配
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <set>
#include <vector>
#include <queue>
#include <stack>
using namespace std;
const int maxn = 510;
int K, C, M, mmax;
int dis[maxn][maxn], graph[maxn][maxn], match[maxn][maxn], vis[maxn];
void Floyd() {
for (int k = 1; k <= K + C; k++)
for (int i = 1; i <= K + C; i++)
for (int j = 1; j <= K + C; j++)
if (i != j && dis[i][j] > dis[i][k] + dis[k][j])
dis[i][j] = dis[i][k] + dis[k][j];
for (int i = 1; i <= K + C; i++)
for (int j = 1; j <= K + C; j++)
mmax = max(dis[i][j], mmax);
}
void Init() {
memset(dis, 0x3f, sizeof(dis));
int x;
for (int i = 1; i <= K + C; i++)
for (int j = 1; j <= K + C; j++) {
cin >> x;
if (x) dis[i][j] = x;
}
Floyd();
}
void Build_graph(int mid) {
for (int i = K + 1; i <= K + C; i++)
for (int j = 1; j <= K; j++)
if (dis[i][j] <= mid) graph[i][j] = 1;
else graph[i][j] = 0;
}
bool dfs(int x, int mid) {
for (int i = 1; i <= K; i++) {
if (graph[x][i] && !vis[i]) {
vis[i] = 1;
if (match[i][0] < M) {
match[i][++match[i][0]] = x;
return true;
}
for (int j = 1; j <= match[i][0]; j++)
if (dfs(match[i][j], mid)) {
match[i][j] = x;
return true;
}
}
}
return false;
}
int Maxmatch(int mid) {
int sum = 0;
memset(match, 0, sizeof(match));
for (int i = K + 1; i <= K + C; i++) {
memset(vis, 0, sizeof(vis));
if (dfs(i, mid)) sum++;
}
return sum;
}
int main() {
cin >> K >> C >> M;
Init();
int lef = 1, rig = mmax, mid = (lef + rig) >> 1, ans;
while (lef <= rig) {
Build_graph(mid);
if (Maxmatch(mid) == C) rig = mid - 1, ans = mid;
else lef = mid + 1;
mid = (lef + rig) >> 1;
}
cout << ans << endl;
return 0;
}
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