HDU 3549 Flow Problem(最大流)

最新推荐文章于 2021-02-02 23:55:16 发布

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Problem Description

Network flow is a well-known difficult problem for ACMers. Given a graph, your task is to find out the maximum flow for the weighted directed graph.

Input

The first line of input contains an integer T, denoting the number of test cases.
For each test case, the first line contains two integers N and M, denoting the number of vertexes and edges in the graph. (2 <= N <= 15, 0 <= M <= 1000)
Next M lines, each line contains three integers X, Y and C, there is an edge from X to Y and the capacity of it is C. (1 <= X, Y <= N, 1 <= C <= 1000)

Output

For each test cases, you should output the maximum flow from source 1 to sink N.

Sample Input

3 2

1 2 1

2 3 1

3 3

1 2 1

2 3 1

1 3 1

Sample Output

Case 1: 1

Case 2: 2

最大流模板题。


#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <queue>
using namespace std;
const int MAXN = 20;
const int INF = 0x3f3f3f3f;
int pre[MAXN];
bool vis[MAXN];
int mp[MAXN][MAXN];
int s, e;
int n, m;
bool bfs() {
    queue<int>q;
    memset(pre, 0, sizeof(pre));
    memset(vis, 0, sizeof(vis));
    vis[s] = 1;
    q.push(s);
    while(!q.empty()) {
        int first = q.front();
        q.pop();
        if(first == e) {
            return true;
        }
        for(int i = 1; i <= n; i++) {
            if(!vis[i] && mp[first][i]) {
                q.push(i);
                pre[i] = first;
                vis[i] = 1;
            }
        }
    }
    return false;
}
int max_flow() {
    int ans = 0;
    while(true) {
        if(!bfs()) {
            return ans;
        }
        int Min = INF;
        for(int i = e; i != s; i = pre[i]) {
            Min = min(Min, mp[pre[i]][i]);
        }
        for(int i = e; i != s; i = pre[i]) {
            mp[pre[i]][i] -= Min;
            mp[i][pre[i]] += Min;
        }
        ans += Min;
    }
    return ans;
}
int main() {
    int t;
    scanf("%d", &t);
    int u, v, c;
    for(int i = 1; i <= t; i++) {
        scanf("%d %d", &n, &m);
        s = 1, e = n;
        memset(mp, 0, sizeof(mp));
        while(m--) {
            scanf("%d %d %d", &u, &v, &c);
            mp[u][v] += c;
        }
        printf("Case %d: %d\n", i, max_flow());
    }
    return 0;
}