POJ 2914 Minimum Cut 全局最小割

求无向图的最小割

刷UOJ用户群的时候看到有人问一道全局最小割的裸题。。忽然想起之前还坑着Stoer Wagner算法。。

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
#define FOR(i,j,k) for(i=j;i<=k;++i)
const int N = 501;
int vis[N], dis[N], v[N], a[N][N];
int stoer_wagner(int n) {
    int i, j, ans = 0x7fffffff, p, last;
    FOR(i,1,n) v[i] = i;
    while (n > 1) {
        p = last = 0;
        FOR(i,2,n) {
            dis[v[i]] = a[v[1]][v[i]];
            if (dis[v[i]] > dis[v[p]]) p = i;
        }
        FOR(i,2,n) vis[v[i]] = 0;
        vis[v[1]] = 1;
        FOR(i,2,n) {
            if (i == n) {
                ans = min(ans, dis[v[p]]);
                FOR(j,1,n) a[v[j]][v[last]] = a[v[last]][v[j]] += a[v[j]][v[p]];
                v[p] = v[n--];
            }
            vis[v[last = p]] = 1; p = -1;
            FOR(j,2,n) if (!vis[v[j]]) {
                dis[v[j]] += a[v[last]][v[j]];
                if (p == -1 || dis[v[p]] < dis[v[j]])
                    p = j;
            }
        }
    }
    return ans;
}

int main() {
    int n, m, u, v, w;
    while (scanf("%d%d", &n, &m) != EOF) {
        memset(a, 0, sizeof a);
        while (m--) {
            scanf("%d%d%d", &u, &v, &w);
            ++u; ++v;
            a[u][v] += w; a[v][u] += w;
        }
        printf("%d\n", stoer_wagner(n));
    }
    return 0;
}

Minimum Cut

Time Limit: 10000MS Memory Limit: 65536K
Total Submissions: 8588 Accepted: 3617
Case Time Limit: 5000MS

Description

Given an undirected graph, in which two vertices can be connected by multiple edges, what is the size of the minimum cut of the graph? i.e. how many edges must be removed at least to disconnect the graph into two subgraphs?

Input

Input contains multiple test cases. Each test case starts with two integers N and M (2 ≤ N ≤ 500, 0 ≤ M ≤ N × (N − 1) ⁄ 2) in one line, where N is the number of vertices. Following are M lines, each line contains M integers A, B and C (0 ≤ A, B < N, A ≠ B, C > 0), meaning that there C edges connecting vertices A and B.

Output

There is only one line for each test case, which contains the size of the minimum cut of the graph. If the graph is disconnected, print 0.

Sample Input

3 3
0 1 1
1 2 1
2 0 1
4 3
0 1 1
1 2 1
2 3 1
8 14
0 1 1
0 2 1
0 3 1
1 2 1
1 3 1
2 3 1
4 5 1
4 6 1
4 7 1
5 6 1
5 7 1
6 7 1
4 0 1
7 3 1

Sample Output

2
1
2