[全局最小割][Stoer-Wagner 算法] 无向图最小割

带有图片例子的 [BLOG]

复杂度是$(n ^ 3)$

HDU3691

// #pragma GCC optimize(2)
// #pragma GCC optimize(3)
// #pragma GCC optimize(4)
#include <algorithm>
#include <iterator>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <iomanip>
#include <bitset>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <stack>
#include <cmath>
#include <queue>
#include <list>
#include <map>
#include <set>
#include <cassert>
//#include <unordered_set>
//#include <unordered_map>
// #include<bits/extc++.h>
// using namespace __gnu_pbds;
using namespace std;
#define pb push_back
#define fi first
#define se second
#define debug(x) cerr << #x << " := " << x << endl;
#define bug cerr << "-----------------------" << endl;
#define FOR(a, b, c) for (int a = b; a <= c; ++a)

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int inf = 0x3f3f3f3f;
const ll inff = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;

template <typename T>
inline T read(T &x) {
    x = 0;
    int f = 0;
    char ch = getchar();
    while (ch < '0' || ch > '9') f |= (ch == '-'), ch = getchar();
    while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
    return x = f ? -x : x;
}

/**********showtime************/
const int maxn = 502;
int mp[maxn][maxn], dis[maxn];
int vis[maxn], bin[maxn];
int n;
int concate(int &s, int &t) {
    memset(dis, 0, sizeof(dis));
    memset(vis, 0, sizeof(vis));

    int k, maxc, mincut = 0;
    for (int i = 1; i <= n; i++) {
        k = -1, maxc = -1;
        for (int j = 1; j <= n; j++) {
            if (bin[j] == 0 && vis[j] == 0 && dis[j] > maxc) {
                k = j;
                maxc = dis[j];
            }
        }
        if (k == -1) return mincut;
        s = t;
        t = k;
        mincut = maxc;
        vis[k] = 1;
        for (int j = 1; j <= n; j++) {
            if (vis[j] == 0 && bin[j] == 0) {
                dis[j] = dis[j] + mp[k][j];
            }
        }
    }
    return mincut;
}

int sw() {
    int mincut = inf, s, t;
    for (int i = 1; i < n; i++) {
        int ans = concate(s, t);
        mincut = min(mincut, ans);
        bin[t] = 1;
        if (mincut == 0) return mincut;
        for (int j = 1; j <= n; j++) {
            if (bin[j] == 0) {
                mp[s][j] = mp[s][j] + mp[t][j];
                mp[j][s] = mp[s][j];
            }
        }
    }
    return mincut;
}
int main() {
    int m, s;
    while (~scanf("%d%d%d", &n, &m, &s) && n + m + s) {
        for (int i = 1; i <= n; i++) {
            bin[i] = 0;
            for (int j = 1; j <= n; j++) {
                mp[i][j] = 0;
            }
        }
        for (int i = 1; i <= m; i++) {
            int u, v, w;
            scanf("%d%d%d", &u, &v, &w);
            mp[u][v] = mp[u][v] + w;
            mp[v][u] = mp[u][v];
        }
        printf("%d\n", sw());
    }

    return 0;
}