[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
", sw());
            }

            return 0;
}

HDU 3691