ACM/ICPC 之 Dinic+枚举最小割点集(可做模板)(POJ1815)

 　　　最小割的好题，可用作模板。

 

//Dinic+枚举字典序最小的最小割点集
//Time:1032Ms   Memory:1492K
#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
using namespace std;

#define MAXN 205
#define INF 0x3f3f3f3f

int N, S, T;
int s,t;
int sres[2*MAXN][2*MAXN];   //source-res
int res[2*MAXN][2*MAXN];
int d[2*MAXN];
int cut[MAXN];  //最小割点集
bool v[2*MAXN];

bool bfs()
{
    memset(d, -1, sizeof(d));
    queue<int> q;
    q.push(s);  d[s] = 0;
    while(!q.empty() && d[t] == -1){
        int cur = q.front();    q.pop();
        for(int i = 1; i <= t; i++)
        {
            if(d[i] == -1 && res[cur][i])
            {
                d[i] = d[cur] + 1;
                q.push(i);
            }
        }
    }
    return d[t] != -1;
}

int dfs(int x, int sum)
{
    if(x == t || sum == 0)  return sum;
    int src = sum;
    for(int i = 1; i <= t; i++)
    {
        if(d[i] == d[x] + 1 && res[x][i])
        {
            int tmp = dfs(i, min(sum, res[x][i]));
            res[x][i] -= tmp;
            res[i][x] += tmp;
            sum -= tmp;
        }
    }
    return src - sum;
}

int Dinic()
{
    memcpy(res, sres, sizeof(sres));
    int maxFlow = 0;
    while(bfs())
        maxFlow += dfs(s,INF);
    return maxFlow;
}

int main()
{
    //freopen("in.txt", "r", stdin);

    while(~scanf("%d%d%d", &N,&S,&T))
    {
        memset(sres, 0 ,sizeof(sres));
        s = 0;  t = 2*N+1;
        sres[0][S] = sres[T+N][t] = INF;
        for(int i = 1; i <= N; i++)
        {
            sres[i][i + N] = 1;
            for(int j = 1; j <= N; j++)
            {
                int num;
                scanf("%d", &num);
                if(num && i != j) sres[i+N][j] = INF;
            }
        }
        sres[S][S+N] = sres[T][T+N] = INF;
        int ans = Dinic();
        if(ans == INF){ //不可分开
            printf("NO ANSWER!\n");
            continue;
        }
        else {
            printf("%d\n", ans);
            if(ans == 0) continue;  //已经分开
        }

        //枚举最小割点集
        int len = 0, tmp = ans;
        for(int i = 1; i <= N && tmp; i++)
        {
            if(i == S || i == T)   continue;
            if(res[i][i+N])    continue;
            sres[i][i+N] = 0;
            int k = Dinic();
            if(k != tmp){
                tmp = k;
                cut[len++] = i;
            }
            else sres[i][i+N] = 1;
        }
        for(int i = 0; i < ans - 1; i++)
            printf("%d ", cut[i]);
        printf("%d\n", cut[ans-1]);
    }

    return 0;
}