No.26 - POJ1815 最小割点

网络流求最小割点，每个点分裂为入点和出点，边权为1

注：S，T分裂为边权为INF的两个点
出点到其它入点边权为INF

// ShellDawn
// POJ1815
// No.26

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<queue>
#define MM(x,y) memset(x,y,sizeof(x))
#define INF 0x3f3f3f3f
using namespace std;

#define maxn 205
int N,S,T;
int G[maxn][maxn];
struct Edge{
    int to;
    int v;
    int rvs;
    int pre;
};
Edge E[maxn*maxn*4];
int pre[maxn*2];
int cnt = 1;
int V[maxn*2];

void addE(int from,int to,int v,int rvs){
    E[cnt].to = to;
    E[cnt].v = v;
    E[cnt].rvs = rvs;
    E[cnt].pre = pre[from];
    pre[from] = cnt++;
}

void build(){
    MM(pre,0);
    cnt = 1;
    for(int i=1;i<=N;i++){
        if(G[i][i] > 0){
            if(i == S || i == T){
                int t = cnt;
                addE(i,i+N,INF,t+1);
                addE(i+N,i,0,t);
            }else{
                int t = cnt;
                addE(i,i+N,1,t+1);
                addE(i+N,i,0,t);
            }
        }
    }
    for(int i=1;i<=N;i++){
        if(G[i][i] == 0) continue;
        for(int j=1;j<=N;j++){
            if( i == j || G[i][j] == 0 || G[j][j] == 0) continue;
            int t = cnt;
            addE(i+N,j,INF,t+1);
            addE(j,i+N,0,t);
        }
    }
}

void printE(){
    for(int i=1;i<=N*2;i++){
        printf("ID:%d ",i);
        for(int j=pre[i];j!=0;j=E[j].pre){
            printf("->%d (%d) ",E[j].to,E[j].v);
        }
        puts("");
    }
}

bool BFS(int s){
    MM(V,0);
    V[s] = 1;
    queue<int> q;
    q.push(s);
    while(!q.empty()){
        int now = q.front();
        q.pop();
        for(int i=pre[now];i!=0;i=E[i].pre){
            if(E[i].v > 0 && V[E[i].to] == 0){
                V[E[i].to] = V[now] + 1;
                q.push(E[i].to);
            }
        }
    }
    if(V[T+N] > 0) return true;
    return false;
}

int DFS(int now,int minflow){
    if(now == T+N) return minflow;
    int flow = 0;
    for(int i=pre[now]; i!=0 && minflow ; i=E[i].pre){
        if(E[i].v > 0 && V[E[i].to] == V[now] + 1){
            int f = DFS(E[i].to,min(minflow,E[i].v));
            flow += f;
            minflow -= f;
            E[i].v -= f;
            E[E[i].rvs].v += f;
        }
    }
    if(flow == 0) V[now] = 0;
    return flow;
}

int main(){
    //freopen("A.txt","r",stdin);
    scanf("%d%d%d",&N,&S,&T);
    for(int i=1;i<=N;i++){
        for(int j=1;j<=N;j++){
            scanf("%d",&G[i][j]);
        }
    }
    if(G[S][T] > 0){puts("NO ANSWER!");return 0;}
    build();
    //printE();
    int maxflow = 0;
    while(BFS(S)) maxflow += DFS(S,INF);
    printf("%d\n",maxflow);
    queue<int> q;
    for(int i=1;i<=N && maxflow;i++){
        if(i == S || i == T) continue;
        G[i][i] = 0;
        build();
        int flow = 0;
        while(BFS(S)) flow+=DFS(S,INF);
        if(flow < maxflow){
            q.push(i);
            maxflow -- ;
        }else G[i][i] = 1;
    }
    while(!q.empty()){
        printf("%d",q.front());
        q.pop();
        if(q.empty()) puts("");
        else printf(" ");
    }
    return 0;
}