ACWing 380 舞动的夜晚( 二分图的可行边与必经边 )

二分图最大匹配的可行边与必经边。

#include 
using namespace std;
typedef long long LL;
typedef int lint;
const lint maxn = 50005;
const lint maxm = 5000000 + 5;
int n,m,tot;
int he[maxn],ne[maxm],ver[maxm],id[maxm];
void Add( int x,int y,int _id ){
    ver[++tot] = y;
    ne[tot] = he[x];
    he[x] = tot;
    id[tot] = _id;
}
struct dinic{
    static const int N = 5000005;
    static const int M = 10000005;
    static const lint inf = 0x3f3f3f3f;
    int he[N],ne[M],ver[M],d[N],id[M];
    lint edge[M];
    int s,t,tot;
    queue que;
    void init( int n ){
        for( int i = 0;i <= n;i++ ){
            he[i] = 0;
        }
        tot = 1;
    }
    void add( int x,int y,lint z,int _id ){
        ver[++tot] = y; ne[ tot ] = he[x]; he[x] = tot; edge[ tot ] = z;id[tot] = _id;
        ver[++tot] = x; ne[tot] = he[y]; he[y] = tot;edge[tot] = 0;id[tot] = _id;
    }
    bool bfs(){
        memset( d,0,sizeof( d ) );
        while( que.size() ) que.pop();
        que.push( s );
        d[s] = 1;
        while( que.size() ){
            int x = que.front();
            que.pop();
            for( int cure = he[x];cure;cure = ne[cure] ){
                int y = ver[cure];
                if( edge[cure] && !d[y] ){
                    que.push( y );
                    d[ y ] = d[x] + 1;
                    if( y == t ) return 1;
                }
            }
        }
        return 0;
    }
    lint dfs( int x,lint flow ){
        if( x== t ) return flow;
        lint rest = flow,k;
        for( int cure = he[x];cure && rest;cure = ne[cure] ){
            int y = ver[cure];
            if( edge[cure] && d[ y ] == d[x] + 1 ){
                k = dfs( y,min( rest,edge[cure] ) );
                if( !k ) d[ y ] = 0;
                edge[cure] -= k;
                edge[ cure^1 ] += k;
                rest -= k;
            }
        }
        return flow - rest;
    }
    lint max_flow( int x,int y ){
        s = x; t = y;
        lint maxflow = 0;
        lint flow = 0;
        while( bfs() )
            while( flow = dfs( s,inf ) ) maxflow += flow;
        return maxflow;
    }
    void solve( int S,int T ){
        for( int i = S;i <= T;i++ ){
            for( int cure=he[i];cure;cure= ne[cure] ){
                int y = ver[cure];
                if( !edge[cure]  ) continue;
                Add( i,y,id[cure] );
            }
        }
    }
} g;
int st[maxn],ins[maxn],c[maxn],dfn[maxn],low[maxn];
int num,top,cnt;
void tarjan( int x ){
    dfn[x] = low[x] = ++num;
    st[++top] = x;ins[x] = 1;
    for( int cure=  he[x];cure;cure=ne[cure] ){
        int y= ver[cure];
        if(!dfn[y]){
            tarjan(y);
            low[x] = min( low[x],low[y] );
        }else if(ins[y])
            low[x] = min( low[x],dfn[y] );
    }
    if( dfn[x]==low[x] ){
        cnt++;int y;
        do{
            y = st[top--];ins[y]=0;
            c[y] =cnt;
        }while(x!=y);
    }
}
vector ans;
int main(){
    int t;
    scanf("%d%d%d",&n,&m,&t);
    int S = 0,T = n+m+1;
    g.init(T);
    for( int i = 1;i <= n;i++ ){
        g.add( S,i,1,0 );
    }
    for( int i = 1;i <= m;i++ ){
        g.add( i+n,T,1,0 );
    }
    for( int x,y,i = 1;i <= t;i++ ){
        scanf("%d%d",&x,&y);
        g.add( x,y+n,1,i );
    }
    g.max_flow(S,T);
    g.solve(S,T);
    for( int i = 0;i <= n+m+1;i++ ){
        if(!dfn[i]) tarjan(i);
    }
    for( int x =1;x <= n;x++ ){
        for( int cure = he[x];cure;cure= ne[cure] ){
            int y = ver[cure];
            if( y == S ) continue;
            int _id = id[cure];
            if( c[x]!=c[y] ) ans.push_back(_id);
        }
    }
    sort( ans.begin(),ans.end() );
    printf("%d\n",ans.size());
    if( ans.size() ) {
        printf("%d", ans[0]);
        for (int i = 1; i < ans.size(); i++) {
            printf(" %d", ans[i]);
        }
    }
    puts("");
    return 0;
}