BZOJ 3546 [ONTAK2010]Life of the Party （二分图最大匹配必须点）

#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
using namespace std;
const int N=20000+10;
const int M=200000+100;
const int INF=0x3f3f3f3f;
int n1,n2,m,s,t,id[M<<1];
struct edge{
    int nxt,to,cap;
}edges[M<<1];
int cnt=1,x[M],y[M],head[N],cur[N];

int add_edge(int x,int y,int z) {
    edges[++cnt].nxt=head[x]; edges[cnt].to=y; edges[cnt].cap=z; head[x]=cnt;
    return cnt;
}

int dep[N]; 
queue<int> q;
bool bfs() {
    while (!q.empty()) q.pop();
    memset(dep,0,sizeof(dep));
    dep[s]=1; q.push(s);
    while (!q.empty()) {
        int x=q.front(); q.pop();
        for (int i=head[x];i;i=edges[i].nxt) {
            edge e=edges[i];
            if (!dep[e.to] && e.cap) {
                dep[e.to]=dep[x]+1;
                q.push(e.to);
            }
        }
    }
    return dep[t];
}

int dfs(int x,int lim) {
    if (x==t) return lim;
    for (int& i=cur[x];i;i=edges[i].nxt) {
        edge e=edges[i];
        if (dep[x]+1==dep[e.to] && e.cap) {
            int flow=dfs(e.to,min(lim,e.cap));
            if (flow>0) {
                edges[i].cap-=flow;
                edges[i^1].cap=+flow;
                return flow;  //找到一条增广路就要return 
            }
        }
    }
    return 0;
}

int Dinic() {
    int maxflow=0;
    while (bfs()) {
        for (int i=s;i<=t;i++) cur[i]=head[i];  //当前弧优化 
        while (int flow=dfs(s,INF)) maxflow+=flow;
    }
    return maxflow;
}

bool vis[N],match[N]; vector<int> G[N];
bool dfs2(int x) {
    vis[x]=1;
    for (int i=0;i<G[x].size();i++) {
        int y=G[x][i];
        if (!vis[y]) dfs2(y);
    }
}

int main()
{
    scanf("%d%d%d",&n1,&n2,&m);
    s=0; t=n1+n2+1;
    for (int i=1;i<=m;i++) {
        scanf("%d%d",&x[i],&y[i]);
        id[i]=add_edge(x[i],y[i]+n1,1);
        add_edge(y[i]+n1,x[i],0);
    }
    for (int i=1;i<=n1;i++) add_edge(s,i,1),add_edge(i,s,0);
    for (int i=1;i<=n2;i++) add_edge(n1+i,t,1),add_edge(t,n1+i,0);
    
    Dinic();
    
    //重新构图 
    for (int i=1;i<=n1+n2;i++) vis[i]=0,match[i]=0,G[i].clear();
    for (int i=1;i<=m;i++)
        if (edges[id[i]].cap) G[x[i]].push_back(n1+y[i]);  //不匹配边左到右连边 
        else G[n1+y[i]].push_back(x[i]),match[x[i]]=1;  //匹配边右到左连边 
    for (int i=1;i<=n1;i++) if (!match[i]) dfs2(i);  //从每个未匹配点出发dfs 
    for (int i=1;i<=n1;i++)
        if (match[i] && !vis[i]) printf("%d\n",i);    //是匹配点且未被 未匹配点 访问的    
    
    for (int i=1;i<=n1+n2;i++) vis[i]=0,match[i]=0,G[i].clear();    
    for (int i=1;i<=m;i++)
        if (edges[id[i]].cap) G[n1+y[i]].push_back(x[i]);  //不匹配边右到左连边 
        else G[x[i]].push_back(n1+y[i]),match[n1+y[i]]=1;  //匹配边左到右连边
    for (int i=1;i<=n2;i++) if (!match[n1+i]) dfs2(n1+i);  //从每个未匹配点出发dfs  
    for (int i=1;i<=n2;i++)
        if (match[n1+i] && !vis[n1+i]) printf("%d\n",i);  //是匹配点且未被 未匹配点 访问的
    return 0;
}