最大流，有向环覆盖问题。
#include<cstdio> #include<cstring> #include<string> #include<cmath> #include<vector> #include<queue> #include<algorithm> using namespace std; const int maxn = 100000 + 10; const int INF = 0x7FFFFFFF; struct Edge { int from, to, cap, flow; Edge(int u, int v, int c, int f) :from(u), to(v), cap(c), flow(f){} }; vector<Edge>edges; vector<int>G[maxn]; bool vis[maxn]; int d[maxn]; int cur[maxn]; int n, m, s, t; void init() { for (int i = 0; i < maxn; i++) G[i].clear(); edges.clear(); } void AddEdge(int from, int to, int cap) { edges.push_back(Edge(from, to, cap, 0)); edges.push_back(Edge(to, from, 0, 0)); int w = edges.size(); G[from].push_back(w - 2); G[to].push_back(w - 1); } bool BFS() { memset(vis, 0, sizeof(vis)); queue<int>Q; Q.push(s); d[s] = 0; vis[s] = 1; while (!Q.empty()) { int x = Q.front(); Q.pop(); for (int i = 0; i<G[x].size(); i++) { Edge e = edges[G[x][i]]; if (!vis[e.to] && e.cap>e.flow) { vis[e.to] = 1; d[e.to] = d[x] + 1; Q.push(e.to); } } } return vis[t]; } int DFS(int x, int a) { if (x == t || a == 0) return a; int flow = 0, f; for (int &i = cur[x]; i<G[x].size(); i++) { Edge e = edges[G[x][i]]; if (d[x]+1 == d[e.to]&&(f=DFS(e.to,min(a,e.cap-e.flow)))>0) { edges[G[x][i]].flow+=f; edges[G[x][i] ^ 1].flow-=f; flow+=f; a-=f; if(a==0) break; } } if(!flow) d[x] = -1; return flow; } int dinic(int s, int t) { int flow = 0; while (BFS()) { memset(cur, 0, sizeof(cur)); flow += DFS(s, INF); } return flow; } int main() { while(~scanf("%d%d",&n,&m)){ init(); s=0;t=2*n+1; for(int i=1;i<=n;i++) AddEdge(s,i,1); for(int i=n+1;i<=2*n;i++) AddEdge(i,t,1); for(int i=1;i<=m;i++) { int u,v; scanf("%d%d",&u,&v); u++; v++; AddEdge(u,v+n,1); } if(dinic(s,t)==n) printf("YES "); else printf("NO "); } return 0; }