题目链接：https://www.luogu.org/problemnew/show/P2764
有向无环图G的最小路径点覆盖包含的路径数等于n减去拆点二分图G2的最大匹配数
1 #include <bits/stdc++.h> 2 3 using namespace std; 4 const int inf=0x3f3f3f3f; 5 const int MAXN=10000; 6 const int MAXM=100000; 7 struct Edge 8 { 9 int to,nxt,cap,flow; 10 }edge[MAXM]; 11 int head[MAXN],tot,dis[MAXN],S,T,n,m; 12 void init() 13 { 14 memset(head,-1,sizeof(head)); 15 tot=0; 16 } 17 void addedge(int u,int v,int cap) 18 { 19 edge[tot].to=v; edge[tot].cap=cap; edge[tot].flow=0; 20 edge[tot].nxt=head[u]; head[u]=tot++; 21 22 edge[tot].to=u; edge[tot].cap=0; edge[tot].flow=0; 23 edge[tot].nxt=head[v]; head[v]=tot++; 24 } 25 queue<int>q; 26 bool bfs() 27 { 28 memset(dis,0,sizeof(dis)); 29 while(!q.empty()) q.pop(); 30 q.push(S); 31 dis[S]=1; 32 while(!q.empty()) 33 { 34 int u=q.front();q.pop(); 35 for(int i=head[u];i!=-1;i=edge[i].nxt) 36 { 37 int v=edge[i].to; 38 if(!dis[v]&&edge[i].cap>edge[i].flow) 39 { 40 dis[v]=dis[u]+1; 41 q.push(v); 42 } 43 } 44 } 45 return dis[T]; 46 } 47 int dfs(int u,int f) 48 { 49 if(u==T) return f; 50 for(int i=head[u];i!=-1;i=edge[i].nxt) 51 { 52 int v=edge[i].to; 53 if(dis[u]+1==dis[v]&&edge[i].cap>edge[i].flow) 54 { 55 int f1=dfs(v,min(f,edge[i].cap-edge[i].flow)); 56 if(f1) 57 { 58 edge[i].flow+=f1; 59 edge[i^1].flow-=f1; 60 return f1; 61 } 62 } 63 } 64 return 0; 65 } 66 int dinic() 67 { 68 int ans=0; 69 while(bfs()) ans+=dfs(S,inf); 70 return ans; 71 } 72 int to[MAXN]; 73 bool vis[MAXN]; 74 int main() 75 { 76 ios::sync_with_stdio(false); 77 cin.tie(0); cout.tie(0); 78 cin>>n>>m; 79 init(); 80 S=0; 81 T=2*n+1; 82 int u,v; 83 for(int i=1;i<=m;i++) 84 { 85 cin>>u>>v; 86 addedge(u,v+n,1); 87 } 88 for(int i=1;i<=n;i++) 89 { 90 addedge(S,i,1); 91 addedge(i+n,T,1); 92 } 93 int ans=n-dinic(); 94 for(int i=1;i<=n;i++) 95 { 96 for(int j=head[i];j!=-1;j=edge[j].nxt) 97 { 98 if(edge[j].flow==1) 99 { 100 to[i]=edge[j].to-n; 101 break; 102 } 103 } 104 } 105 for(int i=1;i<=n;i++) 106 { 107 int flag=0; 108 if(!vis[i]) 109 { 110 while(i) 111 { 112 vis[i]=1; 113 if(flag) cout<<" "; 114 flag=1; 115 cout<<i; 116 i=to[i]; 117 } 118 cout<<endl; 119 } 120 } 121 cout<<ans<<endl; 122 return 0; 123 }