P2764 最小路径覆盖问题

发布时间 2023-03-22 21:27:23作者: towboat

求最少的路径数目覆盖DAG每个点(无点交集

 

#include<iostream>
#include<algorithm>
#include <queue>
using namespace std ;
const int N=500,M=5e5+5;
 const int inf =1e9+7;
  
 int all=1,hd[N],go[M],w[M],nxt[M];
   
 int S,T,n,m;
 int dis[M],now[M];
   
 void add_(int x,int y,int z){
     nxt[++all]=hd[x]; hd[x]=all; go[all]=y;
     w[all]=z;
     swap(x,y);
     nxt[++all]=hd[x]; hd[x]=all; go[all]=y;
     w[all]=0;
 }
  bool bfs(){
     for(int i=0;i<M;i++)dis[i]=inf;
     queue<int> q;
     q.push(S);
     now[S]=hd[S];
     dis[S]=0;
       
     while(q.empty()==0){
         int x=q.front();
         q.pop();
         for(int i=hd[x];i;i=nxt[i]){
             int y=go[i];
             if(w[i]>0&&dis[y]==inf){
                 dis[y]=dis[x]+1;
                 now[y]=hd[y];
                 q.push(y);
                 if(y==T) return 1;
             }
         }
     }
     return 0;
 }
 int dfs(int x,int sum){
     if(x==T) return sum;
     int k,res=0;
       
     for(int i=now[x];i&& sum ;i=nxt[i]){
         now[x]=i;
         int y=go[i];
         if(w[i]>0&&(dis[y]==dis[x]+1)){
             k=dfs(y,min(sum,w[i]));
             if(k==0) dis[y]=inf;
             w[i]-=k;
             w[i^1]+=k;
             res+=k;
             sum-=k;
         }
     }
     return res;
 }
 void print(int x){
 	cout<<x<<' ';
 	for(int i=hd[x];i;i=nxt[i]){
 		int y=go[i]; if(y>n&&w[i]==0) print(y-n);
 	}
 }
 int Fa[N];
 int find(int x){
 	return x==Fa[x]?x:Fa[x]=find(Fa[x]);
 }
 signed main(){
 	int i,x,y; 
 	
 	cin>>n>>m;S=0,T=2*n+1;
 	for(i=1;i<=m;i++){
 		cin>>x>>y; add_(x,y+n,1) ; 
 	}
 	for(i=1;i<=n;i++) add_(S,i,1);
 	for(i=1;i<=n;i++) add_(i+n,T,1);
 	int ans=0;
 	while(bfs()) ans+=dfs(S,inf);
 	
 	for(i=1;i<=2*n;i++) Fa[i]=i;
 	for(i=1;i<=n;i++)
 	 for(int j=hd[i];j;j=nxt[j]){
 	 	y=go[j];
 	 	if(y>n&&y<T&&w[j]==0) Fa[find(y-n)]=find(i);
 	 }
 	for(i=1;i<=n;i++) 
 		if(find(i)==i) print(i),cout<<endl;
 	cout<<n-ans<<endl;
 }