网络流24题之T3 最小路径覆盖问题

#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <cstring>
#include <queue>
using namespace std ;
const int maxn= 2010;
const int oo=10e9;

typedef struct EDGE{
    int u,v;
    int c,f,next;
    EDGE (){
        u=v=c=f=0;
        next=-1;
    }
    EDGE (int a,int b,int d,int e,int g){
        u=a;v=b;c=d;f=e;next=g;
    }
}E;
E edge[maxn*100];
int len=-1,head[maxn],n,m;
int vis[maxn],dis[maxn];
int cur[maxn];
int allp;//总的点个数
int S,T;//源点和汇点的编号
void E_add (int s,int t,int x,int y){
    edge[++len]=EDGE (s,t,x,y,head[s]);
    head[s]=len;
}
void init (){
    cin >>n >>m;
    int i,j,k;
    S=1;
    T=2*n+2;
    allp=T;
    memset (head,-1,sizeof(head));
    for (i=1;i<=m;i++){
        scanf ("%d %d",&j,&k);
        E_add (2*j,2*k+1,1,0);
        E_add (2*k+1,2*j,0,0);
    }
    for (i=1;i<=n;i++){
        E_add (S,i*2,1,0);
        E_add (i*2,S,0,0);
        E_add (i*2+1,T,1,0);
        E_add (T,i*2+1,0,0);
    }
}
int bfs (){
    memset (vis,0,sizeof(vis));
    int q[100*maxn],headx=0,tail=0;
    int now,i;
    q[tail++]=S;
    vis[S]=1;
    dis[S]=1;
    while (headx<tail){
        now=q[headx++];
        for (i=head[now];i!=-1;i=edge[i].next){
            if (!vis[edge[i].v]&&edge[i].c>edge[i].f) {
                q[tail++]=edge[i].v;
                dis[edge[i].v]=dis[now]+1;
                vis[edge[i].v]=1;
            }
        }
    }
    return vis[T];
}
int dfs (int x,int fmax){
    if (x==T||fmax==0)return fmax;
    int f,flow=0,&now=cur[x];
    for (;now!=-1;now=edge[now].next){
        if (dis[edge[now].v]==dis[x]+1&&(f=(dfs (edge[now].v,min(fmax,edge[now].c-edge[now].f))))){
            flow+=f;
            edge[now].f+=f;
            edge[now^1].f-=f;
            fmax-=f;
            if (fmax==0) break;
        }
    }
    return flow;
}
int dinic (){
    int flow=0,i;
    while (bfs ()){
        for (i=1;i<=allp;i++) cur[i]=head[i];
        flow+=dfs (S,oo);
    }
    return flow;
}
int main (){
    init ();
    cout <<n-dinic ();
    return 0;
}