POJ 2594 Treasure Exploration 有源汇上下界网络流 最小流

题意：有一个n点m边的单向无环图，每个士兵可以从某一点沿着某方向出发，并不能返回，问最少要多少个士兵可以遍历全图。

这道题可以当做最小路径覆盖来做。当然也可以当上下界最小流来做。

最小路径覆盖的做法就不说了，百度搜一大把。
上下界最小流建图方式：
把每一个点i拆开为两个点i和i′
对于每个点建边i->i′流量下界为1，上界为oo
若原图存在边e(u,v)，那么建边u′->v，流量下界为0，上界为oo
然后建立超级源点sst和超级汇点eet
以超级源点和超级汇点跑一遍Dinic
然后再加边e(et,st,0,oo)
再以超级源点和超级汇点跑一遍Dinic，此时的流量为最小流。
代码1（有源汇上下界网络流 最小流）：

//author: CHC//First Edit Time:  2015-09-10 14:35#include <iostream>#include <cstdio>#include <cstring>#include <cmath>#include <set>#include <vector>#include <map>#include <queue>#include <set>#include <algorithm>#include <limits>using namespace std;typedef long long LL;const int MAXN=1e+4;const int MAXM=1e+6;const int INF = numeric_limits<int>::max();const LL LL_INF= numeric_limits<LL>::max();struct Edge {    int to,ci,next;    Edge(){}    Edge(int _to,int _ci,int _next):to(_to),ci(_ci),next(_next){}}e[MAXM];int head[MAXN],tot;void init(){    memset(head,-1,sizeof(head));    tot=0;}void AddEdge(int u,int v,int ci0,int ci1=0){    e[tot]=Edge(v,ci0,head[u]);    head[u]=tot++;    e[tot]=Edge(u,ci1,head[v]);    head[v]=tot++;}int dis[MAXN],sta[MAXN],top,cur[MAXN];bool bfs(int st,int et){    memset(dis,0,sizeof(dis));    dis[st]=1;    queue <int> q;q.push(st);    while(!q.empty()){        int now=q.front();q.pop();        for(int i=head[now];~i;i=e[i].next)            if(e[i].ci&&!dis[e[i].to]){                dis[e[i].to]=dis[now]+1;                q.push(e[i].to);            }    }    return dis[et]!=0;}LL Dinic(int st,int et){    LL ans=0;    while(bfs(st,et)){        top=0;        memcpy(cur,head,sizeof(head));        int u=st;        while(1){            //printf("u:%d\n",u);            if(u==et){                int pos,minn=INF;                for(int i=0;i<top;i++){                    if(minn>e[sta[i]].ci){                        minn=e[sta[i]].ci;                        pos=i;                    }                    //printf("%d%c-->%d%c\n",e[sta[i]^1].to>>1,e[sta[i]^1].to&1?'\'':' ',e[sta[i]].to>>1,e[sta[i]].to&1?'\'':' ');                    //printf("%d-->%d\n",e[sta[i]^1].to,e[sta[i]].to);                }                //puts("");                for(int i=0;i<top;i++){                    e[sta[i]].ci-=minn;                    e[sta[i]^1].ci+=minn;                }                top=pos;                u=e[sta[top]^1].to;                ans+=minn;                //printf("minn:%d\n",minn);            }            for(int i=cur[u];~i;cur[u]=i=e[i].next)                if(e[i].ci&&dis[u]+1==dis[e[i].to])break;            if(cur[u]!=-1){                sta[top++]=cur[u];                u=e[cur[u]].to;            }            else {                if(top==0)break;                dis[u]=0;                u=e[sta[--top]^1].to;            }        }    }    return ans;}int du[MAXN],ru[MAXN],chu[MAXN],n,m;int main(){    while(~scanf("%d%d",&n,&m)){        if(n+m==0)break;        init();        memset(du,0,sizeof(du));        memset(ru,0,sizeof(ru));        memset(chu,0,sizeof(chu));        int st=0,et=1;        for(int i=1;i<=n;i++){            AddEdge(i<<1,i<<1|1,INF-1);            chu[i<<1]++;            ru[i<<1|1]++;            du[i<<1]--;            du[i<<1|1]++;        }        for(int i=0,x,y;i<m;i++){            scanf("%d%d",&x,&y);            AddEdge(x<<1|1,y<<1,INF);            //printf("%d-->%d\n",x,y);            chu[x<<1|1]++;            ru[y<<1]++;        }        int sst=n*2+2,eet=n*2+3;        LL ctot=0;        for(int i=1;i<=n;i++){            if(ru[i<<1]==0){                AddEdge(st,i<<1,INF);                //printf("%d-->%d\n",st,i);            }            if(chu[i<<1|1]==0){                AddEdge(i<<1|1,et,INF);                //printf("%d-->%d\n",i,et);            }            if(du[i<<1] > 0)AddEdge(sst,i<<1,du[i<<1]),ctot+=du[i<<1];//,printf("vs-->%d\n",i<<1);            else AddEdge(i<<1,eet,-du[i<<1]);//,printf("%d-->vt\n",i<<1);            if(du[i<<1|1]>0)AddEdge(sst,i<<1|1,du[i<<1|1]),ctot+=du[i<<1|1];//,printf("vs-->%d\n",i<<1|1);            else AddEdge(i<<1|1,eet,-du[i<<1|1]);        }        //puts("");        //printf("sst:%d eet:%d\n",sst,eet);        LL ans=Dinic(sst,eet);        AddEdge(et,st,INF);        LL t=Dinic(sst,eet);        //printf("%d\n",e[tot-1].ci);        printf("%I64d\n",t);    }    return 0;}

代码2（匹配）：

//author: CHC//First Edit Time:  2015-05-10 12:56#include <iostream>#include <cstdio>#include <cstring>#include <cmath>#include <set>#include <vector>#include <map>#include <queue>#include <set>#include <algorithm>#include <limits>using namespace std;typedef long long LL;const int MAXN=1e+4;const int MAXM=1e+6;const int INF = numeric_limits<int>::max();const LL LL_INF= numeric_limits<LL>::max();int dp[510][510],n,m;struct Edge{    int from,to,ci,next;    Edge(){}    Edge(int _from,int _to,int _ci,int _next):from(_from),to(_to),ci(_ci),next(_next){}}e[MAXM];int head[MAXN],tot;int dis[MAXN];int top,sta[MAXN],cur[MAXN];inline void init(){    memset(head,-1,sizeof(head));    tot=0;}inline void AddEdge(int u,int v,int ci0,int ci1=0){    e[tot]=Edge(u,v,ci0,head[u]);    head[u]=tot++;    e[tot]=Edge(v,u,ci1,head[v]);    head[v]=tot++;}inline bool bfs(int st,int et){    memset(dis,0,sizeof(dis));    dis[st]=1;    queue <int> q;    q.push(st);    while(!q.empty()){        int now=q.front();        q.pop();        for(int i=head[now];i!=-1;i=e[i].next){            int next=e[i].to;            if(e[i].ci&&!dis[next]){                dis[next]=dis[now]+1;                if(next==et)return true;                q.push(next);            }        }    }    return false;}LL Dinic(int st,int et){    LL ans=0;    while(bfs(st,et)){        //printf("here\n");        top=0;        memcpy(cur,head,sizeof(head));        int u=st,i;        while(1){            if(u==et){                int pos,minn=INF;                //printf("top:%d\n",top);                for(i=0;i<top;i++)                {                    if(minn>e[sta[i]].ci){                        minn=e[sta[i]].ci;                        pos=i;                    }                    //printf("%d --> %d\n",e[sta[i]].from,e[sta[i]].to);                }                for(i=0;i<top;i++){                    e[sta[i]].ci-=minn;                    e[sta[i]^1].ci+=minn;                }                top=pos;                u=e[sta[top]].from;                ans+=minn;                //printf("minn:%d\n\n",minn);            }            for(i=cur[u];i!=-1;cur[u]=i=e[i].next)                if(e[i].ci&&dis[u]+1==dis[e[i].to])break;            if(cur[u]!=-1){                sta[top++]=cur[u];                u=e[cur[u]].to;            }            else {                if(top==0)break;                dis[u]=0;                u=e[sta[--top]].from;            }        }    }    return ans;}int main(){    while(~scanf("%d%d",&n,&m)){        if(n+m==0)break;        memset(dp,0,sizeof(dp));        init();        for(int i=0,x,y;i<m;i++){            scanf("%d%d",&x,&y);            dp[x][y]=1;        }        for(int k=1;k<=n;k++)        for(int i=1;i<=n;i++)            if(dp[i][k])                for(int j=1;j<=n;j++)                    dp[i][j]|=dp[i][k]*dp[k][j];        int st=0,et=n*3;        for(int i=1;i<=n;i++)            for(int j=1;j<=n;j++){                if(i!=j&&dp[i][j]){                    AddEdge(i<<1,j<<1|1,1);                }            }        for(int i=1;i<=n;i++)            AddEdge(st,i<<1,1),AddEdge(i<<1|1,et,1);        printf("%I64d\n",n-Dinic(st,et));    }    return 0;}