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ii拆开为两个点ii和i′i'
对于每个点建边ii->i′i'流量下界为11，上界为oooo
若原图存在边e(u,v)e(u,v)，那么建边u′u'->vv，流量下界为00，上界为oooo
然后建立超级源点sstsst和超级汇点eeteet
以超级源点和超级汇点跑一遍Dinic
然后再加边e(et,st,0,oo)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;
}