POJ2112 Optimal Milking（最大流）

先Floyd求牛到机器最短距离，然后二分枚举最长的边。

#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
using namespace std;
#define INF (1<<30)
#define MAXN 233 
#define MAXM 233*233*20 

struct Edge{
    int v,cap,flow,next;
}edge[MAXM];
int vs,vt,NE,NV;
int head[MAXN];

void addEdge(int u,int v,int cap){
    edge[NE].v=v; edge[NE].cap=cap; edge[NE].flow=0;
    edge[NE].next=head[u]; head[u]=NE++;
    edge[NE].v=u; edge[NE].cap=0; edge[NE].flow=0;
    edge[NE].next=head[v]; head[v]=NE++;
}

int level[MAXN];
int gap[MAXN];
void bfs(){
    memset(level,-1,sizeof(level));
    memset(gap,0,sizeof(gap));
    level[vt]=0;
    gap[level[vt]]++;
    queue<int> que;
    que.push(vt);
    while(!que.empty()){
        int u=que.front(); que.pop();
        for(int i=head[u]; i!=-1; i=edge[i].next){
            int v=edge[i].v;
            if(level[v]!=-1) continue;
            level[v]=level[u]+1;
            gap[level[v]]++;
            que.push(v);
        }
    }
}

int pre[MAXN];
int cur[MAXN];
int ISAP(){
    bfs();
    memset(pre,-1,sizeof(pre));
    memcpy(cur,head,sizeof(head));
    int u=pre[vs]=vs,flow=0,aug=INF;
    gap[0]=NV;
    while(level[vs]<NV){
        bool flag=false;
        for(int &i=cur[u]; i!=-1; i=edge[i].next){
            int v=edge[i].v;
            if(edge[i].cap!=edge[i].flow && level[u]==level[v]+1){
                flag=true;
                pre[v]=u;
                u=v;
                //aug=(aug==-1?edge[i].cap:min(aug,edge[i].cap));
                aug=min(aug,edge[i].cap-edge[i].flow);
                if(v==vt){
                    flow+=aug;
                    for(u=pre[v]; v!=vs; v=u,u=pre[u]){
                        edge[cur[u]].flow+=aug;
                        edge[cur[u]^1].flow-=aug;
                    }
                    //aug=-1;
                    aug=INF;
                }
                break;
            }
        }
        if(flag) continue;
        int minlevel=NV;
        for(int i=head[u]; i!=-1; i=edge[i].next){
            int v=edge[i].v;
            if(edge[i].cap!=edge[i].flow && level[v]<minlevel){
                minlevel=level[v];
                cur[u]=i;
            }
        }
        if(--gap[level[u]]==0) break;
        level[u]=minlevel+1;
        gap[level[u]]++;
        u=pre[u];
    }
    return flow;
}

int d[MAXN][MAXN],k,c,m,N;
bool available(int mx){
    memset(head,-1,sizeof(head));
    for(int i=1; i<=k; ++i) addEdge(i,vt,m);
    for(int i=1; i<=c; ++i) addEdge(vs,i+k,1);
    for(int i=1; i<=c; ++i){
        for(int j=1; j<=k; ++j){
            if(d[i+k][j]==0 || d[i+k][j]>mx) continue;
            addEdge(i+k,j,1);
        }
    }
    return ISAP()==c;
}
inline void floyd(){
    for(int k=1; k<=N; ++k){
        for(int i=1; i<=N; ++i){
            if(!d[i][k]) continue;
            for(int j=1; j<=N; ++j){
                    if(d[k][j] && (d[i][j]==0 || d[i][j]>d[i][k]+d[k][j])) d[i][j]=d[i][k]+d[k][j];
            }
        }
    }
}
int main(){
    scanf("%d%d%d",&k,&c,&m);
    N=k+c;

    vs=0; vt=N+1; NV=vt+1;

    for(int i=1; i<=N; ++i){
        for(int j=1; j<=N; ++j) scanf("%d",&d[i][j]);
    }
    floyd();

    int l=0,r=INF;
    while(l<r){
        int mid=l+r>>1;
        if(available(mid)) r=mid;
        else l=mid+1;
    }
    printf("%d",l);
    return 0;
}