loj 1167(二分+最大流）

题目链接：http://acm.hust.edu.cn/vjudge/problem/viewProblem.action?id=26881

思路：我们可以二分最大危险度，然后建图，由于每个休息点只能用一次，就要拆点，将每个休息点拆点，边容量为1，代表只能使用一次，然后跑最大流验证。

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<queue>
 #include<cmath>
 using namespace std;
 #define MAXN 222
 #define MAXM 222222
 #define inf 1<<30
 #define FILL(a,b) memset(a,b,sizeof(a))

 struct Edge{
     int v,cap,next;
 }edge[MAXM];

 int n,m,vs,vt,k,NV,NE;
 int head[MAXN];

 void Insert(int u,int v,int cap)
 {
     edge[NE].v=v;
     edge[NE].cap=cap;
     edge[NE].next=head[u];
     head[u]=NE++;

     edge[NE].v=u;
     edge[NE].cap=;
     edge[NE].next=head[v];
     head[v]=NE++;
 }

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

 int pre[MAXN],cur[MAXN];
 int SAP(int vs,int vt)
 {
     bfs(vt);
     memcpy(cur,head,sizeof(head));
     int u=pre[vs]=vs,aug=inf,maxflow=;
     gap[]=NV;
     while(level[vs]<NV){
         bool flag=false;
         for(int &i=cur[u];i!=-;i=edge[i].next){
             int v=edge[i].v;
             if(edge[i].cap>&&level[u]==level[v]+){
                 flag=true;
                 aug=min(aug,edge[i].cap);
                 pre[v]=u;
                 u=v;
                 if(v==vt){
                     maxflow+=aug;
                     for(u=pre[u];v!=vs;v=u,u=pre[u]){
                         edge[cur[u]].cap-=aug;
                         edge[cur[u]^].cap+=aug;
                     }
                     aug=inf;
                 }
                 break;
             }
         }
         if(flag)continue;
         int minlevel=NV;
         for(int i=head[u];i!=-;i=edge[i].next){
             int v=edge[i].v;
             if(edge[i].cap>&&level[v]<minlevel){
                 minlevel=level[v];
                 cur[u]=i;
             }
         }
         if(--gap[level[u]]==)break;
         level[u]=minlevel+;
         gap[level[u]]++;
         u=pre[u];
     }
     return maxflow;
 }

 struct Path{
     int u,v,d;
 }path[MAXM];

 void Build(int limit)
 {
     NE=;
     memset(head,-,sizeof(head));
     vs=,vt=*n+,NV=*n+;
     for(int i=;i<m;i++){
         if(path[i].d<=limit)Insert(path[i].u+n+,path[i].v,);
     }
     for(int i=;i<=n;i++)Insert(i,i+n+,);
     Insert(vs,vs+n+,);
     Insert(n+,vt,);
 }

 int main()
 {
     int _case,u,v,d,low,high,mid,ans,t=;
     scanf("%d",&_case);
     while(_case--){
         scanf("%d%d",&n,&m);
         low=inf,high=;
         for(int i=;i<m;i++){
             scanf("%d%d%d",&path[i].u,&path[i].v,&path[i].d);
             if(path[i].u>path[i].v)swap(path[i].u,path[i].v);
             //cout<<path[i].u<<"&&&&"<<path[i].v<<endl;
             low=min(low,path[i].d);
             high=max(high,path[i].d);
         }
        // cout<<low<<"**"<<high<<endl;
         scanf("%d",&k);
         ans=inf;
         while(low<=high){
             mid=(low+high)>>;
             Build(mid);
             if(SAP(vs,vt)>=k){
                 ans=mid;
                 high=mid-;
             }else
                 low=mid+;
         }
         printf("Case %d: ",t++);
         if(ans!=inf){
             printf("%d\n",ans);
         }else
             puts("no solution");
     }
     return ;
 }