POJ3680 Intervals（最小费用最大流）

选择若干条线段使权值最大，并且点覆盖次数不超过k。

建图如下：vs到0建立容量为k费用为0的边；坐标终点到vt连接一条容量为k费用为0的边；对于每两个相邻坐标连接一条容量为INF费用为0的边；对于线段每两个端点连接一条容量1费用为-cost的边。

这样跑最小费用最大流。相当于找出k个线段集合，每个集合的线段都不重合。原问题就这样求解。

 #include<cstdio>
 #include<cstring>
 #include<queue>
 #include<algorithm>
 using namespace std;
 #define INF (1<<30)
 #define MAXN 444
 #define MAXM 444*444*2
 struct Edge{
     int u,v,cap,cost,next;
 }edge[MAXM];
 int head[MAXN];
 int NV,NE,vs,vt;

 void addEdge(int u,int v,int cap,int cost){
     edge[NE].u=u; edge[NE].v=v; edge[NE].cap=cap; edge[NE].cost=cost;
     edge[NE].next=head[u]; head[u]=NE++;
     edge[NE].u=v; edge[NE].v=u; edge[NE].cap=; edge[NE].cost=-cost;
     edge[NE].next=head[v]; head[v]=NE++;
 }
 bool vis[MAXN];
 int d[MAXN],pre[MAXN];
 bool SPFA(){
     for(int i=;i<NV;++i){
         vis[i]=;
         d[i]=INF;
     }
     vis[vs]=;
     d[vs]=;
     queue<int> que;
     que.push(vs);
     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(edge[i].cap && d[v]>d[u]+edge[i].cost){
                 d[v]=d[u]+edge[i].cost;
                 pre[v]=i;
                 if(!vis[v]){
                     vis[v]=;
                     que.push(v);
                 }
             }
         }
         vis[u]=;
     }
     return d[vt]!=INF;
 }
 int MCMF(){
     int res=;
     while(SPFA()){
         int flow=INF,cost=;
         for(int u=vt; u!=vs; u=edge[pre[u]].u){
             flow=min(flow,edge[pre[u]].cap);
         }
         for(int u=vt; u!=vs; u=edge[pre[u]].u){
             edge[pre[u]].cap-=flow;
             edge[pre[u]^].cap+=flow;
             cost+=flow*edge[pre[u]].cost;
         }
         res+=cost;
     }
     return res;
 }

 int from[],to[],cost[];
 int point[],pn;
 int main(){
     int t,n,k;
     scanf("%d",&t);
     while(t--){
         scanf("%d%d",&n,&k);
         pn=;
         for(int i=; i<n; ++i){
             scanf("%d%d%d",from+i,to+i,cost+i);
             point[pn++]=from[i]; point[pn++]=to[i];
         }
         sort(point,point+pn);
         pn=unique(point,point+pn)-point;

         vs=pn; vt=vs+; NV=vt+; NE=;
         memset(head,-,sizeof(head));

         addEdge(vs,,k,);
         addEdge(pn-,vt,k,);
         for(int i=; i<pn; ++i){
             addEdge(i-,i,INF,);
         }
         for(int i=; i<n; ++i){
             int x=lower_bound(point,point+pn,from[i])-point;
             int y=lower_bound(point,point+pn,to[i])-point;
             addEdge(x,y,,-cost[i]);
         }

         printf("%d\n",-MCMF());
     }
     return ;
 }