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=0; 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=0;i<NV;++i){
        vis[i]=0;
        d[i]=INF;
    }
    vis[vs]=1;
    d[vs]=0;
    queue<int> que;
    que.push(vs);
    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(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]=1;
                    que.push(v);
                }
            }
        }
        vis[u]=0;
    }
    return d[vt]!=INF;
}
int MCMF(){
    int res=0;
    while(SPFA()){
        int flow=INF,cost=0;
        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]^1].cap+=flow;
            cost+=flow*edge[pre[u]].cost;
        }
        res+=cost;
    }
    return res;
}

int from[222],to[222],cost[222];
int point[444],pn;
int main(){
    int t,n,k;
    scanf("%d",&t);
    while(t--){
        scanf("%d%d",&n,&k);
        pn=0;
        for(int i=0; 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+1; NV=vt+1; NE=0;
        memset(head,-1,sizeof(head));

        addEdge(vs,0,k,0);
        addEdge(pn-1,vt,k,0);
        for(int i=1; i<pn; ++i){
            addEdge(i-1,i,INF,0);
        }
        for(int i=0; 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,1,-cost[i]);
        }

        printf("%d
",-MCMF());
    }
    return 0;
}