网络流(最大费用最大流) ：POJ 3680 Intervals

Intervals

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 7218		Accepted: 3011

Description

You are given N weighted open intervals. The ith interval covers (a_i, b_i) and weighs w_i. Your task is to pick some of the intervals to maximize the total weights under the limit that no point in the real axis is covered more than k times.

Input

The first line of input is the number of test case.
The first line of each test case contains two integers, N and K (1 ≤ K ≤ N ≤ 200).
The next N line each contain three integers a_i, b_i, w_i(1 ≤ a_i < b_i ≤ 100,000, 1 ≤ w_i ≤ 100,000) describing the intervals.
There is a blank line before each test case.

Output

For each test case output the maximum total weights in a separate line.

Sample Input

4

3 1
1 2 2
2 3 4
3 4 8

3 1
1 3 2
2 3 4
3 4 8

3 1
1 100000 100000
1 2 3
100 200 300

3 2
1 100000 100000
1 150 301
100 200 300

Sample Output

14
12
100000
100301
　　
　　这题就是求最大区间K覆盖，最大费用最大流走起~~~

#include <algorithm> 
#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
using namespace std;
const int INF=233333333;
const int maxn=2010,maxm=20010;
int cnt,fir[maxn],nxt[maxm],to[maxm],cap[maxm],val[maxm],dis[maxn],path[maxn];
struct data{
    int l,r,v;
    bool operator <(const data A)const{
        if(l!=A.l)
            return l<A.l;
        return r<A.r;     
    }
}ar[maxn];

struct data2{
    int a,pos;
    bool operator <(const data2 A)const{
        if(a!=A.a)
            return a<A.a;
        return pos<A.pos;     
    }
}br[maxn];

void addedge(int a,int b,int c,int v)
{
    nxt[++cnt]=fir[a];to[cnt]=b;cap[cnt]=c;val[cnt]=v;fir[a]=cnt;
}
int S,T;
int Spfa()
{
    queue<int>q;
    memset(dis,-1,sizeof(dis));
    q.push(S);dis[S]=0;
    while(!q.empty())
    {
        int node=q.front();q.pop();
        for(int i=fir[node];i;i=nxt[i])
            if(cap[i]&&dis[node]+val[i]>dis[to[i]]){
                dis[to[i]]=val[i]+dis[node];
                path[to[i]]=i;
                q.push(to[i]);
            }
    }
    return dis[T]==-1?0:dis[T]; 
}

int Aug()
{
    int p=T,f=INF;
    while(p!=S)
    {
        f=min(f,cap[path[p]]);
        p=to[path[p]^1];
    }
    p=T;
    while(p!=S)
    {
        cap[path[p]]-=f;
        cap[path[p]^1]+=f;
        p=to[path[p]^1];
    }
    return f;
}

int MCMF()
{
    int ret=0,d;
    while(d=Spfa())
        ret+=Aug()*d;
    return ret;    
}

int cont;
void Init()
{
    cnt=1;cont=0;
    memset(fir,0,sizeof(fir));
}

int main()
{
    int Q,n,k;
    scanf("%d",&Q);
    while(Q--)
    {
        Init();
        scanf("%d%d",&n,&k);    
        for(int i=1;i<=n;i++)
            scanf("%d%d%d",&ar[i].l,&ar[i].r,&ar[i].v);
        sort(ar+1,ar+n+1);
        for(int i=1;i<=n;i++){
            br[i*2-1].a=ar[i].l;br[i*2].a=ar[i].r;
            br[i*2-1].pos=br[i*2].pos=i;
        }
        sort(br+1,br+2*n+1);
        for(int i=1;i<=n;i++)
            ar[i].l=ar[i].r=0;
        for(int i=1;i<=2*n;i++)
        {
            int p=br[i].pos;
            if(!ar[p].l){
                ar[p].l=++cont;
            }
            else{
                ar[p].r=++cont;
            }
        }

        S=0;T=cont+1;
        for(int i=0;i<cont+1;i++)
            addedge(i,i+1,k,0),addedge(i+1,i,0,0); 
        for(int i=1;i<=n;i++)
            addedge(ar[i].l,ar[i].r,1,ar[i].v),addedge(ar[i].r,ar[i].l,0,-ar[i].v);
        printf("%d
",MCMF());        
    }

    return 0;
}