最大权森林 poj 3723
Description
Windy has a country, and he wants to build an army to protect his country. He has picked up N girls and M boys and wants to collect them to be his soldiers. To collect a soldier without any privilege, he must pay 10000 RMB. There are some relationships between girls and boys and Windy can use these relationships to reduce his cost. If girl x and boy y have a relationship d and one of them has been collected, Windy can collect the other one with 10000-d RMB. Now given all the relationships between girls and boys, your assignment is to find the least amount of money Windy has to pay. Notice that only one relationship can be used when collecting one soldier.
Input
The first line of input is the number of test case.
The first line of each test case contains three integers, N, M and R.
Then R lines followed, each contains three integers xi, yi and di.
There is a blank line before each test case.
1 ≤ N, M ≤ 10000
0 ≤ R ≤ 50,000
0 ≤ xi < N
0 ≤ yi < M
0 < di < 10000
Output
Sample Input
2 5 5 8 4 3 6831 1 3 4583 0 0 6592 0 1 3063 3 3 4975 1 3 2049 4 2 2104 2 2 781 5 5 10 2 4 9820 3 2 6236 3 1 8864 2 4 8326 2 0 5156 2 0 1463 4 1 2439 0 4 4373 3 4 8889 2 4 3133
Sample Output
71071 54223
Source
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
//#include <bits/stdc++.h> #include<iostream> #include<cstdio> #include<queue> #include<cstring> #include<algorithm> using namespace std; #define maxn 100005 #define INF 9999999 int p[maxn],r[maxn],s,n,m,k,ans,cnt; struct edge { int x,y,z; } mp[maxn]; void init(int n) { for(int i=0; i<=n; i++) { p[i]=i; r[i]=0; } } int Find(int x) { return p[x]==x ? x : p[x]=Find(p[x]); } bool cmp(const edge &a,const edge &b) { return a.z<b.z; } void unite(int x,int y) { x=Find(x); y=Find(y); if(x==y) return; if(r[x]<r[y]) p[x]=y; else { p[y]=x; if(r[x]==r[y]) r[x]++; } } void kruskal() { sort(mp,mp+k,cmp); init(s); ans=0; for(int i=0; i<k; i++) { int x=Find(mp[i].x),y=Find(mp[i].y); if(x==y) continue; ans+=mp[i].z; unite(x,y); //cnt++; //if(cnt==s-1) return; } } int main() { int t; scanf("%d",&t); while(t--) { scanf("%d %d %d",&n,&m,&k); s=n+m; memset(mp,0,sizeof(mp)); for(int i=0;i<k;i++) { int a,b,c; scanf("%d %d %d",&a,&b,&c); mp[i].x=a; mp[i].y=b+n; //注意看题男女都是从0开始编号的,要重新编号! mp[i].z=-c; } kruskal(); int sum=10000*s+ans; printf("%d\n",sum); } return 0; }