hdu 4313 Matrix(最大生成树)

Matrix

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 1835 Accepted Submission(s): 703



Problem Description

Machines have once again attacked the kingdom of Xions. The kingdom of Xions has N cities and N-1 bidirectional roads. The road network is such that there is a

unique path between any pair of cities.

Morpheus has the news that K Machines are planning to destroy the whole kingdom. These Machines are initially living in K different cities of the kingdom and

anytime from now they can plan and launch an attack. So he has asked Neo to destroy some of the roads to disrupt the connection among Machines. i.e after destroying those roads there should not be any path between any two Machines.

Since the attack can be at any time from now, Neo has to do this task as fast as possible. Each road in the kingdom takes certain time to get destroyed and they

can be destroyed only one at a time.

You need to write a program that tells Neo the minimum amount of time he will require to disrupt the connection among machines.

Input

The first line is an integer T represents there are T test cases. (0<T <=10)

For each test case the first line input contains two, space-separated integers, N and K. Cities are numbered 0 to N-1. Then follow N-1 lines, each containing three, space-separated integers, x y z, which means there is a bidirectional road connecting city x
and city y, and to destroy this road it takes z units of time.Then follow K lines each containing an integer. The ith integer is the id of city in which ith Machine is currently located.

2 <= N <= 100,000

2 <= K <= N

1 <= time to destroy a road <= 1000,000

Output

For each test case print the minimum time required to disrupt the connection among Machines.

Sample Input

1
5 3
2 1 8
1 0 5
2 4 5
1 3 4
2
4
0

Sample Output

10
Hint
Neo can destroy the road connecting city 2 and city 4 of weight 5 , and the road connecting city 0 and city 1 of weight 5. As only one road can be destroyed at a
time, the total minimum time taken is 10 units of time. After destroying these roads none of the Machines can reach other Machine via any path.

题意：给出n个点，n-1条边，给出k个点，要使这k个点互不相连，要求删除最小权值的边，输出删除的边的权值总和。
思路：生成k课最大生成树，删除k-1条边。用kruskal算法。

AC代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <queue>
#include <vector>
#include <cmath>
#include <stack>
#include <cstdlib>
using namespace std;

const int maxn=100005;
struct node
{
int u,v,w;
} edge[maxn];
int n,k;
int fa[maxn];
bool loc[maxn];
bool cmp(node a,node b)
{
return a.w>b.w;
}
void init()
{
for(int i=0; i<n; i++)
fa[i]=i;
memset(loc,false,sizeof(loc));
}
int Find_set(int x)
{
if(x==fa[x]) return fa[x];
fa[x]=Find_set(fa[x]);
return fa[x];
}
void Union(int ra,int rb)
{
if(loc[ra])
fa[rb]=ra;
else
fa[ra]=rb;
}
int main()
{
int t,a;
scanf("%d",&t);
while(t--)
{
scanf("%d%d",&n,&k);
init();
for(int i=0; i<n-1; i++)
scanf("%d%d%d",&edge[i].u,&edge[i].v,&edge[i].w);
while(k--)
{
scanf("%d",&a);
loc[a]=true;
}
sort(edge,edge+n-1,cmp);
long long ans=0;
for(int i=0; i<n-1; i++)
{
int x=Find_set(edge[i].u);
int y=Find_set(edge[i].v);
if(loc[x]&&loc[y])
ans+=edge[i].w;
else
Union(x,y);
}
printf("%I64d\n",ans);
}
return 0;
}