hdu 3367 Pseudoforest

Pseudoforest

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others) Total Submission(s): 1070    Accepted Submission(s): 417 

Problem Description

In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. The maximal pseudoforests of G are the pseudoforest subgraphs of G that are not contained within any larger pseudoforest of G. A pesudoforest is larger than another if and only if the total value of the edges is greater than another one’s.

 

Input

The input consists of multiple test cases. The first line of each test case contains two integers, n(0 < n <= 10000), m(0 <= m <= 100000), which are the number of the vertexes and the number of the edges. The next m lines, each line consists of three integers, u, v, c, which means there is an edge with value c (0 < c <= 10000) between u and v. You can assume that there are no loop and no multiple edges. The last test case is followed by a line containing two zeros, which means the end of the input.

 

Output

Output the sum of the value of the edges of the maximum pesudoforest.

 

Sample Input

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

 

Sample Output

3 5

 

Source

“光庭杯”第五届华中北区程序设计邀请赛 暨 WHU第八届程序设计竞赛

 

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// 开始我想错了 我是先搞生成树，然后在每个分块加入一条最大边使其 构成环
// 这样是不对的 应该能成环的先让成环 两个成环的就算有边也不连，不然达不到最大的效果
// 这是求最大生成树问题
#include <iostream>

#include <algorithm>

#include <queue>

#include <math.h>

#include <stdio.h>

#include <string.h>

using namespace std;

struct node{

    int u,v,c;

    bool operator <(const node b) const{

        return c>b.c;

    }

}Eg[100010];

int f[10010];

bool flag[10010];

int Find(int x){

   if(x!=f[x])

      f[x]=Find(f[x]);

   return f[x];

}

int main()

{

    int n,m;

    while(scanf("%d %d",&n,&m),n|m){

        int i,j,k;

        int u,v;

        for(i=0;i<m;i++)

          scanf("%d %d %d",&Eg[i].u,&Eg[i].v,&Eg[i].c);

        sort(Eg,Eg+m);

        int sum=0;

        for(i=0;i<n;i++) f[i]=i,flag[i]=false;

        for(i=0;i<m;i++){

          u=Eg[i].u;

          v=Eg[i].v;

          u=Find(u);

          v=Find(v);

          if(u!=v){

            if(!flag[u]&&!flag[v]){

                f[u]=v;

                sum+=Eg[i].c;

            }

            else if(!flag[u]||!flag[v]){

                f[u]=v;

                sum+=Eg[i].c;

                flag[u]=flag[v]=true;

            }

          }

          else{

            if(!flag[u]){

                flag[u]=true;

                sum+=Eg[i].c;

            }

          }

        }

        printf("%d\n",sum);

    }



    return 0;

}