Problem H

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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.<br><br>

 

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.<br>The last test case is followed by a line containing two zeros, which means the end of the input.<br>

 

Output

Output the sum of the value of the edges of the maximum pesudoforest.<br>

 

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

代码： #include<stdio.h>  #include<string.h>  #include<stdlib.h>  #include<algorithm>  using namespace std;  const int maxn = 10005;  const int maxm = 100005;  struct node{      int u,v,val;  }edge[ maxm ];  int fa[ maxn ],circle[ maxn ];  int find( int x ){      if( fa[x]==x ) return x;      fa[x] = find(fa[x]);      return fa[x];  }  bool union_ab( int x,int y ){      int fax = find(x);      int fay = find(y);      if( fax==fay ){          if( circle[ fax ]==-1 ){              circle[ fax ] = 1;              return true;          }//形成一个环          return false;          //已经是环      }      else{          if( circle[ fax ]==circle[ fay ]&&circle[ fax ]==1 )              return false;          if( circle[ fax ]==1 )              fa[ fay ] = fax;          else              fa[ fax ] = fay;          //这里注意把环作为祖先，因为find          return true;      }  }  void init( int n ){      for( int i=0;i<n;i++ ){          fa[i] = i;          circle[ i ] = -1;      }  }  int cmp( node a,node b ){      return a.val>b.val;  }  int main(){      int n,m;      while( scanf("%d%d",&n,&m)==2,n||m ){          //if( n==0&&m==0 ) break;          for( int i=0;i<m;i++ )              scanf("%d%d%d",&edge[i].u,&edge[i].v,&edge[i].val);          init( n );          sort( edge,edge+m,cmp );          int ans = 0;          for( int i=0;i<m;i++ ){              if( union_ab( edge[i].u,edge[i].v) )                  ans += edge[i].val;          }          printf("%d\n",ans);      }      return 0; }