专题四1008

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题意：找到一个这样的图，在这个图中，最多有一个环。使得所有的边的和最大

解题思路：

贪心+并查集。首先把边排序，然后开始分类讨论。对于边ab（含有两个端点ab）如果a，b是属于两个不同的集合， a b 是两个环中的点，则放弃aba b 有一个是环，则把环当做另一个的祖先，之后在回溯祖先的时候，能找到该点是在某个环中。

感想：要考试了，心好累啊。。。

AC源码：

#include<iostream>
#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;

 }

 return false;
 }

 else{

 if( circle[ fax ]==circle[ fay ]&&circle[ fax ]==1 )

 return false;

 if( circle[ fax ]==1 )

 fa[ fay ] = fax;

 else

 fa[ fax ] = fay;

 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( cin>>n>>m &&(n||m)){

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

 cin>>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;

 }

 cout<<ans<<endl;

 }

 return 0;

 }

Problem H

Time Limit : 10000/5000ms (Java/Other) Memory Limit : 65536/65536K (Java/Other)

Total Submission(s) : 39 Accepted Submission(s) : 15

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 30 1 11 2 12 0 14 50 1 11 2 12 3 13 0 10 2 20 0

Sample Output

Statistic |Submit | Back

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