2014
03-16

# Pseudoforest

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.

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.

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.

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

3
5

a b 是两个环中的点，则放弃ab

a 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。

/*
找到一个图，使得每一个连通分量最多有一个环
*/
#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;
}

View Code

1. L（X [0 .. M-1]，Y [0 .. N-1]）= 1 + L（X [0 .. M-2]，Y [0 .. N-1]）这个地方也也有笔误
应改为L（X [0 .. M-1]，Y [0 .. N-1]）= 1 + L（X [0 .. M-2]，Y [0 .. N-2]）