hdu 3367 最大伪森林（kruskal）

最大伪森林：原图的一个子图，在子图的各个连通分量中至多有一个环，且各边权和最大。

方法：kruskal，只是排序按边权从大到小，合并的时候注意判断是否构成多个环。

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;

const int N = 10000;
const int M = 100000;
int f[N];
bool cycle[N];

struct Edge
{
    int u, v, w;
    bool operator < ( const Edge & o ) const
    {
        return w > o.w;
    }
} edge[M];

int findf( int x )
{
    if ( f[x] != x ) f[x] = findf(f[x]);
    return f[x];
}

int main ()
{
    int n, m;
    while ( scanf("%d%d", &n, &m) != EOF )
    {
        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].w);
        }
        for ( int i = 0; i < n; i++ )
        {
            f[i] = i;
        }
        sort( edge, edge + m );
        memset( cycle, 0, sizeof(cycle) );
        int sum = 0;
        for ( int i = 0; i < m; i++ )
        {
            int u = edge[i].u, v = edge[i].v, w = edge[i].w;
            u = findf(u), v = findf(v);
            if ( u == v )
            {
                if ( !cycle[u] )
                {
                    sum += w;
                    cycle[u] = 1;
                }
            }
            else
            {
                if ( cycle[u] && cycle[v] )
                {
                    continue;
                }
                sum += w;
                f[u] = v;
                if ( cycle[u] || cycle[v] )
                {
                    cycle[v] = 1;
                }
            }
        }
        printf("%d
", sum);
    }
    return 0;
}