hdu 5176 并查集

利用最小生成树的思想，用并查集记录点的集合，并且记录每个点集的规模，然后将边按照边权排序，从小到大选取边，因为当前连入的边一定是当前情况下最大的没所以边两侧的点集规模的积就是以它这条边为路径上最长边的所有情况的和，求最小的情况时采取同样的手段即可

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#define MAX 150007

using namespace std;

typedef unsigned long long LL;

int n;

int fa[MAX];
LL siz[MAX];

void init ( )
{
    for ( int i = 1 ; i <= n ; i++ ) 
        fa[i] = i,siz[i] = 1;
}

int find ( int x )
{
    return x==fa[x]?x:fa[x] = find(fa[x]);
}

void link ( int u , int v )
{
    int x = find (u), y = find (v);
    fa[x] = y;
    if ( x != y )
        siz[y] += siz[x];
}

struct Edge
{
    int u,v,c;
}e[MAX];

bool cmp1 ( Edge a , Edge b )
{
    return a.c < b.c;
}

bool cmp2 ( Edge a , Edge b )
{
    return a.c > b.c;
}


int main ( )
{
    int c = 1;
    while ( ~scanf ( "%d" , &n ) )
    {
        for ( int i = 1 ; i < n ; i++ )
            scanf ( "%d%d%d" , &e[i].u , &e[i].v , &e[i].c );
        sort ( e+1 , e+n , cmp1 );
        LL ans = 0;
        init ( );
        for ( int i = 1 ; i < n ; i++ )
        {
            int u = find( e[i].u ) , v = find ( e[i].v );
            ans += (LL)(e[i].c)*siz[u]*siz[v];
            link ( u , v );
        }
        init ( );
        sort ( e+1 , e+n , cmp2 );
        for ( int i = 1 ; i < n ; i++ )
        {
            int u = find(e[i].u) , v = find( e[i].v ) ;
            ans -= (LL)(e[i].c)*siz[u]*siz[v];
            link ( u , v );
        }
        printf ( "Case #%d: %llu\n" , c++ , ans ); 
    }
}