hdu 2419 离线逆序操作+并查集

此题关键在于维护点的连通性以及连通块的信息，容易想到并查集，但是并查集却不支持删边操作，于是考虑逆序处理，这样删边就变成了加边操作，每一个连通块的信息可以用stl中的multiset来维护，注意集合合并的时候要启发式合并（这里是按照集合的大小来合并，每次小的集合合并到大的集合里），不然会超时。

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

const int N = 20001;
const int M = 300001;
int f[N];
int v[N];
multiset<int> s[N];
multiset<int> edge[N];
int n, m, q;

struct Op
{
    char cmd[2];
    int x, y;
} op[M];

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

void union_set( int x, int y )
{
    x = findf(x), y = findf(y);
    if ( x != y )
    {
        if ( s[x].size() > s[y].size() ) swap( x, y );
        f[x] = y;
        for ( multiset<int>::iterator it = s[x].begin(); it != s[x].end(); it++ )
        {
            s[y].insert( *it );
        }
        s[x].clear();
    }
}

int main ()
{
    int _case = 1;
    while ( scanf("%d%d%d", &n, &m, &q) != EOF )
    {
        for ( int i = 1; i <= n; i++ )
        {
            scanf("%d", &v[i]);
            edge[i].clear();
        }
        for ( int i = 1; i <= m; i++ )
        {
            int u, v;
            scanf("%d%d", &u, &v);
            if ( u > v ) swap( u, v );
            edge[u].insert(v);
        }
        for ( int i = 1; i <= q; i++ )
        {
            scanf("%s%d%d", &op[i].cmd, &op[i].x, &op[i].y);
            if ( op[i].cmd[0] == 'U' )
            {
                int tn = op[i].y;
                op[i].y = v[op[i].x];
                v[op[i].x] = tn;
            }
            else if ( op[i].cmd[0] == 'E' )
            {
                if ( op[i].x > op[i].y ) swap( op[i].x, op[i].y );
                edge[op[i].x].erase( edge[op[i].x].find(op[i].y) );
            }
        }
        for ( int i = 1; i <= n; i++ )
        {
            f[i] = i;
            s[i].clear();
            s[i].insert(v[i]);
        }
        for ( int i = 1; i <= n; i++ )
        {
            for ( multiset<int>::iterator it = edge[i].begin(); it != edge[i].end(); it++ )
            {
                union_set( i, (*it) );
            }
        }
        int cnt = 0, sum = 0;
        for ( int i = q; i >= 1; i-- )
        {
            if ( op[i].cmd[0] == 'F' )
            {
                cnt++;
                int x = op[i].x, y = op[i].y;
                x = findf(x);
                multiset<int>::iterator it = s[x].lower_bound(y);
                if ( it != s[x].end() )
                {
                    sum += (*it);
                }
            }
            else if ( op[i].cmd[0] == 'U' )
            {
                int x = op[i].x, y = op[i].y;
                int fx = findf(x);
                multiset<int>::iterator it = s[fx].find(v[x]);
                s[fx].erase(it);
                s[fx].insert(y);
                v[x] = y;
            }
            else
            {
                union_set( op[i].x, op[i].y );
            }
        }
        double avg = ( sum * 1.0 ) / ( cnt * 1.0 );
        printf("Case %d: %.3f
", _case++, avg);
    }
    return 0;
}