1. 程式人生 > >Codeforces Round#250 D. The Child and Zoo(並差集)

Codeforces Round#250 D. The Child and Zoo(並差集)

思路:並差集應用,先對所有的邊從大到小排序,然後列舉邊的時候,如果某條邊的兩個頂點不在同一個集合中就合併,並且用一個sum記錄這兩個集合的大小,這樣這兩個集合中的每一對點都要經過這條邊,然後更新一下sum就可以了。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#define REP(i, a, b) for (int i = (a); i < (b); ++i)
#define FOR(i, a, b) for (int i = (a); i <= (b); ++i)
using namespace std;

const int MAX_N = (100000 + 100);

struct Edge {
	int u, v, w;
} edge[MAX_N << 1];

int cmp(const Edge &p, const Edge &q)
{
	return p.w > q.w;
}
int N, M, a[MAX_N], parent[MAX_N];
long long sum[MAX_N], ans;

int Find(int x)
{
	if (x == parent[x]) return x;
	return parent[x] = Find(parent[x]);
}

int main()
{
	cin >> N >> M;
	FOR(i, 1, N) cin >> a[i], parent[i] = i, sum[i] = 1;
	FOR(i, 1, M) {
		int u, v; cin >> u >> v;
		edge[i].u = u, edge[i].v = v, edge[i].w = min(a[u], a[v]);
	}
	sort(edge + 1, edge + M + 1, cmp);
	ans = 0;
	FOR(i, 1, M) {
		int r1 = Find(edge[i].u), r2 = Find(edge[i].v);
		if (r1 == r2) continue;
		parent[r1] = r2;
		ans += edge[i].w * sum[r1] * sum[r2];
		sum[r2] += sum[r1];
	}
	printf("%.7f\n", 2.0 * ans / (1.0 * N * (N - 1)));
	return 0;
}