构造完全图---最小生成树

 

 

#include<cstring>
#include<iostream>
#include<cstdio>
#include<queue>
#include<algorithm>
#define maxn 200200
using namespace std;
typedef long long ll;
int par[maxn];
ll num[maxn];
int find(int x) {
	if (par[x] == -1) return x;
	return par[x] = find(par[x]);
}
int n, m;
struct Node {
	int be, en;
	ll len;
}que[maxn];
bool bml(Node a, Node b) {
	return a.len < b.len;
}
int main() {
	memset(par, -1, sizeof(par));
	scanf("%d", &n);
	for (int i = 0; i <= n; i++) num[i] = 1;
	for (int i = 0; i < n - 1; i++) {
		scanf("%d %d %lld", &que[i].be, &que[i].en,&que[i].len);
	}
	sort(que, que + n - 1,bml);
	long long ans = 0;
	for (int i = 0; i < n - 1; i++) {
		int a = find(que[i].be);
		int b = find(que[i].en);
		if (a != b) {
			par[a] = b;
	
			ans += (num[a] * num[b] - 1)*(que[i].len + 1);
			ans += que[i].len;
			num[b] += num[a];
		}
	}
     
	printf("%lld\n", ans);
	return 0;
}