牛客国庆 Day4 H 巧妙的用树的直径！！

传送门  https://ac.nowcoder.com/acm/contest/1109#question

刚开始吓得我以为要搞树分治，差点就捞了哦！

 

 这个定理要铭记于心啊！！！

#include<cstring>
#include<iostream>
#include<queue>
#include<algorithm>
#include<cstdio>
#define maxn 100010
using namespace std;
typedef long long ll;
int n, m;
struct Node {
	int p;
	int len;
	Node(int a, int b) :p(a), len(b) {}
};
vector<Node>G[maxn];
void insert(int be, int en, int len) {
	G[be].push_back(Node(en, len));
}
ll dis[maxn];
ll dis1[maxn];
ll dis2[maxn];
int dfs(int x, ll dep, int fa, ll d[]) {
	d[x] = dep;
	for (int i = 0; i < G[x].size(); i++) {
		int p = G[x][i].p;
		if (p == fa) continue;
		dfs(p, dep + G[x][i].len, x, d);
	}
	return 0;
}
int main() {
	while (~scanf("%d", &n)) {
		int be, en, len;
		for (int i = 0; i < n - 1; i++){
			scanf("%d %d %d", &be, &en, &len);
			insert(be, en, len);
			insert(en, be, len);
		}
		int s=1, t=1;
		dfs(1, 0, -1, dis);
		for (int i = 1; i <= n; i++) {
			if (dis[i] > dis[s]) s = i;
		}
		dfs(s, 0, -1, dis1);//dis1从s开始
		for (int i = 1; i <= n; i++) {
			if (dis1[i] > dis1[t]) t = i;
		}
		//t从s开始
		dfs(t, 0, -1, dis2);
		ll ans = 0;
		for (int i = 1; i <= n; i++) {
			ans += max(dis1[i], dis2[i]);
		}
		ans -= dis1[t];
		printf("%lld\n", ans);
		for (int i = 0; i < maxn; i++)  G[i].clear();
	}
	return 0;
}