C++ :

#include <bits/stdc++.h>
using namespace std;

const int N = 2e5 + 9, M = 4e5 + 9;
int n, len;
int h[N], to[M], wt[M], ne[M], idx;
void add(int u, int v, int w) {
	++ idx; to[idx] = v; wt[idx] = w; ne[idx] = h[u]; h[u] = idx;
}

int d[N];
void dfs(int u, int fa) {
	for (int i = h[u]; i; i = ne[i]) {
		int v = to[i], w = wt[i];
		if (v == fa) continue;
		
		dfs(v, u);
		len = max(len, d[u] + d[v] + w);
		d[u] = max(d[u], d[v] + w);
	}
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i < n; i ++) {
		int u, v, w;
		scanf("%d %d %d", &u, &v, &w);
		add(u, v, w); add(v, u, w);
	}
	
	dfs(1, 0);
	cout << 10 * len + len * (len + 1) / 2;

	return 0;
}

Java :

import java.io.*;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Map;
import java.util.Queue;

/**
 * @author yale.liu
 * @since 2022/8/31 10:34
 */
public class Main {

    static int MAX_N ;
    static int h[],to[],next[],cost[];
    static int idx;
    static int max;
    static int i1,i2;
    static int[] ans;

    public static void main(String[] args) throws IOException {


        StreamTokenizer in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));

//         new BufferedReader(new InputStreamReader(System.in))
        in.nextToken();
        int n = (int)in.nval;

        MAX_N = 2*n +1;
        h = new int[MAX_N];
        Arrays.fill(h,-1);
        to = new int[MAX_N];
        next = new int[MAX_N];
        cost = new int[MAX_N];
        ans = new int[MAX_N];
        for (int i = 0; i < n-1; i++) {
            in.nextToken();
            int a =(int)in.nval;
            in.nextToken();
            int b =(int)in.nval;
            in.nextToken();
            int c =(int)in.nval;
            insert(a,b,c);
            insert(b,a,c);
        }

        dfs(1,-1,0);
        max=0;
        dfs2(i1,-1,0);
        System.out.println(ans[i2]);

    }

    private static void dfs(int root, int fa, int dep){
        if (dep>max){
            max = dep;
            i1 = root;
        }
        for (int i = h[root]; i !=-1 ; i=next[i]) {
            if (to[i] == fa) continue;
            dfs(to[i],root,dep+cost[i]);
        }
    }

    private static void dfs2(int root, int fa, int dep){
        if (dep>max){
            max = dep;
            i2 = root;
            ans[root] = dep*10+ (int)((1+dep)*(dep/2.0));
        }
        for (int i = h[root]; i !=-1 ; i=next[i]) {
            if (to[i] == fa) continue;
            dfs2(to[i],root,dep+cost[i]);
        }


    }


    private static void insert(int a, int b, int c){
        to[idx] = b;
        cost[idx] = c;
        next[idx] = h[a];
        h[a] = idx;
        idx++;
    }
}