1. 将所有边看成无向边
2. 枚举每一个点作为root的时候这棵树的权重
3. 求第二步 中的最小res

下面是dfs 和 bfs的实现

dfs：

#include <iostream>
#include <unordered_map>
#include <vector>
using namespace std;

class Solve {
   public:
    Solve(int _n) : n(_n), g(n + 1), vertexToWegeight(n + 1)
    {
        for (int i = 1; i <= n; ++i) {
            int a, b, w;
            cin >> w >> a >> b;
            vertexToWegeight[i] = w;
            if (a) g[i].push_back(a), g[a].push_back(i);
            if (b) g[i].push_back(b), g[b].push_back(i);
        }
    }

    void operator()()
    {
        int res = 0x3f3f3f3f;
        for (int i = 1; i <= n; ++i) {
            res = min(res, dfs(i, -1, 0));
        }
        cout << res << endl;
    }

   private:
   // 返回以 root为根结点，father为父节点的树
   // 的权重之和
    int dfs(int root, int father, int k)
    {
        int res = vertexToWegeight[root] * k; // 加上这个结点的值
        for (const auto v : g[root])
            if (v != father)                 // 不能往回走
                res += dfs(v, root, k + 1);  // 加上儿子结点的路径
        return res;
    }

   private:
    int n;
    vector<int> vertexToWegeight;
    vector<vector<int>> g;
};
int main()
{
    ios::sync_with_stdio(false);
    int n;
    cin >> n;

    Solve{n}();
    return 0;
}

bfs

#include <iostream>
#include <unordered_map>
#include <vector>
using namespace std;

class Solve {
   public:
    Solve(int _n) : n(_n), g(n + 1), vertexToWegeight(n + 1)
    {
        for (int i = 1; i <= n; ++i) {
            int a, b, w;
            cin >> w >> a >> b;
            vertexToWegeight[i] = w;
            if (a) g[i].push_back(a), g[a].push_back(i);
            if (b) g[i].push_back(b), g[b].push_back(i);
        }
    }

    void operator()()
    {
        int res = 0x3f3f3f3f;
        for (int i = 1; i <= n; ++i) {
            vector<int> q{i};
            vector<int> st(n + 1);
            st[i] = true;
            int w = 1;  // 每一层的权重
            int sub = 0;  // 这颗树 的权重和
            while (!q.empty()) {
                vector<int> tmp;
                for (const auto qi : q) {
                    for (const auto v : g[qi]) {  // 邻接点
                        if (!st[v]) {
                            tmp.push_back(v);
                            sub += vertexToWegeight[v] * w;
                            st[v] = true;
                        }
                    }
                }
                ++w;
                q = move(tmp);
            }
            // cout << sub << "sub  " << endl;
            res = min(sub, res);
        }
        cout << res << endl;
    }

   private:
    int n;
    vector<int> vertexToWegeight;
    vector<vector<int>> g;
};
int main()
{
    ios::sync_with_stdio(false);
    int n;
    cin >> n;

    Solve{n}();
    return 0;
}