<p>There is an undirected connected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code> and <code>n - 1</code> edges.</p>

<p>You are given the integer <code>n</code> and the array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p>

<p>Return an array <code>answer</code> of length <code>n</code> where <code>answer[i]</code> is the sum of the distances between the <code>i<sup>th</sup></code> node in the tree and all other nodes.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-sumdist1.jpg" style="width: 304px; height: 224px;" />
<pre>
<strong>Input:</strong> n = 6, edges = [[0,1],[0,2],[2,3],[2,4],[2,5]]
<strong>Output:</strong> [8,12,6,10,10,10]
<strong>Explanation:</strong> The tree is shown above.
We can see that dist(0,1) + dist(0,2) + dist(0,3) + dist(0,4) + dist(0,5)
equals 1 + 1 + 2 + 2 + 2 = 8.
Hence, answer[0] = 8, and so on.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-sumdist2.jpg" style="width: 64px; height: 65px;" />
<pre>
<strong>Input:</strong> n = 1, edges = []
<strong>Output:</strong> [0]
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-sumdist3.jpg" style="width: 144px; height: 145px;" />
<pre>
<strong>Input:</strong> n = 2, edges = [[1,0]]
<strong>Output:</strong> [1,1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>edges.length == n - 1</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>The given input represents a valid tree.</li>
</ul>

class Solution {
public:
    array<int, 2>  dfs(int node, int par, vector<int> &vis, vector<int> &parent,
     vector<int> &val, vector<int> &size, vector<vector<int>> &adj) {
        parent[node] = par;
        vis[node] = 1;
        int f_val = 0;
        int f_size = 1;
        for (auto it : adj[node]) {
            if (vis[it] == 0) {
                auto m_ans = dfs(it, node, vis, parent, val, size, adj);
                f_val = f_val + m_ans[0] + m_ans[1];
                f_size = f_size + m_ans[1];
            }
        }
        val[node] = f_val;
        size[node] = f_size;
        return {f_val, f_size};
    }
    
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        vector<int> parent(n, -1);
        vector<int> size(n);
        vector<int> val(n), vis(n), vis1(n);
        vector<vector<int>> adj(n);
        for (auto edge : edges) {
            int u = edge[0];
            int v = edge[1];
            adj[u].push_back(v);
            adj[v].push_back(u);
        }
        vector<int> ans(n);
        auto z_ans = dfs(0, -1, vis, parent, val, size, adj);
        // cout<<"val --->  "<<endl;
        // for (auto it : val) cout<<it<<"  ";
        // cout<<endl;

        // cout<<"size --->  "<<endl;
        // for (auto it : size) cout<<it<<"  ";
        // cout<<endl;

        // cout<<"parent --->  "<<endl;
        // for (auto it : parent) cout<<it<<"  ";
        // cout<<endl;


        int total = z_ans[1];
        ans[0] = z_ans[0];
        queue<int> q;
        q.push(0);
        vis1[0] = 1;
        // cout<<"vis1 --> "<<endl;
        // for (auto it : vis1) cout<<it<<"  ";
        // cout<<endl;
        while(!q.empty()) {
            int node = q.front();
            // cout<<node<<"  ";
            q.pop();
            if (parent[node] != -1) {
                ans[node] = ans[parent[node]] + total - (2 * size[node]);
            }
            for (auto it : adj[node]) {
                if (vis1[it] == 0) {
                    vis1[it] = 1;
                    q.push(it);
                }
            }
        }
        cout<<endl;

        return ans;
    }
};
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