<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:
pair<int,int> f(int node , int parent,vector<int>&children, vector<int>&sum,vector<int> adj[]){

    pair<int,int> curr ;
    for(auto it : adj[node]){
        if(it==parent){
            continue;
        }

        pair<int,int> child = f(it,node,children,sum,adj);
        children[node] += child.first;
        sum[node] += child.first + child.second;
    }

    curr.first = children[node];
    curr.second = sum[node];
    return curr;

}
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {

        vector<int> adj[n];
        for(auto it :edges){
            adj[it[0]].push_back(it[1]);
            adj[it[1]].push_back(it[0]);
        }

        vector<int> children(n,1);
        vector<int> sum(n,0);
        pair<int,int> info = f(0,-1,children,sum,adj);
        vector<int> ans(n);
        ans[0] = info.second;
      queue<pair<int,int>> q;
      q.push({0,-1});
      while(!q.empty()){
        int size = q.size();
        while(size--){
            int node = q.front().first;
            int parent  = q.front().second;
            q.pop();
            for(auto it : adj[node]){
                if(it==parent){
                    continue;
                }

                ans[it] = ans[node] - children[it] + (n-children[it]);
                q.push({it,node});
            }
        }


      }
      return ans;


        
    }
};
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