<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:

    void dfs(vector<vector<int>>&g,vector<int>&vis,vector<int>&dp, vector<int>&c, int i){
        vis[i]=1;
        int ans=0;
        
        for(auto it: g[i]){
            if(vis[it]==0){
               dfs(g,vis,dp,c,it);
               c[i]+= (1+ c[it]);
               ans+= dp[it];
            }
        }
        
        dp[i]= c[i]+ ans;
        return;
    }

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

        vector<int>vis(n,0);
        vector<int>dp(n,0);
        vector<int>c(n,0);
         dfs(g,vis,dp,c,0);

        queue<pair<int,int>>q;

        q.push({0,-1});
        for(auto &it: vis) it=0;

        while(!q.empty()){
            auto it= q.front();
            q.pop();
            int curr= it.first;
            int par= it.second;

            if(par!= -1){
                int dis= dp[par]-( dp[curr]+ c[curr]+1);
                int rem_c= n- (c[curr]+1);
                dp[curr]+= dis+ rem_c;
            }

            vis[curr]=1;
            for(auto next: g[curr]){
                
                if(vis[next]==0){
                    q.push({next,curr});
                }
            }

        }

        return dp;


    }
};
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