<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> dfs_1 (int node , map<int , vector<int>>  & adj_list  , vector<pair<int , int>> & temp , int par){
        // cout<<node<<endl ; 
        vector<int> v = adj_list[node] ; 

        int count = 0 ; 
        int sum = 0 ; 

        for(int j=0 ; j<v.size() ; j++){
            if (v[j]!=par){
                pair<int  , int> p = dfs_1(v[j] , adj_list , temp , node) ; 
                count +=p.second ; 
                sum +=p.first ; 
            }
        }

        sum +=count ; 
        temp[node] = {sum , count+1} ; 

        return {sum , count+1} ; 
    }
    void dfs_2(int node , map<int , vector<int>> & adj_list  , vector<pair<int , int>> & temp , vector<int> & ans , int par , int n ){
       
        vector<int> v = adj_list[node] ; 

        if(par ==-1){
            ans[node] = temp[node].first ; 
        }
        else{
            ans[node] = ans[par] - (temp[node].first + temp[node].second) + (n-temp[node].second) + temp[node].first ; 
        }

        for(int j=0 ; j<v.size() ; j++){
            if (v[j]!=par){
                dfs_2(v[j] , adj_list , temp , ans , node , n) ; 
            }
        }
    }
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        
        

        map<int  , vector<int>> adj_list ; 

        for(int j=0 ; j<edges.size() ; j++){
            adj_list[edges[j][0]].push_back(edges[j][1]) ; 
            adj_list[edges[j][1]].push_back(edges[j][0]) ; 
        }

        vector<pair<int , int>> temp (n) ; 

        vector<int> ans(n) ; 


        dfs_1(0 ,adj_list , temp , -1 )  ;

        // cout<<"hello"<<endl ;

        dfs_2(0 , adj_list , temp , ans  , -1 , n) ;  

        return ans ; 







    }
};
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