<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 {
private:
    int root_cst=0;
    int n_;
    int recursion(int i,int parent,unordered_map<int,vector<int>>&adj,unordered_map<int,int>&cnt,int curr_depth)
    {
        int ans=1;
        root_cst+=curr_depth;

        for (auto x : adj[i]) {
            if (x != parent) {
                ans += recursion(x, i, adj, cnt,curr_depth+1);
            }
        }

        return cnt[i]=ans;
    }

    void recursion2(int i,int parent,unordered_map<int,vector<int>>&adj,unordered_map<int,int>&cnt,vector<int>&ans)
    {
        for (auto& x : adj[i]) {
            if (x != parent) {
                // Recalculate the sum of distances for the child node
                ans[x] = ans[i] - cnt[x] + (n_ - cnt[x]);
                recursion2(x, i, adj, cnt, ans); // Recurse for the child
            }
        }

    }
public:
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        n_=n;
        vector<int>ans(n,-1);
        unordered_map<int,vector<int>>adj;

        for(auto &x:edges)
        {
            adj[x[0]].push_back(x[1]);
            adj[x[1]].push_back(x[0]);
        }

        unordered_map<int,int>cnt;

        recursion(0,-1,adj,cnt,0);

        // vector<int>ans(n,0);
        ans[0]=root_cst;

        recursion2(0,-1,adj,cnt,ans);
        return ans;
        
    }
};
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