<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 helper(int curr,vector<pair<int,int>> &dp,vector<int> &parent,vector<vector<int>> &adj){
        int ans = 0;
        int num = 0;
        for(auto i:adj[curr]){
            if(i == parent[curr]){
                continue;
            }
            parent[i] = curr;
            helper(i,dp,parent,adj);
            ans += dp[i].first;
            num += dp[i].second;
        }
        ans += num;
        num += 1;
        dp[curr] = make_pair(ans,num);
    }

    void helper2(int curr,vector<pair<int,int>> &dp,vector<int> &parent,vector<vector<int>> &adj){
        if(parent[curr] != -1){
            int other_num = dp[parent[curr]].second - dp[curr].second;
            int other_ans = dp[parent[curr]].first - dp[curr].first - dp[curr].second;
            dp[curr].second += other_num;
            dp[curr].first += other_ans + other_num;
        }

        for(auto i:adj[curr]){
            if(parent[curr] == i){
                continue;
            }
            helper2(i,dp,parent,adj);
        }
    }

    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        vector<pair<int,int>> dp(n,pair<int,int>(0,0));
        vector<int> parent(n);
        vector<vector<int>> adj(n,vector<int>());
        for(int i=0;i<edges.size();i++){
            adj[edges[i][0]].push_back(edges[i][1]);
            adj[edges[i][1]].push_back(edges[i][0]);
        }
        parent[0] = -1;
        helper(0,dp,parent,adj);
        helper2(0,dp,parent,adj);

        vector<int> ans(n);
        for(int i=0;i<n;i++){
            ans[i] = dp[i].first;
        }

        return ans;
    }
};
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