<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:
typedef pair<int,int> pii;
vector<int> dp;

    pii dfs(vector<int> adj[], int node, int wt, int par){
        int cnt = 0;
        int totalWt = wt;

        for(int nbr : adj[node]){
            if(nbr != par){
                auto pair = dfs(adj, nbr, wt+1, node);
                cnt += pair.first;
                totalWt += pair.second;
            }
        }

        dp[node] = cnt + 1;
        return {dp[node], totalWt};
    }
public:
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        dp.resize(n,0);
        vector<int> adj[n];
        for(auto edge : edges){
            int u = edge[0];
            int v = edge[1];
            adj[u].push_back(v);
            adj[v].push_back(u);
        }
        
        vector<int> ans(n,0);
        int wt = 0;
        auto pair = dfs(adj, 0, wt, -1);

        ans[0] = pair.second;

        queue<pii> q;
        q.push({0,ans[0]});
        vector<bool> vis(n,0);
        vis[0] = 1;

        while(!q.empty()){
            int fNode = q.front().first;
            int dist = q.front().second;
            q.pop();

            for(int nbr : adj[fNode]){
                if(!vis[nbr]){
                    int total = dist - dp[nbr] + (n-dp[nbr]);
                    ans[nbr] = total;
                    q.push({nbr, total});
                    vis[nbr] = 1;
                }
            }
        }

        return ans;
    }
};
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