<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:
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        unordered_map<int, vector<int>> adj={};
        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]);
        }

        vector<int> parent(n);
        parent[0] = -1;

        vector<int> numchildreninc(n, 1);
        vector<int> visited(n, 0);

        stack<vector<int>> s;
        int rootdists = 0;
        s.push({0, 0});
        while(s.size()>0){
            vector<int> node = s.top();
            visited[node[0]] = 1;
            for(auto nbr: adj[node[0]])
                if(visited[nbr]==0){
                    parent[nbr] = node[0];
                    s.push({nbr, node[1]+1});
                }

            if(s.top()==node){
                rootdists += node[1];
                s.pop();
                visited[node[0]] = 2;

                for(auto nbr: adj[node[0]]){
                    if(visited[nbr]==2)
                        numchildreninc[node[0]] += numchildreninc[nbr];
                }
            }
        }

        // BFS
        queue<int> q;
        q.push(0);
        visited = vector<int>(n, 0);
        vector<int> ans(n, 0);
        ans[0] = rootdists;

        while(q.size()>0){
            int node = q.front();
            visited[node]=1;
            q.pop();

            for(auto nbr: adj[node])
                if(visited[nbr]==0){
                    ans[nbr] = ans[node]-2*numchildreninc[nbr] + n;
                    q.push(nbr);
                }
        }
        return ans;
    }
};
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