<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:

    // Traverse from 0 store count of children at each node
    int storeCnt(unordered_map<int,list<int>> &adj,vector<int> &cnt, int parent, int node) {
        int ans = 0;
        for(auto v: adj[node]) {
            if(v!=parent) {
                ans += storeCnt(adj,cnt,node,v);
            }
        }
        cnt[node] = ans+1;
        return ans+1;
    }
    
    // calculate answer for 0
    int calcDis(unordered_map<int,list<int>> &adj,int n) {
        int sumDis = 0;
        queue<pair<int,int>> q;
        q.push({0,0});
        vector<bool> vis(n,0); vis[0] = 1;
        while(!q.empty()) {
            auto node = q.front(); q.pop();
            int u = node.first, dis = node.second;
            sumDis+=dis;
            for(auto v: adj[u]) {
                if(!vis[v]) {
                    q.push({v,dis+1});
                    vis[v] = 1;
                }
            }
        }
        return sumDis;
    }

    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        unordered_map<int,list<int>> adj;
        for(auto e: edges) {
            adj[e[0]].push_back(e[1]);
            adj[e[1]].push_back(e[0]);
        }

        vector<int> cnt(n,0);
        storeCnt(adj,cnt,-1,0);

        vector<int> dis(n);
        dis[0] = calcDis(adj,n);

        queue<pair<int,int>> q;
        q.push({0,-1});
        vector<int> vis(n,0); vis[0] = 1;

        // Use parent to find result for children
        while(!q.empty()) {
            auto front = q.front(); q.pop();
            int u = front.first, parent = front.second;
            
            int myFamily = cnt[u];
            int others = n - cnt[u];

            if(parent!=-1) {  // handling root node
                dis[u] = dis[parent] - myFamily + others;
            }

            for(auto v: adj[u]) {
                if(!vis[v]) {
                    q.push({v,u});
                    vis[v] = 1;
                }
            }
        }

        return dis;
    }
};
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