<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 find_children(int node, map<int, list<int>> &mp, vector<int> &noc, int parent){
        // if(mp[node].size()==1 && mp[node].front()==parent){
        //     noc[node]=1;
        //     return;
        // }

        for(auto nodes:mp[node]){
            if(nodes!=parent){
                find_children(nodes, mp, noc, node);
                noc[node]+=noc[nodes];
            }
        }
        return;
        
    }

    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        // map<int, list<int>> mp;
        // for(int i=0; i<edges.size(); i++){
        //     mp[edges[i][0]].push_back(edges[i][1]);
        //     mp[edges[i][1]].push_back(edges[i][0]);
        // }
        // vector<int> ans(n,0);
        // for(int i=0; i<n; i++){
        //     map<int,int>parent;
        //     for(int i=0; i<n; i++){
        //         parent[i]=-1;
        //     }
        //     queue<int> q;
        //     for(auto node:mp[i]){
        //         parent[node]=i;
        //         q.push(node);
        //     }
        //     int num=1;
        //     while(!q.empty()){
        //         int qsize=q.size();
        //         ans[i]+=num*qsize;
        //         for(int j=0; j<qsize; j++){
        //             int f=q.front();
        //             q.pop();
        //             for(auto node:mp[f]){
        //                 if(node==parent[f]) continue;
        //                 parent[node]=f;
        //                 q.push(node);
        //             }
        //         }
        //         num++;
        //     }
        // }
        // return ans;


        map<int, list<int>> mp;
        for(int i=0; i<edges.size(); i++){
            mp[edges[i][0]].push_back(edges[i][1]);
            mp[edges[i][1]].push_back(edges[i][0]);
        }

        vector<int> children(n,1);
        find_children(0, mp, children, -1);
    
        vector<int> ans(n,0);
        map<int,int>parent;
        for(int i=0; i<n; i++){
            parent[i]=-1;
        }
        queue<int> q;
        for(auto node:mp[0]){
            parent[node]=0;
            q.push(node);
        }
        int num=1;
        while(!q.empty()){
            int qsize=q.size();
            ans[0]+=num*qsize;
            for(int j=0; j<qsize; j++){
                int f=q.front();
                q.pop();
                for(auto node:mp[f]){
                    if(node==parent[f]) continue;
                    parent[node]=f;
                    q.push(node);
                }
            }
            num++;
        }

        for(auto node:mp[0]){
            q.push(node);
        }
        while(!q.empty()){
            int qsize=q.size();
            for(int j=0; j<qsize; j++){
                int f=q.front();
                q.pop();
                ans[f]=ans[parent[f]]-children[f]+(n-children[f]);
                for(auto node:mp[f]){
                    if(node==parent[f]) continue;
                    q.push(node);
                }
            }
        }
        return ans;
    }
};
140018