<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<vector<int>>adj;
    vector<int>vis;
    map<pair<int,int>,int>mp;
    vector<int>dist;
    vector<int>ans;
    int N;

    int dfs(int u){
        // cout<<u<<" !! ";
        vis[u]=1;
        int val = 0;
        int val2=0;
        for(auto x : adj[u]){
            if(!vis[x]){
                val2 = dfs(x);
                mp[{x,u}]=val2;
                mp[{u,x}]=val2;
                val+=val2;
            }
            
        }
        val++;
        return val;
    }

    void dfsUtil(int u,int p){
        // cout<<u<<" %% "<<p<< "$$ ";
        if(u!=0){
            // cout<<mp[{p,u}]<<" ^^ ";
            ans[u] = (ans[p]-mp[{p,u}]+N-mp[{p,u}]);
        }
        vis[u]=1;
        for(auto x : adj[u]){
            if(!vis[x])
                dfsUtil(x,u);
        }
    }
    
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        adj.resize(n);
        dist.resize(n,INT_MAX);
        N=n;
        ans.resize(n,0);
        vis = vector<int>(n,0);
        for(auto x : edges){
            adj[x[0]].push_back(x[1]);
            adj[x[1]].push_back(x[0]);
        }

        dfs(0);
        

        priority_queue<int,vector<int>,greater<int>>pq;
        pq.push(0);
        dist[0]=0;
        vis = vector<int>(n,0);
        while(!pq.empty()){
            int u = pq.top();
            pq.pop();
            if(vis[u])
                continue;
            vis[u]=1;
            for(auto x : adj[u]){
                if(dist[x]>dist[u]+1){
                    dist[x]=dist[u]+1;
                    pq.push(x);
                }
            }
        }
        // for(auto x : dist)
        //     cout<<x<< "## ";
        cout<<endl;
        int val= 0;
        for(auto x : dist)
            val+=x;
        ans[0] = val;
        
        vis = vector<int>(n,0);
        dfsUtil(0,0);
        return ans;
    }
};
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