<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 dfs(int n, vector<int>& depth, vector<int>& visited, int node, vector<vector<int>>& mat, vector<int>& parent, int count,vector<int>& treesize) {
    visited[node] = 1;
    treesize[node]=1;

    for (auto k : mat[node]) {
        if (!visited[k]) {
            parent[k] = node;  
            dfs(n, depth, visited, k, mat, parent, count + 1,treesize); 
            treesize[node]+=treesize[k];
            
        }
    
    depth[node] = count; 
    }
}
    
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        vector<int> v(n);
        vector<vector<int>> mat(n);
        for(int i=0;i<n-1;i++){
            int u=edges[i][0];
            int v=edges[i][1];
            mat[u].push_back(v);
            mat[v].push_back(u);
        }
        vector<int> parent(n,-1);
        vector<int> depth(n,0);
        vector<int> visited(n,0);
        vector<int> treesize(n);
        parent[0]=-1;
        dfs(n,depth,visited,0,mat,parent,0,treesize);
        vector<int> dp(n,0);
        // for(int i=0;i<n;i++){
        //     printf("dep=%d",depth[i]);
        // }
        for(int i=1;i<n;i++){
            dp[0]+=depth[i];
        }
         std::fill(visited.begin(),visited.end(),0);
       queue<int> q;

    // Start BFS from the root (node 0 in this case)
    q.push(0);
    visited[0] = 1;

    while (!q.empty()) {
        int node = q.front();
        q.pop();

        for (auto k : mat[node]) {
            if (!visited[k]) {
                visited[k] = 1;
                q.push(k);
                
                
                dp[k] = dp[node] - treesize[k] + (n - treesize[k]);
            }
        }
    }
        return dp;
    }
};
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