<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 Graph{
    public:
    int n;
    vector<vector<int>> adj;
    vector<bool> visited;
    vector<int> subtree_sizes;
    vector<int> subtree_distances;
    vector<int> parents;
    vector<int> distances;

    Graph (int V){
        this->n=V;
        adj=vector<vector<int>>(V);
        visited=vector<bool>(V, false);
        subtree_sizes=vector<int>(V, 0);
        subtree_distances=vector<int>(V,0);
        parents=vector<int>(V,0);
        distances=vector<int>(V,0);
    }

    void addEdge(int a, int b){
        adj[a].push_back(b);
        adj[b].push_back(a);
    }

    void fill_subtree_sizes(int root){
        int sum=1;
        int subtree_dist=0;
        visited[root]=true;
        for (int a: adj[root]){
            if (!visited[a]){
                fill_subtree_sizes(a);
                sum+=subtree_sizes[a];
                subtree_dist+=subtree_distances[a]+subtree_sizes[a];
                parents[a]=root;
            }
        }
        subtree_sizes[root]=sum;
        subtree_distances[root]=subtree_dist;
    }

    int return_answer(int root){
        if (root!=0){
            distances[root]=distances[parents[root]]+n-2*subtree_sizes[root];
        }
        visited[root]=true;
        for (int a: adj[root]){
            if (!visited[a]){
                return_answer(a);
            }
        }
        // cout << distances[root] << "\n";
        return distances[root];
    }
};

class Solution {
public:
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        Graph g(n);
        for (vector<int> a: edges){
            g.addEdge(a[0], a[1]);
        }
        g.fill_subtree_sizes(0);
        g.visited.clear();
        g.visited.resize(n, false);
        g.distances[0]=g.subtree_distances[0];
        g.return_answer(0);
        return g.distances;
    }
};
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