<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 {
private:
    pair<int, int> dfs(int n, unordered_map<int, vector<int>>& adj_list, vector<int>& nodes_encountered, vector<int>& res, vector<bool>& visited){
        if (visited[n]){
            return {0, 0};
        }
        visited[n] = true;

        int nodes = 0;
        int dist = 0;

        for(int next: adj_list[n]){
            if (!visited[next]){
                pair<int, int> sub = dfs(next, adj_list, nodes_encountered, res, visited);
                nodes += sub.first + 1;
                dist += sub.second + sub.first + 1;
            }
        }
        res[n] = dist;
        nodes_encountered[n] = nodes + 1;
        return {nodes, dist};
    }

    void second_dfs(int n, int p, unordered_map<int, vector<int>>& adj_list, vector<int>& nodes_encountered, vector<int>& res, vector<bool>& visited, int total){
        res[n] = res[p] + (-nodes_encountered[n] + (total - nodes_encountered[n]));
        visited[n] = true;
        for (int next: adj_list[n]){
            if (!visited[next]){
                second_dfs(next, n, adj_list, nodes_encountered, res, visited, total);
            }
        }
    }
public:
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        unordered_map<int, vector<int>> adj_list;

        vector<int> res(n, 0);
        vector<int> nodes_encountered(n, 0);
        vector<bool> visited(n, false);

        for (vector<int> edge: edges){
            adj_list[edge[0]].push_back(edge[1]);
            adj_list[edge[1]].push_back(edge[0]);
        }
        dfs(0, adj_list, nodes_encountered, res, visited);

        visited = vector<bool>(n, false);
        visited[0] = true;
        for (int second_level: adj_list[0]){
            second_dfs(second_level, 0, adj_list, nodes_encountered, res, visited, n);
        }
        return res;
    }
};
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