<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<bool> vis;
    vector<vector<int>> adj;
    vector<pair<int, int>> dist;
    void dfs(int i) {
        vis[i] = true;
        for (auto node : adj[i]) {
            if (!vis[node]) {
                dfs(node);
                if (dist[node].first == 0) {
                    dist[i].first += 1;
                    dist[i].second += 1;
                } else {
                    dist[i].first += (dist[node].first + 1);
                    dist[i].second +=
                        (dist[node].first + dist[node].second + 1);
                }
            }
        }
    }
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        adj.resize(n);
        vis.resize(n, false);
        // (count_nodes, distance_sum)
        dist.resize(n, {0, 0});
        for (auto edge : edges) {
            adj[edge[0]].push_back(edge[1]);
            adj[edge[1]].push_back(edge[0]);
        }
        dfs(0);
        vector<int> ans(n, 0);
        // (node, parent)
        queue<pair<int, int>> q;
        q.push({0, 0});
        while (!q.empty()) {
            int x = q.size();
            while (x--) {
                auto fr = q.front();
                q.pop();
                if (dist[fr.first].first < (n - 1)) {
                    ans[fr.first] =
                        dist[fr.second].first - 2*dist[fr.first].first - 1 +
                        dist[fr.second].second;
                    dist[fr.first].first = n-1;
                    dist[fr.first].second = ans[fr.first];
                } else {
                    ans[fr.first] = dist[fr.first].second;
                }
                for (auto node: adj[fr.first]) {
                    if (node != fr.second) q.push({node, fr.first});
                }
            }
        }
    return ans;
    }
}
;
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