<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>

constexpr int MAX = 30010;

int dp[MAX][2];
std::vector<int> adj[MAX];

void DFS1(int x, int p) {
  dp[x][0] = 1;
  dp[x][1] = 0;
  for (int y : adj[x]) {
    if (y != p) {
      DFS1(y, x);
      dp[x][0] += dp[y][0];
      dp[x][1] += dp[y][0] + dp[y][1];
    }
  }
}

void DFS2(int x, int p, int c0, int c1, int* ret) {
  ret[x] = dp[x][1] + c0 + c1;
  for (int y : adj[x]) {
    if (y != p) {
      int v0 = dp[x][0] - dp[y][0] + c0;
      int v1 = dp[x][1] - dp[y][0] - dp[y][1] + c0 + c1;
      DFS2(y, x, v0, v1, ret);
    }
  }
}

class Solution {
public:
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
      for (int i = 0; i < n; ++i) {
        adj[i].clear();
      }
      for (const auto& e : edges) {
        int u = e[0], v = e[1];
        adj[u].push_back(v);
        adj[v].push_back(u);
      }
      std::vector<int> ret(n);
      DFS1(0, -1);
      DFS2(0, -1, 0, 0, ret.data());
      return ret;
    }
};
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