<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>

from typing import List


class Solution:
    def __init__(self):
        self.num_nodes = 0
        self.adjacency_list = []
        self.subtree_size = []
        self.subtree_distance_sum = []
        self.result = []

    def sumOfDistancesInTree(self, n: int, edges: List[List[int]]) -> List[int]:
        """
        Returns the sum of distances of all nodes in a tree.
        """
        self.initialize_tree(n, edges)
        self.calculate_subtree_sizes_and_distances(0, -1)
        self.calculate_result(0, -1, 0)
        return self.result

    def initialize_tree(self, num_nodes, edges):
        """
        Initializes the adjacency list and related lists for the tree.
        """
        self.num_nodes = num_nodes
        self.adjacency_list = [[] for _ in range(self.num_nodes)]
        self.subtree_size = [0] * self.num_nodes
        self.subtree_distance_sum = [0] * self.num_nodes
        self.result = [0] * self.num_nodes

        for edge in edges:
            self.adjacency_list[edge[0]].append(edge[1])
            self.adjacency_list[edge[1]].append(edge[0])

    def calculate_subtree_sizes_and_distances(self, current_node, parent_node):
        """
        First DFS to calculate subtree sizes and distance sums for each node.
        """
        for neighbor in self.adjacency_list[current_node]:
            if neighbor != parent_node:
                self.calculate_subtree_sizes_and_distances(neighbor, current_node)
                self.subtree_size[current_node] += self.subtree_size[neighbor]
                self.subtree_distance_sum[current_node] += (
                    self.subtree_distance_sum[neighbor] + self.subtree_size[neighbor]
                )
        self.subtree_size[current_node] += 1

    def calculate_result(self, current_node, parent_node, parent_contribution):
        """
        Second DFS to calculate the result for each node based on the contributions
        from the parent node and the subtree distance sums.
        """
        self.result[current_node] = (
            self.subtree_distance_sum[current_node]
            + parent_contribution
            + (self.num_nodes - self.subtree_size[current_node])
        )

        for neighbor in self.adjacency_list[current_node]:
            if neighbor != parent_node:
                new_parent_contribution = (
                    self.result[current_node]
                    - self.subtree_distance_sum[neighbor]
                    - self.subtree_size[neighbor]
                )
                self.calculate_result(neighbor, current_node, new_parent_contribution)
36650