<p>There is an <strong>undirected</strong> tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and rooted at node <code>0</code>. You are given a 2D integer array <code>edges</code> of length <code>n - 1</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>A node is <strong>good</strong> if all the <span data-keyword="subtree">subtrees</span> rooted at its children have the same size.</p>

<p>Return the number of <strong>good</strong> nodes in the given tree.</p>

<p>A <strong>subtree</strong> of <code>treeName</code> is a tree consisting of a node in <code>treeName</code> and all of its descendants.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]</span></p>

<p><strong>Output:</strong> <span class="example-io">7</span></p>

<p><strong>Explanation:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/05/26/tree1.png" style="width: 360px; height: 158px;" />
<p>All of the nodes of the given tree are good.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges = [[0,1],[1,2],[2,3],[3,4],[0,5],[1,6],[2,7],[3,8]]</span></p>

<p><strong>Output:</strong> <span class="example-io">6</span></p>

<p><strong>Explanation:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/06/03/screenshot-2024-06-03-193552.png" style="width: 360px; height: 303px;" />
<p>There are 6 good nodes in the given tree. They are colored in the image above.</p>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges = [[0,1],[1,2],[1,3],[1,4],[0,5],[5,6],[6,7],[7,8],[0,9],[9,10],[9,12],[10,11]]</span></p>

<p><strong>Output:</strong> <span class="example-io">12</span></p>

<p><strong>Explanation:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/08/08/rob.jpg" style="width: 450px; height: 277px;" />
<p>All nodes except node 9 are good.</p>
</div>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</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>The input is generated such that <code>edges</code> represents a valid tree.</li>
</ul>

from collections import defaultdict
from typing import List, Tuple


class Solution:
    def countGoodNodes(self, edges: List[List[int]]) -> int:
        graph = defaultdict(list)
        for a, b in edges:
            graph[a].append(b)
            graph[b].append(a)

        # OOPS HACK REALIZED THIS IS A NAST "UNDIRECTED" TREE
        visited = {0}

        def count_good_subtrees(node: int) -> Tuple[int, int]:
            """
            returns (total_nodes_count, good_nodes_count)
            """
            child_good_counts = []
            child_total_counts = []
            total_nodes_count = 1
            for child in graph[node]:
                if child in visited:
                    continue
                visited.add(child)

                child_total_count, child_good_node_count = count_good_subtrees(child)
                child_good_counts.append(child_good_node_count)
                child_total_counts.append(child_total_count)
                total_nodes_count += child_total_count

            sum_child_counts = sum(child_good_counts) if child_good_counts else 0
            this_node_is_good = len(set(child_total_counts)) <= 1

            if this_node_is_good:
                this_count = sum_child_counts + 1
            else:
                this_count = sum_child_counts

            # print(f'node: {node} this_count: {this_count}')
            return total_nodes_count, this_count

        return count_good_subtrees(0)[1]

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