Count the Number of Good Nodes
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3249.Count%20the%20Number%20of%20Good%20Nodes/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3249.Count%20the%20Number%20of%20Good%20Nodes/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3249.Count%20the%20Number%20of%20Good%20Nodes/images/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>
Tree; Depth-First Search
class Solution {
public:
    int countGoodNodes(vector<vector<int>>& edges) {
        int n = edges.size() + 1;
        vector<int> g[n];
        for (const auto& e : edges) {
            int a = e[0], b = e[1];
            g[a].push_back(b);
            g[b].push_back(a);
        }
        int ans = 0;
        auto dfs = [&](this auto&& dfs, int a, int fa) -> int {
            int pre = -1, cnt = 1, ok = 1;
            for (int b : g[a]) {
                if (b != fa) {
                    int cur = dfs(b, a);
                    cnt += cur;
                    if (pre < 0) {
                        pre = cur;
                    } else if (pre != cur) {
                        ok = 0;
                    }
                }
            }
            ans += ok;
            return cnt;
        };
        dfs(0, -1);
        return ans;
    }
};
