3249 - Count the Number of Good Nodes.

Medium

There is an undirected tree with n nodes labeled from 0 to n - 1, and rooted at node 0. You are given a 2D integer array edges of length n - 1, where <code>edgesi = a_i, b_i</code> indicates that there is an edge between nodes <code>a_i</code> and <code>b_i</code> in the tree.

A node is good if all the subtrees rooted at its children have the same size.

Return the number of good nodes in the given tree.

A subtree of treeName is a tree consisting of a node in treeName and all of its descendants.

Example 1:

Input: edges = [0,1,0,2,1,3,1,4,2,5,2,6]

Output: 7

Explanation:

All of the nodes of the given tree are good.

Example 2:

Input: edges = [0,1,1,2,2,3,3,4,0,5,1,6,2,7,3,8]

Output: 6

Explanation:

There are 6 good nodes in the given tree. They are colored in the image above.

Example 3:

Input: 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]

Output: 12

Explanation:

All nodes except node 9 are good.

Constraints:

• <code>2 <= n <= 10⁵</code>

• edges.length == n - 1

• edges[i].length == 2

• <code>0 <= a_i, b_i< n</code>

• The input is generated such that edges represents a valid tree.