Count Nodes Equal to Subtree Average

Problem Statement

Given the root node of a binary tree, find and return the count of nodes where the node's value is exactly equal to the integer average of all values in its subtree.

Note:

• The average of k numbers is the total sum divided by k, rounded down to the nearest integer.
• A subtree of a node includes the node itself and all its descendants.

Examples

Example 1:

Input: root = [5,10,7,0,2,null,8]
Output: 4
Explanation:
- Node with value 5: subtree sum is 5+10+7+0+2+8 = 32, count = 6, average = 32 / 6 = 5 (integer division)
- Node with value 7: subtree sum is 7+8 = 15, count = 2, average = 7
- Node with value 0: subtree sum is 0, count = 1, average = 0
- Node with value 8: subtree sum is 8, count = 1, average = 8
Nodes matching their subtree average: 5, 7, 0, 8 (total 4)

Example 2:

Input: root = [3]
Output: 1
Explanation:
Only one node with value 3 whose subtree average is 3 / 1 = 3.

Constraints

• Number of nodes in the tree: 1 to 1200
• Node values range from 0 to 1200 inclusive