Count Nodes Equal to Average of Subtree

Count Nodes Equal to Average of Subtree - Problem

Given the root of a binary tree, return the number of nodes where the value of the node is equal to the average of the values in its subtree.

Note:

The average of n elements is the sum of the n elements divided by n and rounded down to the nearest integer.
A subtree of root is a tree consisting of root and all of its descendants.

Input & Output

Example 1 — Complete Binary Tree

$ Input: root = [4,8,5,0,1,null,6]

› Output: 5

💡 Note: Node 4: subtree sum=24, count=6, average=4 ✓. Node 5: subtree sum=11, count=2, average=5 ✓. Leaf nodes 0, 1, 6 all equal their own values ✓. Node 8: subtree sum=9, count=3, average=3 ≠ 8.

Example 2 — Simple Tree

$ Input: root = [1]

› Output: 1

💡 Note: Single node with value 1. Subtree sum=1, count=1, average=1 ✓. The node equals its subtree average.

Example 3 — No Matches

$ Input: root = [1,2,3]

› Output: 2

💡 Note: Node 1: subtree sum=6, count=3, average=2 ≠ 1. Node 2: sum=2, count=1, average=2 ✓. Node 3: sum=3, count=1, average=3 ✓. Total matching nodes: 2.

Constraints

The number of nodes in the tree is in the range [1, 10⁵]
0 ≤ Node.val ≤ 1000

Visualization

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Asked in

f Facebook 15 a Amazon 12 M Microsoft 8

The key insight is to calculate subtree sums and counts in a single DFS traversal, checking if each node equals its subtree average. Best approach uses bottom-up DFS to visit each node once. Time: O(n), Space: O(h) where h is tree height.

Common Approaches

✓ Optimized

⏱️ Time: N/A Space: N/A

Brute Force - Separate Traversal for Each Node

⏱️ Time: O(n²) Space: O(h)

Visit every node in the tree, and for each node, perform a complete DFS traversal of its subtree to calculate the sum and count of nodes. Then check if the node's value equals the integer average.

Optimized DFS - Single Traversal

⏱️ Time: O(n) Space: O(h)

Use depth-first search to visit each node once. For each node, calculate its subtree sum and count by combining results from left and right children. Check if node value equals average during the traversal.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

⚠ Quadratic Growth

Space Complexity

✓ Linear Space

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Smart Actions

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