K-th Largest Perfect Subtree Size in Binary Tree

K-th Largest Perfect Subtree Size in Binary Tree - Problem

K-th Largest Perfect Subtree Size in Binary Tree

You're given the root of a binary tree and an integer k. Your task is to find the size of the k-th largest perfect binary subtree within this tree.

A perfect binary tree is a special type of tree where:
• All leaf nodes are at the same level
• Every internal node has exactly two children

Return the size (number of nodes) of the k-th largest perfect subtree, or -1 if fewer than k perfect subtrees exist.

Example: In a tree with perfect subtrees of sizes [7, 3, 3, 1, 1], the 2nd largest would be size 3.

Input & Output

example_1.py — Basic Perfect Subtrees

$ Input: root = [5,3,6,5,2,5,7,1,null,null,null,null,null,null,8], k = 2

› Output: 1

💡 Note: The perfect subtrees have sizes [3,1,1,1,1,1]. After sorting in descending order, the 2nd largest size is 1.

example_2.py — Single Node Tree

$ Input: root = [1], k = 1

› Output: 1

💡 Note: The only perfect subtree is the root itself with size 1.

example_3.py — No Perfect Subtrees of Required Rank

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

› Output: -1

💡 Note: Only one perfect subtree exists (leaf node 3 with size 1), but we need the 2nd largest.

Constraints

The number of nodes in the tree is in the range [1, 2000]
1 ≤ Node.val ≤ 2000
1 ≤ k ≤ 1024

Visualization

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Asked in

G Google 45 a Amazon 38 f Meta 32 ⊞ Microsoft 28

The optimal approach uses a single DFS traversal to identify perfect subtrees by checking if both children are perfect with equal heights. We collect sizes during traversal and sort once at the end, achieving O(n + p log p) time complexity where p is the number of perfect subtrees.

Common Approaches

✓ Optimized

⏱️ Time: N/A Space: N/A

Brute Force (Check All Subtrees)

⏱️ Time: O(n²) Space: O(n)

This approach examines every possible subtree in the binary tree, checks if it's perfect, collects all perfect subtree sizes, sorts them, and returns the k-th largest. While straightforward, it's inefficient due to redundant height calculations.

Single DFS with Size Collection (Optimal)

⏱️ Time: O(n log n) Space: O(n)

This optimal approach uses a single DFS traversal where each recursive call returns information about whether the subtree is perfect, its height, and size. We collect perfect subtree sizes during the traversal and sort them once at the end.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

⚠ Quadratic Growth

Space Complexity

⚡ Linearithmic Space

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Smart Actions

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