Is K-th Largest Perfect Subtree Size in Binary Tree easy or hard?

The problem is generally rated Medium because it combines multiple concepts: recognizing perfect subtree conditions, implementing post-order DFS, and selecting the k-th largest value. The logic is manageable once you realize the subtree validity must be determined bottom-up.

K-th Largest Perfect Subtree Size in Binary Tree Python/Java solution

The implementation is nearly identical across Python, Java, C++, C#, JavaScript, and C. A recursive DFS returns subtree height when the subtree is perfect. When both children return equal heights, compute the subtree size and store it. After traversal, sort the sizes or maintain a heap to extract the k-th largest.

How to solve K-th Largest Perfect Subtree Size in Binary Tree in O(n)?

The subtree validation itself runs in O(n) using a single post-order DFS. Each node returns the height of its subtree if it is perfect, or -1 otherwise. Perfect subtree sizes are computed during traversal. If only detection is required the algorithm is O(n); retrieving the k-th largest requires either sorting or a heap on top of that traversal.

What is the best approach for K-th Largest Perfect Subtree Size in Binary Tree?

The best approach uses post-order depth-first search to evaluate subtree properties bottom-up. Each node checks whether its left and right subtrees are perfect and have the same height. If they do, the subtree is perfect and its size is recorded. After collecting sizes, either sort them or maintain a min-heap to retrieve the k-th largest value.

Is K-th Largest Perfect Subtree Size in Binary Tree asked at Google/Amazon/Meta?

Binary tree DFS problems that evaluate subtree properties are common in interviews at companies like Google, Amazon, and Meta. Variants include checking balanced trees, computing subtree sizes, or validating structural constraints. This problem tests similar bottom-up reasoning using post-order traversal.

What data structure is used in K-th Largest Perfect Subtree Size in Binary Tree?

The solution primarily uses a binary tree traversal with recursion (DFS). An auxiliary list or a min-heap is used to store sizes of perfect subtrees. The heap variant helps efficiently track the k-th largest value without sorting all results.

What is the time complexity of K-th Largest Perfect Subtree Size in Binary Tree?

The DFS traversal visits each node once, giving O(n) base complexity. If you store all perfect subtree sizes and sort them, the total complexity becomes O(n log n). Using a min-heap of size k improves it to O(n log k) while keeping the same O(n) traversal cost.

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3319. K-th Largest Perfect Subtree Size in Binary Tree

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You are given the root of a binary tree and an integer k.

Return an integer denoting the size of the k^th largest perfect binary subtree, or -1 if it doesn't exist.

A perfect binary tree is a tree where all leaves are on the same level, and every parent has two children.

Example 1:

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

Output: 3

Explanation:

The roots of the perfect binary subtrees are highlighted in black. Their sizes, in non-increasing order are [3, 3, 1, 1, 1, 1, 1, 1].
The 2^nd largest size is 3.

Example 2:

Input: root = [1,2,3,4,5,6,7], k = 1

Output: 7

Explanation:

The sizes of the perfect binary subtrees in non-increasing order are [7, 3, 3, 1, 1, 1, 1]. The size of the largest perfect binary subtree is 7.

Example 3:

Input: root = [1,2,3,null,4], k = 3

Output: -1

Explanation:

The sizes of the perfect binary subtrees in non-increasing order are [1, 1]. There are fewer than 3 perfect binary subtrees.

Constraints:

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

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Hint 1

For a subtree to form a perfect binary subtree, its children should also be perfect binary subtrees.

Hint 2

Check recursively that both the node and its children are perfect binary subtrees.

Hint 3

Gather all the perfect binary subtrees and return the kth largest.

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3319. K-th Largest Perfect Subtree Size in Binary Tree

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