How do you solve K-th Largest Perfect Subtree Size in Binary Tree on LeetCode?

K-th Largest Perfect Subtree Size in Binary Tree (LeetCode #3319) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: A perfect binary subtree must have both children as perfect binary subtrees.

What is the brute force solution for K-th Largest Perfect Subtree Size in Binary Tree?

The brute force approach for K-th Largest Perfect Subtree Size in Binary Tree is Brute Force, with O(n²) time complexity and O(n) space complexity. We can check every subtree in the binary tree to see if it's a perfect binary subtree. If it is, we can record its size. After collecting all sizes, we can sort them to find the k-th largest. The optimal Optimal Solution approach improves this to O(n log n).

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

K-th Largest Perfect Subtree Size in Binary Tree uses the following concepts: Tree, Depth-First Search, Sorting, Binary Tree. The recommended patterns to study are: Depth-First Search, Recursion.

What are the interview tips for K-th Largest Perfect Subtree Size in Binary Tree?

Always clarify the definition of a perfect binary tree before starting. Think about edge cases, such as trees with only one node or no perfect subtrees. Practice writing recursive functions, as they are common in tree problems.

What are common mistakes when solving K-th Largest Perfect Subtree Size in Binary Tree?

Not checking if both children are perfect before counting the size. Forgetting to handle the case where k is larger than the number of perfect subtrees.

#3319

K-th Largest Perfect Subtree Size in Binary Tree

Medium

TreeDepth-First SearchSortingBinary TreeDepth-First SearchRecursion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(n)	O(n)

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Intuition

Time O(n log n)Space O(n)

We can use a depth-first search (DFS) to identify perfect binary subtrees while calculating their sizes. This allows us to gather sizes in a single traversal, making it more efficient.

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Algorithm

3 steps

1Step 1: Use a DFS approach to traverse the tree and check if each subtree is perfect.
2Step 2: For each perfect subtree found, record its size in a list.
3Step 3: Sort the list of sizes in non-increasing order and return the k-th largest size.

solution.py23 lines

1class TreeNode:
2    def __init__(self, val=0, left=None, right=None):
3        self.val = val
4        self.left = left
5        self.right = right
6
7class Solution:
8    def kthLargestPerfectSubtreeSize(self, root, k):
9        sizes = []
10        def dfs(node):
11            if not node:
12                return 0
13            left_size = dfs(node.left)
14            right_size = dfs(node.right)
15            if left_size == right_size:
16                size = left_size + right_size + 1
17                sizes.append(size)
18                return size
19            return -1
20
21        dfs(root)
22        sizes.sort(reverse=True)
23        return sizes[k-1] if k <= len(sizes) else -1

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the sizes after collecting them, while the DFS traversal itself is O(n). The space complexity is O(n) for storing the sizes.

1A perfect binary subtree must have both children as perfect binary subtrees.
2Using DFS allows us to efficiently check and collect sizes in one pass.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.