What is the optimal time complexity of solving AVL Tree?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for AVL Tree?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in AVL Tree?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for AVL Tree?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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DSA SectionMedium

AVL Tree

Learn how to solve the 'AVL Tree' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

Write a function is_avl_balanced(tree_arr) that takes an array representation of a binary tree tree_arr and returns True if the tree is height-balanced (for every node, the height of its left and right subtrees differs by at most 1) and is a valid BST, or False otherwise.

Constraints

•0 <= len(tree_arr) <= 1000

Examples

Example 1

Input

tree_arr = [3, 9, 20, None, None, 15, 7]

Output

True

Explanation

The tree is a valid BST and the depth difference of left/right subtrees of all nodes is at most 1.

Example 2

Input

tree_arr = [1, 2, None, 3, None, None, None, 4]

Output

False

Explanation

The tree is unbalanced because leaf node 4 is at depth 4 while right subtree of node 1 is empty.

Need a Hint?

Perform a recursive tree traversal (DFS) or level-order traversal (BFS) using a queue/stack.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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