What is the optimal time complexity of solving Binary 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 Binary 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 Binary 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 Binary 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

Binary Tree

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

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Problem Statement

Medium

Write a function is_univalued_binary_tree(tree_arr) that takes an array representation of a binary tree tree_arr (where the root is at index 0, and children of index i are at 2i + 1 and 2i + 2, with None representing empty nodes) and returns True if every node in the tree has the same value, or False otherwise.

Constraints

•0 <= len(tree_arr) <= 1000

Examples

Example 1

Input

tree_arr = [1, 1, 1, 1, 1, None, 1]

Output

True

Explanation

All nodes in the tree contain the value 1.

Example 2

Input

tree_arr = [2, 2, 2, 5, 2]

Output

False

Explanation

One node has value 5, which differs from other nodes (value 2).

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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