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Question: What is the time complexity of searching for an element in a balanced Binary Search Tree (BST) containing n nodes?

Options:

        
• A) O(1)
        
• B) O(log n)
        
• C) O(n)
        
• D) O(n log n)
    

Correct Answer: Option B — O(log n)

Explanation:

In a balanced Binary Search Tree (such as an AVL tree or Red-Black tree), the height of the tree is bounded by log₂(n).

        
• Each search step compares the target value to the current node and eliminates half of the remaining subtree.
        
• Therefore, the maximum number of operations required to find a node (or determine it does not exist) is proportional to the tree's height, leading to a time complexity of O(log n).
    

Analysis of Incorrect Options:

        
• Option A [O(1)]: Constant time is typical for hash table lookups under ideal conditions, not tree traversals.
        
• Option C [O(n)]: Linear time occurs only in degenerate (unbalanced) BSTs that resemble linked lists, not balanced trees.
        
• Option D [O(n log n)]: This complexity is common for comparison-based sorting algorithms (e.g., Merge Sort), not single search operations.