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Question: What is the worst-case 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: B) O(log n)

Explanation:

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

Here is why this occurs:

    
• During each step of the search, the algorithm compares the target value with the current node.
    
• Because the tree is ordered, this comparison allows the search to discard roughly half of the remaining subtrees at each level.
    
• The maximum number of comparisons required to locate an element (or determine that it does not exist) corresponds directly to the height of the tree.

Therefore, the worst-case time complexity is O(log n).

Note: If the tree were not balanced (i.e., degenerate or skewed), the worst-case time complexity would degrade to O(n), behaving similarly to a singly linked list.