Which of the following words is not related to 'laughing'?

Question:

What is the worst-case time complexity of searching for an element in a balanced Binary Search Tree (BST) containing n elements?

Options:

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

Correct Answer: B) O(log n)

Detailed Explanation:

In a Binary Search Tree (BST), each node has at most two children. The left subtree contains values strictly smaller than the node, while the right subtree contains values strictly greater.

Why O(log n) is correct:

    
• In a balanced BST (such as an AVL tree or Red-Black tree), the height of the tree is strictly kept at O(log n).
    
• At each comparison step, the search eliminates roughly half of the remaining nodes.
    
• Therefore, in the worst-case scenario, the algorithm traverses from the root down to the deepest leaf node, requiring at most steps proportional to the tree's height, which is O(log n).

Why the other options are incorrect:

    
• A) O(1): Constant time is typical for direct array indexing or hash table lookups (on average), not tree traversals where decisions must be made across levels.
    
• C) O(n): Linear time occurs in an unbalanced (skewed) BST where the tree degrades into a linked list. However, the problem explicitly specifies a balanced tree.
    
• D) O(n log n): This is the standard time complexity for efficient comparison-based sorting algorithms (such as Merge Sort or Heap Sort), not a search operation on an already constructed BST.