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Question: What is the worst-case time complexity of searching for a target 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:

A Binary Search Tree (BST) ensures that all values in the left subtree of a node are strictly less than the node's value, and all values in the right subtree are strictly greater. Searching proceeds by comparing the target value with the current node and traversing either left or right, effectively halving the search space at each level.

    
• Why Option B is correct: In a balanced BST (such as an AVL or Red-Black tree), the height of the tree is strictly kept at O(log n). The maximum number of comparisons required to locate an element or determine it is absent corresponds to the tree's height, leading to a worst-case time complexity of O(log n).
    
• Why Option A is incorrect: Constant time O(1) is characteristic of direct indexing or ideal hash table lookups, not tree traversals.
    
• Why Option C is incorrect: Linear time O(n) would only occur in a skewed, unbalanced tree that degrades into a linked list. The question explicitly specifies that the tree is balanced.
    
• Why Option D is incorrect: O(n log n) is typically the time complexity for comparison-based sorting algorithms (e.g., Merge Sort), not a single search operation.