বৃটিশ ইস্ট ইন্ডিয়া কোম্পানী কোন সালে দিউয়ানী লাভ করে?

Question:

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

Options:

    
1. O(1)
    
2. O(log n)
    
3. O(n)
    
4. O(n log n)

Correct Answer: B) O(log n)

Detailed Explanation:

In a balanced Binary Search Tree (such as an AVL Tree or Red-Black Tree), the height of the tree is strictly maintained at O(log n). During each step of the search process:

    
• The algorithm compares the target value with the current node's value.
    
• Because the tree is ordered, one of the two subtrees is discarded entirely at each step.
    
• In the worst case, the path traveled goes from the root down to the deepest leaf node, requiring at most as many comparisons as the height of the tree.

Why Other Options Are Incorrect:

    
• Option A (O(1)): Constant time is typical for hash table lookups under ideal conditions, but searching a tree requires traversing levels.
    
• Option C (O(n)): This occurs in an unbalanced (degenerate) BST where all nodes fall in a single line, effectively behaving like a linked list.
    
• Option D (O(n log n)): This is characteristic of efficient comparison-based sorting algorithms (such as Merge Sort), not single-element lookup.