ভারতীয় উপমহাদেশে দ্বৈত শাসন ব্যবস্থার প্রবর্তক-

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)

Detailed Explanation:

In a Binary Search Tree (BST), each node contains at most two children. The elements are arranged so that for any given node, values in the left subtree are strictly smaller, and values in the right subtree are strictly larger.

When searching for an element:

    
• At each step, the algorithm compares the target key with the current node.
    
• Based on the comparison, the search proceeds either to the left or right subtree, effectively halving the search space at each level.
    
• Because the tree is balanced, the height of the tree is guaranteed to be proportional to log2(n).
    
• Consequently, the maximum number of operations required is equal to the height of the tree, resulting in a worst-case time complexity of O(log n).

Why Other Options Are Incorrect:

    
• A) O(1): Constant time lookup is characteristic of Hash Tables (under ideal conditions), not tree-based structures where traversal is required.
    
• C) O(n): Linear search time occurs only in an unbalanced or degenerate BST (which behaves like a linked list). However, the problem explicitly states the tree is balanced.
    
• D) O(n log n): This time complexity is typical for efficient comparison-based sorting algorithms (such as Merge Sort or Heap Sort), not single-element lookups.