ইংরেজ ইস্ট ইন্ডিয়া কোম্পানী কখন বাংলা, বিহার ও উড়িষ্যার দেওয়ানী লাভ করে?

Question:

What is the worst-case time complexity of searching for an element in a balanced Binary Search Tree (such as an AVL tree or Red-Black tree) with 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 (BST), the height of the tree is strictly maintained to be logarithmic relative to the total number of nodes, specifically h = O(log n).

During a search operation:

        
• At each node, a comparison is made in O(1) constant time.
        
• Based on the comparison, the search algorithm traverses down either the left or the right subtree, discarding half of the remaining nodes at each step.
        
• The maximum number of comparisons required equals the height of the tree.
    

Why the other options are incorrect:

        
• Option A [O(1)]: Constant time lookup is characteristic of Hash Tables with optimal hash distribution, not tree structures where traversal from root to leaf is required.
        
• Option C [O(n)]: Linear time occurs in an unbalanced or degenerate Binary Search Tree (which behaves like a linked list), but self-balancing mechanisms prevent this degradation.
        
• Option D [O(n log n)]: This is the typical time complexity for efficient comparison-based sorting algorithms (such as Merge Sort or Heap Sort), not an individual search operation.