”রাষ্ট্র বনাম শেখ মুুজিবুর রহমান ও অন্যান্য” এই মামলা থেকে 1969 সালে নিম্নের কোন তারিখে পাকিস্তানি সরকার বঙ্গবন্ধুকে মুক্তি দেন?

Question:

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

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 balanced Binary Search Tree (such as an AVL tree or Red-Black tree), the height of the tree is strictly kept at O(log n). The search operation functions as follows:

        
• The search begins at the root node and compares the target value with the current node's key.
        
• Based on the comparison, the search proceeds either to the left child or the right child, cutting the remaining search space in half at each step.
        
• Since each level traversal takes constant time O(1) and the maximum depth of a balanced tree with n nodes is proportional to log2(n), the worst-case time complexity is O(log n).
    

Why Other Options Are Incorrect:

        
• Option A [O(1)]: Constant time lookup is typical for hash tables (on average), not comparison-based trees where traversal depends on tree height.
        
• Option C [O(n)]: Linear time complexity occurs in an unbalanced or degenerate BST (which behaves like a linked list), but the question explicitly specifies a balanced BST.
        
• Option D [O(n log n)]: This complexity is characteristic of efficient comparison-based sorting algorithms (e.g., Merge Sort), not single-element search operations.