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    Question

    What is the time complexity of searching an element in

    a balanced binary search tree (BST) with nnn nodes?
    A O(n) Correct Answer Incorrect Answer
    B O(log⁡n) Correct Answer Incorrect Answer
    C O(n2) Correct Answer Incorrect Answer
    D O(1) Correct Answer Incorrect Answer
    E O(nlog⁡n) Correct Answer Incorrect Answer

    Solution

    In a balanced binary search tree (BST) , the height of the tree is maintained as O(log ⁡ n)), ensuring that each level of the tree splits the search space roughly in half. This property allows searching for an element in the tree with logarithmic time complexity. For example, consider a balanced BST with 15 nodes. The height is approximately log ⁡ 215≈4, so searching for any element will involve checking at most 4 nodes from the root to a leaf. The logarithmic reduction at each step (halving the search space) makes this approach efficient for large datasets. Balanced trees such as AVL or Red-Black trees maintain this logarithmic height through rotation operations during insertion and deletion, ensuring the O(log ⁡ n) search time even after multiple modifications. Explanation of Incorrect Options: A) O(n) : This would be the time complexity for searching in an unbalanced BST or a linked list, where all nodes are skewed to one side. However, a balanced BST ensures O(log ⁡ n) complexity. C) O(n2) This complexity is not applicable to BST search operations. It might appear in poorly optimized nested loops or certain pathological cases in other algorithms. D) O(1) Constant time search is achieved in hash tables, not in BSTs, as BSTs require traversing nodes to locate the target element. E) O(nlog ⁡ n) This is the complexity of sorting algorithms like Merge Sort or Heap Sort, not searching in a BST.

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