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    Question

    Which of the following techniques is most efficient for

    finding the kth smallest element in a Binary Search Tree (BST)?
    A Perform an Inorder Traversal and index the kth element. Correct Answer Incorrect Answer
    B Use a Breadth-First Search (BFS) and store all nodes in a queue. Correct Answer Incorrect Answer
    C Convert the BST to an array and sort it. Correct Answer Incorrect Answer
    D Use a Min-Heap to extract the kth smallest element. Correct Answer Incorrect Answer
    E Recursively traverse the left and right subtrees while keeping a counter. Correct Answer Incorrect Answer

    Solution

    In a Binary Search Tree (BST), an Inorder Traversal retrieves elements in sorted order. To find the kth smallest element, an efficient approach is to perform an Inorder Traversal and stop after visiting the kth element. This method is efficient because it directly leverages the BST's inherent properties without extra data structures. Steps:

    1. Perform a recursive Inorder Traversal.
    2. Maintain a counter to track the number of visited nodes.
    3. When the counter equals k , return the current node's value.
    This approach has a time complexity of O(k) for balanced trees, as the traversal stops early. Why Other Options Are Wrong Option B: Use BFS BFS does not maintain the sorted property of a BST. Traversing all levels and then extracting the kth element is inefficient and unnecessary. Option C: Convert the BST to an array and sort it Sorting the array is redundant because the BST already provides sorted access. This approach has a time complexity of O(n log n) , which is less efficient. Option D: Use a Min-Heap Using a Min-Heap adds overhead as it requires extracting elements and maintaining the heap structure, making it less efficient than a direct traversal. Option E: Recursively traverse the left and right subtrees while keeping a counter While conceptually similar, this approach is more complex and harder to implement correctly compared to a straightforward Inorder Traversal.

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