What is the worst-case time complexity for deleting the minimum element from a m

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Question: What is the worst-case time complexity for deleting the minimum element from a min-heap?

Options:

Correct Answer: O(log n)

Solution:

Deleting the minimum element from a min-heap involves removing the root and then re-heapifying, which takes O(log n) time.

What is the worst-case time complexity for deleting the minimum element from a min-heap?

What is the worst-case time complexity for deleting the minimum element from a min-heap?

Step 1: Understand that a min-heap is a special tree structure where the smallest element is always at the root.
Step 2: Identify that the minimum element in a min-heap is located at the root of the tree.
Step 3: To delete the minimum element, remove the root node.
Step 4: Replace the root with the last element in the heap to maintain the complete tree structure.
Step 5: After replacing the root, the heap property may be violated, so we need to re-heapify the tree.
Step 6: Re-heapifying involves comparing the new root with its children and swapping it with the smaller child until the heap property is restored.
Step 7: The re-heapifying process can take time proportional to the height of the tree, which is log(n) for a heap with n elements.
Step 8: Therefore, the worst-case time complexity for deleting the minimum element from a min-heap is O(log n).

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