What is the time complexity of deleting the maximum element from a max-heap?

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Question: What is the time complexity of deleting the maximum element from a max-heap?

Options:

Correct Answer: O(log n)

Solution:

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

What is the time complexity of deleting the maximum element from a max-heap?

What is the time complexity of deleting the maximum element from a max-heap?

Step 1: Understand that a max-heap is a special tree structure where the largest element is always at the root.
Step 2: Identify that the maximum element in a max-heap is located at the root node.
Step 3: To delete the maximum element, remove the root node.
Step 4: Replace the root with the last element in the heap to maintain the complete tree property.
Step 5: After replacing the root, the heap may no longer satisfy the max-heap property.
Step 6: To fix the heap, perform a process called 're-heapifying' or 'heapify down', which involves comparing the new root with its children and swapping it with the larger child until the max-heap property is restored.
Step 7: The re-heapifying process takes O(log n) time because the height of the heap is log n, and you may need to traverse from the root to the leaves.

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