GATE CS 2016 Set 1 — Question 47
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Programming & Data Structures → Heaps → Heapify & Build-Heap
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Question
An operator for a binary heap data structure is to be designed to delete the item in the -th node. Assume that the heap is implemented in an array and refers to the -th index of the array. If the heap tree has depth (number of edges on the path from the root to the farthest leaf), then what is the time complexity to re-fix the heap efficiently after the removal of the element?
Correct answer
(B) O(d) but not O(1)
Solution
To delete an element at index in a binary heap (implemented as an array):
Since depends on , it is not .
Thus, the time complexity is but not .
1.Replace the element at index with the last element in the heap (the rightmost leaf at the deepest level).
2.Remove the last element.
3.Restore the heap property by sifting the new element at index either up or down (heapify).
The height of the heap is . The sift operation takes time proportional to the height of the tree, which is .Since depends on , it is not .
Thus, the time complexity is but not .
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