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Data Structures | Heap | Question 12

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Which of the following Binary Min Heap operation has the highest time complexity?

(A)

Inserting an item under the assumption that the heap has capacity to accommodate one more item

(B)

Merging with another heap under the assumption that the heap has capacity to accommodate items of other heap

(C)

Deleting an item from heap

(D)

Decreasing value of a key



Answer: (B)

Explanation:

The time complexity of Binary Min Heap operations can vary, but let’s analyze each option:

a) Inserting an item under the assumption that the heap has the capacity to accommodate one more item:
  – Time complexity for insertion in a binary heap is O(log n), where n is the number of elements in the heap.

b) Merging with another heap under the assumption that the heap has the capacity to accommodate items of the other heap:
  – The time complexity for merging two binary heaps is O(n), where n is the total number of elements in both heaps.

c) Deleting an item from the heap:
  – The time complexity for deleting an item from a binary heap is O(log n), where n is the number of elements in the heap.

d) Decreasing the value of a key:
  – The time complexity for decreasing the value of a key in a binary heap is O(log n), where n is the number of elements in the heap.

Comparing the time complexities, we can see that option (b) – Merging with another heap under the assumption that the heap has the capacity to accommodate items of the other heap – has the highest time complexity, O(n). This is because it involves merging two heaps and may require rearranging elements to maintain the heap property, resulting in a linear time complexity proportional to the total number of elements in both heaps.


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Last Updated : 28 Jun, 2021
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