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In: Computer Science

prove the running time of heap sort.

prove the running time of heap sort.

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Expert Solution

ABOUT : Heap sort is a comparison based sorting technique where we first find the maximum element and place the maximum element at the end. We repeat the same process for the remaining elements.

heapsort has a running time of O(nlogn).

There are two kinds of binary heaps: max-heap and min-heap.

ALGORITHM :

  1. Build a max-heap from an unordered array.
  2. Find the maximum element, because the heap is a max-heap.
  3. Swap the root and last elements of the heap, then eliminate root element
  4. Adjust new root node to its proper place
  5. Repeat steps 2 and 3 (heapify) until you’re down to just 1 element in the heap, sorting the array.

prove :

Conclusions:

  • Time-complexity for buildMaxHeap() is O(n)
  • Time complexity for each instance of heapify() is O(log n)
  • Time complexity for heap sort is O(n log n)

venereology answered 2 hours ago
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