Question

Show (diagrammatically) all the steps involved in the heap sort on the following input sequence: 18, 45, 9, 2, 21, 64, 4, 7,1, 6. You should sort the sequence in the increasing order.

Answer 1

Heap sort is a comparison-based sorting technique that builds a max heap from the data, then repeatedly swaps the root with the last item and heapifies to sort the data.

Step-by-step explanation:

The heap sort process involves creating a max heap from the input sequence and then repeatedly removing the largest element from the heap and adding it to the end of the sequence. Here is a step-by-step diagrammatic representation of applying heap sort on the given sequence: 18, 45, 9, 2, 21, 64, 4, 7, 1, 6.

1. Build a max heap from the input sequence.
2. Swap the first element of the max heap with the last item of the heap, then reduce the size of the heap by one.
3. Heapify the root of the tree.
4. Repeat steps 2 and 3 until the size of the heap is 1.

After completion, the sequence will be sorted in increasing order.

Note: Due to the constraints of the platform, it is not possible to include actual diagrams. However, diagrams would typically show the tree structure at each step, with the root node being the largest value and nodes being swapped as described.