Heap sort algorithm:

Step-1: Build the binary tree with the given elements.

Step-2: Heapify the tree into either max-heap or min-heap.

Step-2.1: In max-heap, the parent nodes are greater than the child nodes, and in min-heap, parent nodes are lesser than the child nodes.

Step-3: Swap the root node of the tree with the last leaf node.

Step-4: Delete the leaf node and insert into the list from the last.

Step-5: Repeat the steps 2, 3, and 4 until all nodes are deleted from the binary tree.

To sort the array:

Given elements are listed below,

0 1 2 3 4 5 6 7 8 9
11 27 8 14 45 6 24 81 29 33

To build a binary tree:

Assume that the first element as the root node.

If indexing of the elements starts from “0” then left child is considered as “2i+1” and right child is considered as “2i+2”.

If indexing starts from “1” then the left child is considered as “2i”, and right child is considered as “2i+1”.

The constructed binary tree is as follows,

To heapify the tree:

Construct a max-heap for this exercise.

For max-heap, the parent nodes are greater than the child nodes.

The tree after heapified is as follows,

Swap the root node with the last leaf node as follows,

Delete the last leaf node from the tree and insert to the list at the last as follows,

0 1 2 3 4 5 6 7 8 9
11 45 24 29 33 6 8 14 27 81

Again heapify the tree as follows,

Swap the root node with the last leaf node as follows,

Delete the last leaf node from the tree and insert to the list as follows,

0 1 2 3 4 5 6 7 8 9
27 33 24 29 11 6 8 14 45 81

Again heapify the tree as follows,

Swap the root node with the last leaf node as follows,

Delete the last leaf node from the tree and insert to the list at the last as follows,

0 1 2 3 4 5 6 7 8 9
11 45 24 29 33 6 8 33 45 81

Again heapify the tree as follows,

Swap the root node with the last leaf node as follows,

Delete the last leaf node from the tree and insert to the list at the last as follows,

0 1 2 3 4 5 6 7 8 9
8 27 24 14 11 6 29 33 45 81

Again heapify the tree as follows,

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Chapter 17, Problem 27RE

Chapter 17, Problem 1PE

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