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Heapsort is executed on the structure of the heap data. We know heap is a complete tree in binary form. The heap tree can be of two different types: Min-heap, or heap max. The root element is minimal for min-heap, and maximum for a max heap. Upon forming a heap, we can remove an object from the root and transfer the last element to the root. After this procedure of swapping, we have to heap the whole array again. We can filter the entire array by removing elements from the root.

The complexity of Heap Sort Technique

• Time Complexity: O(n log n)
• Space Complexity: O(1)

#### Input and Output

Input:

A list of unsorted data: 50 4 11 40 32 81 70

Output:

Array before Sorting: 50 4 11 40 32 81 70

Array after Sorting: 4 11 32 40 50 70 81

Algorithm

Input: A data array, and the total number in the array

Output: Max heap using an element in an array

### What is a Binary Heap?

This Binary Heap is a complete binary tree in which entities are placed in a special order, such that a parental node’s value is greater than its two nodes’ values. The former is called a heap max, while the latter a heap min. The heap can be described through an array or binary tree.

Algorithm for sorting in increasing order:-

1. Create a maximum heap of the data input.
2. The greatest element is placed at the root of the heap at this stage. Replace it with the last heap component, then increase the heap size by 1.
3. Repeat steps above whilst heap size is greater than 1.

### How to create a heap?

The heapify procedure can only be implemented to a node if it heaps its children’s nodes. Thus heapification must be carried out in the order from the bottom up.

Using an example let’s understand:

The numbers in bracket represent the indices in the array representation of data.

Example of heap sort implementation: