Heap Sort In Data Structures: Application & Significance   

Introduction to Heap Sorts  

A heap is a complete binary tree, while a binary tree is a tree in which each node can have no more than two offsprings. A full binary tree is one in which all levels except the final, i.e., the leaf node, are entirely filled, and all nodes are left-justified. One of the sorting algorithms used to put a list of elements in order is heap sort. The Heapsort method makes use of a tree idea known as the Heap Tree. We utilize Max Heap to organize list elements in higher to smaller order and Min Heap to arrange list elements in small to big order in our sorting method.  

What Is Heap Sort?  

It means a sorting technique that uses comparisons and is based on the Binary Heap. Its selection sort is similar in that we discover the minimal element first and set it at the beginning. Repeating the previous steps for the remaining parts. 

• Heap sort is an algorithm that works in place. 
• Its conventional implementation is unstable, although it is possible to make it stable. 
• QuickSort is often 2-3 times slower. A lack of location of reference causes slowness. 

Significance of Heap Sort 

Efficiency: The time required to do Heap sort grows logarithmically as the number of objects to sort grows, whereas alternative methods may become exponentially slower. This sorting method is really effective. 

Memory Consumption: Memory usage is small since, aside from the initial list of objects to be sorted, it requires no further memory space to function. 

Simplicity: Because it does not involve difficult Computer Science concepts like recursion, it is easier to grasp than other equally efficient sorting algorithms. 

Heap Sort Algorithm: The Process  

The first step of heap sort is to heapify the array into a heap data structure, then the Max-heap root node should be deleted one by one and replaced with the heap’s last node, and finally, heapify the heap’s root. Repeat this method until the size of the heap exceeds 1. 

The Heap sort algorithm uses the following stages to organize a list of entries in ascending order. 

Step 1: Create a Binary Tree from the supplied list of Elements.
Step 2: Convert the Binary Tree to a Min Heap.
Step 3: Using the Heapify technique, delete the root element from the Min Heap.
Step 4: Insert the removed item into the Sorted list.
Step 5: Continue until the Min Heap is empty.
Step 6: Show the sorted list. 

Let’s take a closer look at how heap sort works using an example. To illustrate, consider an unsorted array and attempt to sort it using heap sort. It will make the information simpler and easier to understand. 

To further understand heap sort, consider taking an unsorted array and attempting to sort it using heap sort. 

Consider the following array: arr[] = 4, 10, 3, 5, 1. 

Complete Binary Tree:  

• From the array, create a complete binary tree. 
• After that, the objective is to create a tree from the unsorted array and attempt to convert it to the max heap. 
• In order to convert a heap into a max heap, the parent node should be equal to or greater than the child nodes. 
• In this example, because the child node 10 should be bigger than the parent node 4, they are swapped to form a max-heap. 
• Make it into a max heap image widget. 

• As can be seen, 4 as a parent is smaller than 5, so swap both of them, and the resulting heap and array should look like this: 
• Perform heap sorting by removing the maximum element in each stage (i.e., moving it to the end position and removing it), then considering the remaining elements and transforming them into a max heap. 
• Remove the maximum heap’s root element (10) To remove this node, try swapping it with the last node, i.e., (1). After deleting the root element, heapify it one more to convert it to the max heap. 
• The heap and array that results should look like this: 
• Repeat the preceding steps to create the following: 

• Remove the root (i.e., 3) once more and heapify. 
• When the root is removed, it gets sorted, and the sorted array will look something like arr[] = 1, 3, 4, 5, 10. 

Properties Of Heap Sort  

It has two characteristics:

1. Structure Property
   The structure property signifies that all of the tree’s nodes or levels are fully filled. A heap data structure is an entire binary tree.
2. Heap Sort Property  

A heap sort property is a binary tree with unique properties. It is divided into two types: 

• Max Heap: A Max-Heap occurs when the parent nodes are greater than the child nodes. 

• Min Heap: A Min-Heap exists when the parent nodes are smaller than the child nodes. 

Significance Of Heap Sort  

Heapsort is most commonly found in hybrid algorithms such as IntroSort. 

Sort a nearly sorted (or K sorted) array by k greatest (or lowest) components 

In fact, heap sort has limited applications because Quicksort and Mergesort are superior. Nonetheless, the Heap data structure is widely utilized. 

Application Of Heap Sort  

Security and embedded systems, such as the Linux kernel, employ Heap Sort due of its O(n log n) upper constraint on running time and constant O(1) upper bound on auxiliary storage. 

Even though Heap Sort has an O(n log n) time complexity in the worst scenario, it has fewer applications (compared to other sorting algorithms like Quick Sort and Merge Sort). However, its underlying data structure, heap, may be employed to extract the smallest (or biggest) from a list of things without incurring the burden of keeping the other items sorted—for example, Priority Queues. 

Conclusion  

Advantages and drawbacks are always present in any sorting or searching method. There are very few drawbacks to Heap Sorting algorithms. There is no additional memory space needed. Time is another consideration. The time complexity is calculated to be nlog(n), although the actual Heap Sort is less than O(nlog(n)). The rationale for this is that as the process progresses, reduction or extraction from the Heap Sort decreases the size and takes considerably less time. As a result, Heap Sorting is regarded as one of the “greatest” sorting algorithms in the realm of Data Structure for a variety of reasons. Most genuine Data Science programs teach you the application of Heap Sort in real-world scenarios.