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.
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.
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:
Properties Of Heap Sort
It has two characteristics:
A heap sort property is a binary tree with unique properties. It is divided into two types:
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.
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.