Implementation of Heap Sort in Data Structure

Heap Sort is a popular sorting algorithm in Data Structure. It is frequently asked in BTech, BCA, MCA and other competitive exams. Heap Sort is uses a specialized data structure c alled a Heap.

This is an algorithm with good performance and linear space complexity.

Introduction

This term refers to ordering data in a sequence, whether from smallest to largest, or largest to smallest. In computer science, sorting can even improve the speed of search as well as help in proper organisation of data.

HEAP SORT in C – a MANUAL approach Heap sort is comparison based sorting algorithm using Binary Heap. Unlike Merge Sort, it does not require an extra storage and more efficient than Bubble Sort and Selection Sort for large data.

Due to the guaranteed time complexity of Heap Sort, it is heavily utilized in real timed systems and exams.

What is Heap Sort?

Heap Sort is a sorting algorithm that uses the array as the implementation of heap to sort elements.

First it creates a heap from the input array

And deletes the biggest or smallest item again and again

Finally it drops the element to it’s correct sorted position.

Heap Sort is an in-place sort.

What is Heap in Data Structure?

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Heap Property

There are two types of heaps:

Types of Heap

• Max Heap
• A parent node is larger than its children nodes.
• Employed to arrange items in an ascending order
• Example:
• Parent ≥ Left Child
• Parent ≥ Right Child
• Min Heap
• The parent node will always be less than its children nodes.
• Formerly in order to order by reverse, i.e. largest first
• Example:
• Parent ≤ Left Child
• Parent ≤ Right Child

Heap Sort Algorithm (Step-by-Step)

• Heap Sort operates in the two key phases:
• Phase 1: Build a Max Heap
• Convert the array to Max Heap Given an array, convert the array into max heap.
• The maximum element is moved to the root
• Phase 2: Sort the Elements
• Exchange the elements at root and last position.
• Reduce heap size
• Apply heapify
• Repeat the steps until and unless the array is sorted.

How Heap Sort Works (Analogous Example)

• Let’s see Heap Sort step by step.
• Take an unsorted array
• Create the Max Heap from the array
• The topmost node contains the largest element
• Exchange the root with the last item.
• Extract last element from the heap
• Call heapify to maintain the property of a heap.
• Repeat to process all items

Heap Sort Example

• Given array:
• [4, 10, 3, 5, 1]
• Step 1: Build Max Heap
• Max Heap becomes:
• [10, 5, 3, 4, 1]
• Step 2: Replace root with the last element
• [1, 5, 3, 4, 10]
• Step 3: Heapify remaining elements
• [5, 4, 3, 1, 10]
• Repeat the loop until the sorted array is obtained:
• Final sorted array (Ascending):
• [1, 3, 4, 5, 10]

Heapify Operation

• Heapify( O(logn) ) is heap property maintaining.
• Compare parent with children
• Swap if heap rule is violated
• Continue until heap becomes valid
• Heapify is an important operation in the Heap Sort.

Time Complexity of HeapSort

Case	Time Complexity
Best Case	O(n log n)
Average Case	O(n log n)
Worst Case	O(n log n)

Space Complexity of Heap Sort Time and space complexity has been published.

• O(1) (Constant space)
• Sorting is done in-place
• No extra memory required
• This is what makes Heap Sort an efficient memory-based sorting.

Advantages of Heap Sort

• Complexity in O(nlog n) ensured
• Does not require extra memory
• Works well for large datasets
• Superior to Bubble and Selection Sort
• Suitable for real-time systems

Disadvantages of Heap Sort

• Not a stable sorting algorithm
• Practically slower than the other version of Quick Sort
• Complex to understand for beginners
• Cache performance is poor

Applications of Heap Sort

• Priority Queue implementation
• Operating system scheduling
• Finding top K elements
• Large data sorting
• Embedded and real-time systems

Comparison Attained between Heap Sort and Other Sorting Algorithms

Algorithm	Time Complexity	Stable	Extra Space
Heap Sort	O(n log n)	❌ No	O(1)
Quick Sort	O(n log n)	❌ No	O(log n)
Merge Sort	O(n log n)	✅ Yes	O(n)
Bubble Sort	O(n²)	✅ Yes	O(1)

Frequently Asked Questions (FAQs)

What is Heap Sort? Explain briefly.

• Answer:

Heap Sort is a comparison-based sorting algorithm that uses a Heap data structure to sort elements. It first converts the given array into a Max Heap (or Min Heap) and then repeatedly removes the root element and places it in its correct position. Heap Sort works in-place and has a time complexity of O(n log n) in all cases.

Explain the working of Heap Sort.

• Answer:
• Heap Sort works in two main steps:

First, the given array is converted into a Max Heap, where the largest element is at the root.

Then, the root element is swapped with the last element of the heap.

The heap size is reduced and heapify is applied to maintain the heap property.

These steps are repeated until all elements are sorted.

What is a Heap? Explain its types.

• Answer:

A Heap is a special type of complete binary tree that follows the heap property.

Types of Heap:

Max Heap: The value of the parent node is greater than or equal to its child nodes.

Min Heap: The value of the parent node is smaller than or equal to its child nodes.

Heap Sort generally uses a Max Heap for sorting in ascending order.

Write the time and space complexity of Heap Sort.

• Answer:
• Time Complexity:
• Best Case: O(n log n)
• Average Case: O(n log n)
• Worst Case: O(n log n)
• Space Complexity:
• O(1) (constant space)
• Heap Sort is an in-place sorting algorithm and does not require extra memory.

Write advantages and disadvantages of Heap Sort.

Answer:

Advantages:

• Guaranteed O(n log n) time complexity
• Does not require extra memory
• Suitable for large datasets
• Disadvantages:
• Not a stable sorting algorithm
• Slower than Quick Sort in practice
• Difficult to understand compared to simple sorting algorithms