What Is Sorting In Data Structure, And Its Types?

Q: What is sorting in a data structure?

Sorting is a method of arranging the unorganized data in increasing or decreasing order based on different sorting algorithms.

Q: Name some of the recursive sorting algorithms that work on the divide and conquer approach.

Quick sort and merge sort are two of the most famous recursive algorithms, and they work on the divide and conquer approach.

Q: Which is the most efficient sorting algorithm?

Quick sort and merge sorts are considered to be the most efficient sorting algorithms. They have a time complexity of O (n logn) in their worst cases.

Different sorting algorithms have different time and space complexities, giving us a range of efficient sorting algorithms based on our needs.

In this post, we will learn about sorting and its types in detail. You just need to stay with us till the end of the article to know everything about sorting in detail.

Table of Contents

What Is Sorting In Data Structure?

Sorting in data structure is the process of arranging different elements in a particular order based on a particular set of criteria. In computer science and mathematics, sorting is a fundamental operation used in various applications, including data analysis, searching, and organizing information to retrieve data in various fields efficiently. The primary goal of sorting is to impose a meaningful order on a collection of items, making it easier to process and retrieve data efficiently.

Sorting in data structure is essential in various real-world applications, including database management, search algorithms, and maintaining the order of data in arrays or lists for efficient access. There are various types of sorting, with each having different approaches to its implementation. They have different time and space complexities, which helps us choose the best one according to our needs. The choice of sorting algorithm often depends on the specific use case and the characteristics of the data being sorted.

Uses Of Sorting

Sorting is like the alphabetization of our digital world. It helps us bring clarity to the pile of information. Let us imagine we are trying to find a book in a library, and all the books are randomly placed on the shelves. It would be a time-consuming and frustrating task to pick the one we are searching for.

Similarly, sorting plays a vital role in the digital world. It simplifies our lives by arranging information, whether a list of contacts on our phone, search results on a website, or financial data in a spreadsheet. This orderly arrangement enhances efficiency, making retrieving, analyzing, and understanding data easier.

Sorting works in the background when selecting a song in your playlist or searching for a product on an e-commerce website. It helps to simplify our interactions while analyzing a large data set.

Major Types Of Sorting Algorithms

There are various types of sorting algorithms available for us that work on different approaches and have different complexities. Let us look at various essential sorting algorithms one by one.

Bubble Sort Algorithm

In this algorithm, adjacent elements are compared one by one repeatedly and swapped if they are in the wrong order. There are generally n-1 passes until all the elements are in their correct places.

Some essential characteristics of the bubble sort algorithm are given here.

There are a total of n-1 passes.
The total number of comparisons is O(n^2).
It is a stable algorithm.
It is not an adaptive algorithm.
The worst time complexity of the bubble sort algorithm is O(n^2).
It can be made adaptive by using flags.

Pseudocode

Bubble Sort Algorithm

bubbleSort(arr)

n = length (arr);

for i from 0 to n-1:

swapped = false

for j from 0 to n-i-1:

if arr[j] > arr[j+1]:

swap(arr[j], arr[j+1])

swapped = true

if swapped is false:

break;

Insertion Sort Algorithm

Insertion sort divides the array into two different parts. They are sorted and unsorted parts. It then compares the sorted parts and, after comparison, swaps them if needed. It makes the final sorted array one at a time, at its correct position within the sorted array.

The time complexity of the insertion sort is O(n^2).
It is a stable algorithm.
It is an adaptive algorithm.

Pseudocode

Insertion Sort Algorithm

insertionSort(arr):

n = length(arr)

for i from 1 to n-1

key = arr[i]

j = i – 1

while j >= 0 and arr[j] > key:

arr[j+1] = arr[j]

j = j – 1

arr[j+1] = key

Selection Sort Algorithm

In selection sort, we need to ensure that the smallest element of the current unsorted subarray goes to its final position which is done by finding the smallest element in the subarray. This algorithm reduces the size of the unsorted part by 1 and increases the size of the sorted part by 1 at each pass.

The time complexity of the selection sort algorithm is O(n^2).
It is not a stable algorithm.
It is a non-recursive algorithm.
It is also not an adaptive algorithm.
It offers the benefits of the least number of swaps to sort the array, unlike insertion sort.

Pseudocode

Selection Sort Algorithm

selectionSort(arr):

n = length(arr)

for i from 0 to n-1:

min_index = i

for j from i+1 to n-1:

if arr[j] < arr[min_index]:

min_index = j

swap(arr[i], arr[min_index])

Quick Sort Algorithm

Quick Sort uses a divide-and-conquer strategy. It selects a pivot element and partitions the array into two sub-arrays. It arranges the element in such a way that it contains elements less than the pivot elements ion one side of the pivot and elements greater than the pivot on the other side. It then sorts the subarrays recursively.

Some important characteristics of the quick sort algorithm is given here.

The worst scenario takes place in a quick sort when the array is already sorted.
The time complexity of the quick sort algorithm is O (n^2).
It is also a recursive algorithm.
It also follows the divide-and-conquer approach.
It works by selecting a pivot element and then partitioning the array into two major parts.

Quick Sort Algorithm

quickSort(arr, low, high):

if low < high:

pivot_index = partition(arr, low, high)

quickSort(arr, low, pivot_index – 1)

quickSort(arr, pivot_index + 1, high)

partition (arr, low, high):

pivot = arr [high]

i = low – 1

for j from low to high-1:

if arr[j] <= pivot:

i = i + 1

swap(arr[i], arr[j])

swap(arr[i + 1], arr[high])

return i + 1

Merge Sort

Merge sorting is a type of divide-and-conquer algorithm. It divides the unsorted list into n subparts, each containing one element, and then repeatedly merges them to produce new sorted parts until only one remains.

Some of the important Merge sort characteristics are given here.

It works on a divide-and-conquer approach.
It is a stable algorithm.
It is also an adaptive algorithm.
The time complexity of merge sort is O(n logn)
It is an easy and reliable algorithm whose time complexity is better than the rest.
It is a recursive sorting algorithm.

Heap Sort

Heap Sort is a comparison-based sorting algorithm that operates by first converting the array of elements into a binary heap data structure.

Each parent node in a binary heap has a value that is either greater than or equal to that of its children or less than or equal to those of the parent node. Heap sort typically uses a max-heap when sorting data.

It is a recursive algorithm and uses a tree data structure to sort the array.
The heap sort algorithm has a time complexity of O(n logn).
It is an in-place algorithm. Hence, no extra space is needed for this algorithm to occur.
It is not a stable algorithm, and as a result, relative order may change during the sorting output.

Time Complexity Of Various Sorting In Data Structure

Let us check the time complexity of different sorting in data structure is based on three cases.

Time Complexity Of Sorting Algorithms
Algorithm	Best Case	Average Case	Worst Case
Bubble Sort	O (n)	O (n^2)	O (n^2)
Selection Sort	O (n^2)	O (n^2)	O (n^2)
Insertion Sort	O (n)	O (n^2)	O (n^2)
Merge Sort	O (n log n)	O (n log n)	O (n log n)
Quick Sort	O (n log n)	O (n log n)	O (n^2)
Heap Sort	O(n log n)	O (n log n)	O (n log n)
Counting Sort	O (n + k)	O (n + k)	O (n + k)
Radix Sort	O (nk)	O (nk)	O (nk)
Bucket Sort	O(n^2)	O(n^2)	O(n^2)

Space Complexity Of Sorting In Data Structure

Let us have a look at the space complexity of different sorting algorithms.

Space Complexity Of Sorting Algorithms
Algorithm	Space Complexity
Bubble Sort	O(1)
Selection Sort	O(1)
Insertion Sort	O(1)
Merge Sort	O(n)
Quick Sort	O(log n)
Heap Sort	O(1)
Counting Sort	O(n + k)
Radix Sort	O(n + k)
Bucket Sort	O(n)

Sorting In Data Structure FAQs

What is sorting in a data structure?

Sorting is a method of arranging the unorganized data in increasing or decreasing order based on different sorting algorithms.

Name some of the recursive sorting algorithms that work on the divide and conquer approach.

Quick sort and merge sort are two of the most famous recursive algorithms, and they work on the divide and conquer approach.

Which is the most efficient sorting algorithm?

Quick sort and merge sorts are considered to be the most efficient sorting algorithms. They have a time complexity of O (n logn) in their worst cases.