What are sorting algorithms?

In this Answer, we’ll cover the basics of the sorting algorithms.

History of sorting algorithms

The history of sorting algorithms has evolved with the advancements in computer systems. In early low-powered computer systems, simpler sorting algorithms were popular, such as, bubble sort, which repeatedly swaps the adjacent elements. The 1950s and 1960s decades were the turning point where many well-known sorting algorithms were developed, such as quick sort, bucket sort, heap sort, and others. These algorithms used approaches such as divide and conquer to sort the data. In the early 21st century, the Timsort algorithm was designed using the hybrid approach.

Importance of sorting algorithms

Sorting plays an important role in different applications. Here are some of them:

Finding data: Looking for the required data from a large dataset could be very difficult. Sorting can make the search easy and quick.
Analyzing data: Data analysis is a technique for understanding data to perform future actions. Sorting plays an important role in data analysis tasks, such as finding medians, minimums, maximums, quartiles, and percentiles.
Optimized data structures: An optimized data structure can enhance the performance of many computer applications. Sorted data can lead to optimized data structures that can perform different data operations quickly.
Data presentation: Data representation techniques are useful for exploring various features of the data. Sorted data is easier to represent visually in charts, graphs, or other visualization methods.
Information retrieval: Finding the most relevant information is a complex task to engage the user and provide useful information. Sorting can play a crucial role in providing relevant search results.
File management: File systems are designed to manage and organize files so that they can be retrieved efficiently. Sorting can help retrieve files faster and create and maintain structured file systems.
Database management: Database systems are responsible for managing records, responding to user queries, and performing other database operations. Sorting helps database systems perform these tasks efficiently.
Network routing: Finding the optimal path or route for data packets is a crucial job in network routing. Sorting algorithms can help select such paths to ensure data transfer and network performance.
User experience: User experience is key to keeping users engaged with our services for a long time. Sorted data can lead to a better user experience, as users expect data to be sorted in their preferred order.

Different approaches to sorting algorithms

Sorting algorithms use different methods to sort elements. Let’s discuss some approaches used for sorting.

Comparison-based sorting: The first approach is to compare elements for sorting. In this approach, the elements are directly compared using any comparison operator (e.g., less than, equal to, greater than) and perform the relevant operation. Bubble sort, selection sort, insertion sort, merge sort, quick sort, and heap sort are examples of comparison-based sorting algorithms.
Distribution-based sorting: Another approach to sorting is to distribute the elements in different buckets based on some criteria and sort each bucket individually. Radix sort, bucket sort, and pigeonhole sort are examples of distribution-based sorting algorithms.
Divide and conquer sorting: In this approach, the data elements are divided into smaller subproblems, and solve each subproblem individually. Lastly, these solutions are combined to obtain the elements in sorted order. Merge sort, bitonic sort, and quick sort are examples of the divide and conquer approach of sorting.
Hybrid sorting: The hybrid sorting approach combines different sorting techniques to perform the sorting efficiently by using the strength of each method. Timsort (a combination of merge sort and insertion sort) is an example of the hybrid sorting approach.

Properties of sorting algorithms

Let’s discuss the properties of the sorting algorithms below:

Adaptive: A sorting algorithm is adaptive if it uses input data features to improve its performance. An adaptive sorting algorithm performs better on partially sorted data. Insertion sort, bubble sort, timsort, and merge sort are examples of adaptive sorting algorithms.
In-place: If an algorithm doesn’t require any extra space and performs sorting within the given data structure, it is called an in-place sorting algorithm. It may use the constant additional memory. Bubble sort, insertion sort, selection sort, quick sort, heap sort, shell sort, and comb sort are examples of in-place sorting algorithms.
Stable: A sorting algorithm that takes care of the relative position of similar elements is called a stable sorting algorithm. In a stable sorting algorithm, the similar elements in the sorted data are placed in the order they were present in the unsorted data. Insertion sort, merge sort, bubble sort, timsort, and counting sort are examples of stable sorting algorithms.
Online: An online sorting algorithm can process input data based on its availability. It doesn’t require the whole data to perform sorting. The new element is inserted into its location upon arrival. Insertion sort and heap sort with a priority queue are examples of online sorting algorithms.

Time and space complexity

The time a program or algorithm requires to execute completely is called its time complexity. Multiple factors could affect the program’s total time, e.g., hardware, compiler, operating system, algorithm, input size, etc. In sorting algorithms, the time complexity of an algorithm is the number of elementary operations with respect to the input size. The time complexity is divided into three categories:

Best case: This is the minimum time to sort a sorted array.
Average case: This is the expected time to sort any possible input array.
Worst-case: This is the maximum time to sort an unsorted array.

In sorting algorithms, the space complexity of an algorithm is the amount of allocated extra memory with respect to the input size to complete the program execution.

Comparison of sorting algorithms

Let’s compare different sorting algorithms:

Algorithm	Properties				Time Complexity
Algorithm	Adaptive	In-place	Stable	Online	Best	Average	Worst
Bubble sort (simple)	No	Yes	Yes	No	O(n²)	O(n²)	O(n²)
Bubble sort (with `swapped` flag)	Yes	Yes	Yes	No	O(n)	O(n²)	O(n²)
Insertion sort	Yes	Yes	Yes	Yes	O(n)	O(n²)	O(n²)
Selection sort	No	Yes	No	No	O(n²)	O(n²)	O(n²)
Merge sort	No	No	Yes	No	O(nlogn)	O(nlogn)	O(nlogn)
Quick sort	No	Yes	No	No	O(nlogn)	O(nlogn)	O(n²)
Heap sort	No	No	No	No	O(nlogn)	O(nlogn)	O(nlogn)
Count sort	No	No	Yes	No	O(n+k)	O(n+k)	O(n+k)
Radix sort	No	No	Yes	No	O(kn)	O(kn)	O(kn)
Bucket sort	No	No	Yes	No	O(n+k)	O(n+k)	O(n²)
Timsort	Yes	No	Yes	No	O(n)	O(nlogn)	O(nlogn)
Flash sort	Yes	Yes	No	No	O(n)	O(n)	O(n²)
Comb sort	Yes	Yes	No	No	O(nlogn)	O(n²)	O(n²)
Cocktail sort	Yes	Yes	Yes	No	O(n)	O(n²)	O(n²)
Pigeonhole sort	No	No	Yes	No	O(n+k)	O(n+k)	O(n²)
Gnome sort	Yes	Yes	No	No	O(n)	O(n²)	O(n²)
Pancake sort	No	Yes	No	No	O(n²)	O(n²)	O(n²)
Bitonic sort	No	No	No	No	O(nlogn)	O(nlogn)	O(nlogn)
Shell sort	No	Yes	No	No	O(nlogn)	O(nlogn)	O(n²)
Tree sort	No	No	Yes	Yes	O(nlogn)	O(nlogn)	O(n²)

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