Difference Between Quick Sort and Merge Sort

Differences Analysis of Algorithms Data Structure Algorithms

The task of arranging the elements of an array in a particular order is referred to as sorting. The sorting of an array or a list is mainly done to make the searching easier. There are several types of sorting algorithms, but in this article, we will concentrate on quick sort and merge sort. Both quick sort and merge sort algorithms are based on the divide-and-conquer sorting algorithms, hence they work almost in a similar way.

Read this article to learn more about quick sort and merge sort and how these sorting techniques are different from each other.

What is Quick Sort?

Quick Sort is considered as an internal sorting algorithm. In quick sort, the elements need to be partitioned into different parts repeatedly until it can't be divided further. Thus, the array is split into a specific number of parts, in a specific ratio, and it is not divided necessarily into exactly half. Quick sort algorithm is based on the divide-and-conquer strategy. It is also known as partition exchange sort.

In quick sort, the worst case complexity is . It uses a key/pivot element to sort the elements. It works well with a small number of elements in an array. Quick sort is better than other sorting algorithms since it is quick. Also, it requires less additional space/memory. However, it does not work well when an array contains a large number of elements.

Quick sort is not a stable sorting method because it does not maintain the relative order of two equal elements in the sorted output. Two equal elements may not appear in the same order in the sorted output as they appear in the input array to be sorted.

What is Merge Sort?

Merge Sort is considered as an external sorting algorithm. In merge sort, the array is split into two sub-arrays where is the number of elements in the array. This is done until only on the element is left after splitting the array. Merge sort too is based on the divide-and-conquer strategy. The worst case complexity in merge sort is, where is the number of elements.

The advantage of using merge sort is that it works with any array size, be it small or large. However, it uses additional storage, since it needs to sort the auxiliary array. It mainly uses three arrays, where two of them store two halves of the array and the third array stores the final sorted list.

Merge sort works well at a good speed on any data size, and is considered to be efficient. Merge sort is a stable sorting algorithm because it maintains the relative order of equal elements in the sorted output.

Difference between Quick Sort and Merge Sort

The following are the important differences between quick sort and merge sort −

S.No.	Quick Sort	Merge Sort
1.	Quick Sort is considered as an internal sorting algorithm.	Merge Sort is considered as an external sorting algorithm.
2.	In Quick Sort, the elements need to be partitioned into different parts repeatedly until it can't be divided further.	In the merge sort, the array is split into two sub-arrays where is the number of elements in the array.
3.	The worst-case complexity is.	The worst case complexity in the case of merge sort is, where is the number of elements.
4.	It works well with a small number of elements in an array.	The merge sort is that it works with any size of the array, be it small or large.
5.	It requires less additional space/memory	It uses additional storage, since it needs to sort the auxiliary array.
6.	It does not work well with large number of elements in an array.	It works well at a good speed on any data size, and is considered to be efficient

Conclusion

The most significant difference between the two is that quick sort uses a pivot element to sort, while merge sort does not use the pivot element to sort an array. However, both work on the divide-and-conquer algorithm.

Kiran Kumar Panigrahi

Updated on: 21-Feb-2023

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