A sorting algorithm is the most commonly used algorithm. It is used to sort or arrange elements in an array/ or a list in a particular order. Various sorting algorithms are available to complete different operations of sorting. It is usually done in both ascending and descending order. Sorting algorithms are selected as per requirements. let us know about that the Quick Sort Vs Merge Sort.

**Different Sorting Algorithms**

Different sorting algorithms are Bubble Sort, Bucket Sort, Counting Sort, Heap Sort, Insertion Sort, MergeSort, Quicksort, Radix Sort, Shell Sort, and Selection Sort.

**Quick Sort**

Quicksort is one of the sorting algorithms. It follows the divide and conquers rule. The main steps are given below.

- Start by dividing the given array into subarrays.
- Select a pivot element.
- Choose the pivot element (on the left side of the pivot, elements smaller than the pivot are placed and on the right of the pivot, elements larger are placed).
- Then, the left and right sub-arrays are divided further using the same way.
- Repeat the process until the array size becomes one.
- Now, elements of the array are sorted using quicksort.
- Combine the subarrays.

**Quicksort Complexity**

**Time Complexity**

The time complexity of an algorithm is the total time taken by the algorithm, i.e the amount of time taken by a particular algorithm to complete executing a function. It is different for different algorithms. The time complexity of Quick Sort is given as, The best case is O(n*log n), The worst case is O(n2), and The average Case is O(n*log n)

**Space Complexity**

The space complexity of an algorithm is the total space taken i.e the storage space taken by a particular algorithm during the time of the execution of a function, concerning the input size. The space complexity of Quick Sort is in the order of n, O(log n).

**Quick Sort Applications**

The quicksort algorithm is used in fields like Commercial Computing. It is applied in different private and government organizations. The main use is to sort various data like sorting files by name or date or price, sorting students by their roll no, sorting account profiles by given id, etc.

**Merge Sort**

MergeSort is one of the most popularly used sorting algorithms, similar to that of a quick sort. Mergesort follows the Divide and conquer rule. Here, an array is divided into several arrays, and later it is combined.

**Merge Sort Algorithm**

The Merge Sort function starts by making the array into two halves. The dividing takes place until the size of the subarray is one i.e. a single element is left. Then, the merge function combines the sorted arrays into larger arrays one by one till it becomes a combined complete array.

The function MergeSort(A, 0, length(A)-1) is to be called for sorting the array given. The merge sort algorithm is a recursive algorithm (where a function calls itself). The function is called until the array has a single element, later it is combined to form the sorted array.

**The Merge Step of Merge Sort**

The merge step is used to merge two sorted arrays. It is done in such a way that merging the two sorted arrays can make a sorted large array. The algorithm has and maintains three-pointers, one each for the subarrays and another one for positioning the current index of the sorted array.

Here, the task of the algorithm is to merge two subarrays, A[a..b] and A[b+1..c], creating a sorted array A[a..c], inputs to the function are A, a, b and c.

**Working**

The working of the mergesort algorithm is as follows.

- Create copies of the subarrays L ← A[a..b] and M ← A[b+1..c].
- Create three-pointers i, j and k
- “i” – current index of L, starts at 1
- “j” – current index of M, starts at 1
- “k” – current index of A[p..q], starts at p.

- Find the largest among L and M and put it in the correct position at A[a..b]. This is done until it reaches the end of Either L or M.
- When elements are no longer available in either L or M, pick up the remaining elements and put them in A[a..b].

**Merge Sort Complexity**

**Time Complexity**

The time complexity of the merge sort is, The best case is O(n*log n), The worst case is O(n*log n), and the average case is O(n*log n). It varies for different algorithms.

**Space Complexity **

Merge sort has a space complexity in the order of n, i.e O(n).

**Merge Sort Applications**

Merge sort is one of the best and most popularly used sorting algorithms. It is used mainly in E-commerce applications, External sorting, and Inversion Count Problems.

Mergesort is a stable sort so that it can be easily applied on linked lists and huge lists stored on slow-to-access media such as disk storage or network-attached storage.

**Conclusion**

Sorting algorithms are used almost everywhere for making life easy for computers. Quicksort and merge sort are two of these. Quicksort is an internal algorithm, unlike merge sort. It works on a divide and conquer strategy. Whereas Merge sort is an external algorithm and is also based on the divide and conquer strategy. Quicksort is always considered to be the best in the application and is better than merge sort. It is defined by main reasons such as Auxiliary space (space taken by merge sort is larger than quicksort), the Worst case of merge sort, and locality of reference (quicksort is faster in most cases like in virtual environments). Apart from all these disadvantages of merge sort, merge sort has its advantage when it is used for large data structures i.e.

**Frequently Asked Questions**

- What is a divide and conquer strategy?

The divide and Conquer rule is used to divide a given problem into different subproblems. When their subproblems are solved individually, and later, it is combined to get the final result.

- What are the steps involved in the divide and conquer rule?

It is done in 3 steps. They are “divide”, “conquer” and “combine”.

**Divide**

Let b be the halfway point between a and c, then split the subarray A[a..c] into two arrays A[a..b] and A[b+1, c].

**Conquer**

Here in this step, sort both the subarrays A[a..b] and A[b+1, c].If it does not reach the best case, then divide both these subarrays again and sort the same way.

**Combine**

Here, in this step, we get the sorted arrays A[a..b] and A[b+1, c] for the array A[a..c]. Now, combine these arrays, creating a sorted array.