Sorting is the method used to arrange the elements in proper order. It is a technique used in Data Structures and Algorithms. Sorting can be done using many methods. Both Quicksort and Merge Sort use the divide and conquer method to sort the elements. It is a method where we will part the elements into two and will combine them after rearranging the elements.

**Quick Sort vs Merge Sort**

**The main difference between the Quick Sort and Merge Sort is that the quicksort is used to compare each element with another element named a pivot, while merge sort is used to divide the array into two until it is left with one element. When you have limited space, it would be better if you use quicksort. If you have limited time, then it would be good if you use merge sort.**

In quick sort, you choose any random element and name it as a pivot. This is the element that will divide or partition the array. If you are confused on which element should be taken as a pivot. Then you can go for the first element as the pivot element. The worst-case is o (n^2). The average case is o (n log n). The best-case is o (n).

Merge sort is one of the most frequently used and respected algorithms in data structures. It has many advantages when compared with quicksort because of its time complexity. The worst-case is o (n log n). The average case is o (n log n). The best-case is o (n log n).

**Comparison Table Between Quick Sort and Merge Sort**

Parameters of Comparison | Quick Sort | Merge Sort |

Definition | It is one of the sorting algorithms to place the elements in order. | It is an algorithm used to sort the elements by comparing them. |

Space | It uses minimum space. | It uses more space. |

Array Efficiency | It is good to work with smaller arrays. | It can work with all types of arrays. |

Working Speed | It will work faster for smaller data sets. | It maintains the same speed for all data sets. |

Method of Sorting | It uses Internal Sorting. | It uses External Sorting. |

**What is Quick Sort?**

In quick sort choosing the pivot, the element is very important to solve the problem. One simple mistake will take more time. Once you finish the partition process, make the elements divided into two. Such as one row should contain elements that are less than the pivot, and the other row should contain elements greater than the pivot.

Then the next step is to sort the elements recursively. The leftmost section is called the left partition. The rightmost section is called the right partition. Dividing the problem into two means, you are reducing it into a linear time-bound. This is the reason for its average time complexity.

Quick Sort is to be used when you think you have very few elements. Because when you try to sort it with a large number of elements you might make a mistake if you try to do it for the first time. Also, it takes more time to solve the problem for bigger elements.

It is an easier method as it requires a limited amount of space and some good knowledge. The pivot element compares the element to its left and right side as well. It used to do this till all the elements are arranged in proper order.

**What is Merge Sort?**

Merge Sort is a comparison-based algorithm. It still preserves the order of elements even after sorting. It is used to split the array into two sections. It will sort each array and then combine them together. This sorting technique requires additional memory space to sort the auxiliary array.

Since this divides the element again and again till it becomes one. This technique reduces the sorting time. This method uses three arrays. The first two arrays are used for storing half of the elements. Then the next one is used to store the final sorted list of arrays.

After this process, each array will be sorted recursively. One of the key steps in merge sort is you have to identify the breakpoints. It is basically identifying the ascending or descending number in the set of elements. Then store them in the array and finally merge them using the techniques.

Merge sort is a great place to start with the divide and conquer process. The disadvantage is that it has to make all the elements of the subarray in a separate recursive cell, but the answer will be precise. One of the important concepts related to the merge sort algorithm is the inversion method.

**Main Differences Between Quick Sort and Merge Sort**

- Merge Sort gives you a precise value irrespective of a large number of elements but takes more space to calculate than quicksort.
- Merge sort is somewhat faster when compared with quicksort.
- Quicksort is mostly based on swapping the elements. On the other hand, merge sort is based on merging the sorted arrays.
- Quicksort requires some additional memory for recursion. But Merge sort requires additional memory for both recursions as well as for merging.
- Quicksort is faster when compared with merge sort in solving the problem because of its space requirement.

**Conclusion**

Both sorting methods will provide the same result at the end. It depends upon the kind of problem we are given so that we can choose the perfect method to solve the problem in the given amount of time. If you find the problem seems more complicated, think about the method and analyze it so that you will get the precise result.

Our main aim is to get the result at the end. Try to do it by both methods if you are a beginner so that you will understand the differences and help you solve the upcoming problems. In simple words, quicksort can be called a Place Sorting Algorithm, and merge sort can be called as Out Place Sorting Algorithm.

**References**

- https://link.springer.com/chapter/10.1007/978-3-540-87744-8_21
- https://www.mdpi.com/2073-8994/9/9/176

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