Quick Sort vs Merge Sort: Difference and Comparison

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 partition the elements into two and will combine them after rearranging the elements. 

Key Takeaways

  1. Quick Sort is a sorting algorithm that uses a pivot element to divide the array into two partitions and recursively sort them. In contrast, Merge Sort divides the array into two halves, sorts them separately, and merges them.
  2. Quick Sort has a worst-case time complexity of O(n^2), but on average, it has a time complexity of O(n log n), whereas Merge Sort has a guaranteed time complexity of O(n log n).
  3. Quick Sort is an in-place sorting algorithm, meaning it doesn’t require additional memory, while Merge Sort requires additional memory to store the temporary arrays during the merge step.

Quick Sort vs Merge Sort

Quick sort is a sorting algorithm that uses a divide-and-conquer approach to sort an array or list of elements. Quick sort is efficient and is used in practice. Merge sort is a divide-and-conquer algorithm that divides an array into two halves. It is useful for large data sets.

Quick Sort vs Merge Sort

In quick sort, you choose any random element and name it a pivot. This is the element that will divide or partition the array if you are confused about 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

Parameters of ComparisonQuick SortMerge Sort
DefinitionIt is one of the sorting algorithms to place the elements in order.It is an algorithm used to sort the elements by comparing them. 
SpaceIt uses minimum space.It uses more space.
Array EfficiencyIt is good to work with smaller arrays.It can work with all types of arrays.
Working SpeedIt will work faster for smaller data sets.It maintains the same speed for all data sets.
Method of SortingIt 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.

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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 sides as well. It used to do this till all the elements were arranged in proper order

quick sort

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. 

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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.

merge sort

Main Differences Between Quick Sort and Merge Sort

  1. Merge Sort gives you a precise value irrespective of a large number of elements but takes more space to calculate than quicksort. 
  2. Merge sort is somewhat faster when compared with quicksort.
  3. Quicksort is mostly based on swapping the elements. On the other hand, merge sort is based on merging the sorted arrays.
  4. Quicksort requires some additional memory for recursion. But Merge sort requires additional memory for both recursions as well as for merging.
  5. Quicksort is faster when compared with merge sort in solving the problem because of its space requirement.
Difference Between Quick Sort and Merge Sort
References
  1. https://link.springer.com/chapter/10.1007/978-3-540-87744-8_21
  2. https://www.mdpi.com/2073-8994/9/9/176

Last Updated : 12 July, 2023

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24 thoughts on “Quick Sort vs Merge Sort: Difference and Comparison”

  1. The article’s explanation of the recursive sorting process and the specific use cases of Quick Sort and Merge Sort is very enlightening. It covers the optimal scenarios for implementing each sorting method and highlights the advantages and potential drawbacks of both algorithms.

    Reply
    • I share your perspective, Kevin. The article’s elucidation of the recursive sorting processes and the real-world application of Quick Sort and Merge Sort provides a well-rounded comparison, making it easier to discern when to use each algorithm for optimal results.

      Reply
  2. The detailed analysis of the Merge Sort algorithm and its comparison to Quick Sort is incredibly valuable. The article elegantly describes the process of merge sorting and the additional memory space required for this sorting technique.

    Reply
    • I couldn’t agree more, Charlie. The article’s breakdown of the merge sorting process and the use of auxiliary arrays effectively portray the intricacies of Merge Sort, contributing to a comprehensive understanding of the algorithm.

      Reply
  3. The article’s detailed explanation of the importance of choosing the pivot element in Quick Sort and the working principles of Merge Sort is highly informative. It provides a comprehensive understanding of the internal and external sorting methods used by both algorithms.

    Reply
    • I echo your sentiment, Lola. The article’s comprehensive illustration of the internal and external sorting methods used by Quick Sort and Merge Sort enhances the readers’ understanding of the operational differences and use cases of each algorithm.

      Reply
    • Absolutely, Richardson. The detailed explanations offered in the article about Quick Sort and Merge Sort’s operational approaches provide valuable insights into the complexities and nuances of each sorting method.

      Reply
  4. The article’s detailed description of the key concepts and comparison of Quick Sort and Merge Sort is highly beneficial. It effectively highlights the differences in the sorting approaches, enabling readers to make informed decisions when selecting a suitable sorting algorithm based on their specific needs.

    Reply
    • I completely resonate with your perspective, Tjackson. The article’s comprehensive comparison of Quick Sort and Merge Sort’s foundational principles and application scenarios equips readers with essential insights for evaluating and implementing the appropriate sorting algorithm.

      Reply
    • Absolutely, Tjackson. The article lucidly elucidates the essential differences between Quick Sort and Merge Sort, providing a comprehensive understanding of the unique capabilities of each sorting algorithm and their practical implications.

      Reply
  5. The article presents the complexity of Quick Sort and Merge Sort in a precise manner, making it easier to comprehend. The comparison table is an effective way to highlight the differences between the two sorting methods.

    Reply
    • The detailed explanation about how Quick Sort and Merge Sort work in different scenarios is very enlightening. I appreciate the practical application and best use case scenarios provided in the article.

      Reply
    • Absolutely, Carrie. The explanation of the parameters of comparison between Quick Sort and Merge Sort provides a clear understanding of the efficiency, working speed, and space used by each algorithm. This makes it easier to choose the right sorting method based on specific requirements.

      Reply
  6. The article makes a clear distinction between Quick Sort and Merge Sort, by explaining in detail the key takeaways and the comparison between both. It also provides a comprehensive definition of Quick Sort and Merge Sort, with a detailed explanation of each algorithm’s purpose and best use case scenario.

    Reply
    • I completely agree with you, Cox. It’s a very informative article that provides all the necessary information one might need to understand Quick Sort and Merge Sort. Furthermore, the comparison table between the two algorithms is exceptionally helpful in understanding the practical application of each sorting method.

      Reply
  7. The article thoroughly describes the Quick Sort algorithm, providing a step-by-step guide on how to execute Quick Sort effectively. The explanation of the importance of choosing the pivot element and the partition process is particularly insightful.

    Reply
    • I completely agree, Karlie. The article does an excellent job of simplifying the complex process of Quick Sort, making it easy to understand the step-by-step approach and its significance in sorting elements.

      Reply
  8. The thorough overview of Quick Sort and Merge Sort, along with their respective working speed and space usage, offers a well-organized comparison. The article effectively highlights the method of sorting used by each algorithm and their suitability for different types of data sets.

    Reply
    • I agree, Natasha. The article’s emphasis on the array efficiency, working speed, and method of sorting provides valuable insights into the practicality of Quick Sort and Merge Sort, enabling readers to make informed decisions when choosing a sorting method.

      Reply
    • Indeed, the detailed comparison of the algorithms’ space usage and array efficiency is particularly helpful. It allows developers to evaluate the optimal sorting algorithm based on the specific requirements of their applications.

      Reply
  9. The detailed explanation of the importance of choosing the pivot element in the Quick Sort algorithm and the potential pitfalls in making a mistake during this process is very informative. It provides a clear understanding of the intricacies involved in executing Quick Sort.

    Reply
    • Agreed, Ibailey. The article’s emphasis on the importance of pivot selection is crucial, and the caution against potential mistakes in choosing the pivot element is beneficial for readers seeking to implement Quick Sort correctly.

      Reply
  10. The article’s explanation of the working principles and application scenarios of Quick Sort and Merge Sort is remarkably detailed and informative. It elegantly explains the significance of reducing sorting time through the recursive approach adopted by Merge Sort.

    Reply
    • I couldn’t agree more, Irussell. The article’s delineation of the operational intricacies and use case scenarios of Quick Sort and Merge Sort provides a comprehensive understanding of the strategies employed by these algorithms for efficient sorting.

      Reply

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