In the computer science field, Quick sort and merge sort play an important role, especially in sorting unorganized data. Sorting is an algorithm that puts the elements of a list into order. The most frequently used orders are numerical order, lexicographical order, and either ascending or descending order. There are several popular sorting algorithms that are used according to their characteristics.
In this article, we will be discussing in detail the differences between the Quick Sort and Merge Sort methods.
What is Quick Sort?
Quicksort can sort items of any type for which a comparison is defined because it is a comparison sort. This sorting algorithm is effective and versatile. It employs a divide-and-conquer strategy. It works by taking a pivot (key) element from an array and dividing the remaining elements into two sub-arrays. Quicksort’s mathematical analysis reveals that it takes O (n log n) comparisons to sort n items.Â
It divides the array into smaller sub-arrays, chooses a pivot element again for each sub-array, and repeats this step until all the elements are arranged in a list.
If we do not take the recursive stack space into account, the auxiliary space is O(1). In the worst-case scenario, quicksort could result in O(N) if we consider the recursive stack space.Â
What is Merge Sort?
Merge sort is another comparison-based sorting algorithm. Additionally, it is a divide-and-conquer algorithm developed by John von Neumann in 1945.Â
Merge sort divides an unsorted list into n sublists, each of which contains one element (a list with one element is sorted). It merges the sublists to create a new sorted sublist until only one sublist remains. For each element in the list, the merge function performs O(1) (constant) number of operations. Due to the n elements, the list’s size is O(n). Merge runs in O(n) time because it performs the same amount of work O(n) times.Â
The dimension of auxiliary space is O(N). When using merge sort, each element is copied into a separate array. As a result, N auxiliary spaces are required for merge sort
Difference between Quick Sort and Merge Sort
- Quick sort arranges the elements in ascending order by comparing and interchanging the actual positions of the elements in a particular array, whereas Merge sort arranges the given sets in ascending order using the divide-and-conquer technique and then compares them with corresponding elements to sort the array.
- Quick sort is more efficient for smaller arrays as compared to Merge sort.
- Merge sort is more efficient for larger arrays as compared to Quick sort.
- The average time complexity of quick sorting is O (N log (N)), whereas the time complexity of generic merge sorting does not depend on the contents of the array. It performs N.log(N) comparisons and moves. Some enhanced versions may recognize special cases and complete them in O(N) time. The worst-time complexity of the Quick sort is O (n2), whereas it is O (n log n) for the Merge sort.
- The divide step in merge sort does very little, and the combine step does all of the heavy lifting. Quicksort is the inverse: all of the real work takes place during the divide step. In fact, the combined step in quicksort has no effect.
- Quick Sort is an internal sorting method that sorts the array available on main memory, whereas Merge Sort is an external sorting method that sorts the array available on an external file.
- Quick sort doesn’t require any additional space to perform sorting, whereas Merge sort requires additional space to merge subarrays. The space utilized by the merge algorithm is temporary.
Algorithms of Quick Sort and Merge Sort
Quick Sort
The algorithm of Quick sort algorithm is given here in the table. You can check the algorithm and develop the code based on any language of your choice.
If T(n) is the time required to sort an array of size n using quick sort, the recurrence relation for quick sort is given byÂ
                                          T(n)= T(n-1) + O(n)
| Quick Sort Algorithm |
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Quick sort is completed by the partition algorithm. It takes the two ends and switches them at their respective positions to rearrange the subarray from beginning to end at their location.
| Quick Sort Algorithm |
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Merge Sort
Merge sort works on the divide and approach technique. It first divides the array into smaller parts and then combines it in a sorted way. Suppose merge sort requires T(n) time to sort an array of size n, then the recurrence relation is given by           Â
                                         T(n) = 2T(n/2) + θ(n)
| Quick Sort Algorithm |
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Advantages of Quick Sort and Merge Sort
Let us check some of the important benefits of the most famous sorting algorithm approach in this article.
Advantages of Quick Sort
- It is a divide-and-conquer algorithm that makes it easier to solve problems.
- It is efficient for large data sets.
- Due to the fact that it only needs a small amount of memory to run, it has a low overhead.
Advantages of Merge Sort
- Merge sort is a stable sorting algorithm, which means it keeps equal elements in the input array in their relative order.
- Merge sort functions well even on large datasets thanks to its worst-case time complexity of O(N log N).
- Merge sort is an algorithm that naturally scales to multiple processors or threads, making it easy to parallelize.
Disadvantages of Quick Sort and Merge Sort
Now, let us talk about some of the disadvantages that these two sorting algorithms possess in this article.
Disadvantages of Quick Sort
- When the pivot is selected incorrectly, it has a worst-case time complexity of O(N2).
- Small data sets should not be used with it.
- It is not a stable sort because we are swapping elements based on the pivot’s position (without taking into account their original positions), so if two elements have the same key, their relative order will not be preserved in the sorted output in a quick sort.
Drawbacks of Merge Sort
- During the sorting process, the merged sub-arrays must be stored in additional memory, which is necessary for merge sort.Â
- Since merge sort is not an in-place sorting algorithm, the sorted data must be stored in additional memory. This could be a drawback for programs where memory usage is a concern.
- In comparison to other sorting algorithms like insertion sort, Merge sort has a higher time complexity for small datasets. This may cause performance to be slower for very small datasets.
Application of Quick Sort and Merge SortÂ
Here, we will check the uses of both algorithms. Let us know the specific purposes for these algorithms in real life.
Application of Quick SortÂ
- Quicksort is a cache-friendly algorithm because, when applied to arrays, it has a good locality of reference.
- It is used in situations where a stable sort is not required.
- It is an in-place sort that requires no additional storage memory and is used in operational research and event-driven simulation.
- Because it is tail-recursive, it allows for complete call optimization.
Application of Merge Sort
- Merge sort is especially well-suited for sorting large datasets due to its guaranteed worst-case time complexity of O(n log n).
- Merge sort can be customized to handle a variety of input distributions, including partially sorted, nearly sorted, and completely unsorted data.
- Merge sort is frequently used in external sorting when the data to be sorted is too large to fit into memory.
FREQUENTLY ASKED QUESTIONS (FAQs)
Q1. Is quick sorting faster than merge sorting?
Ans. The quick sort algorithm is typically faster than the merge sort algorithm. However, when the data is huge and stored on external devices such as a hard drive, merge sort is the clear winner in terms of speed.
Q2. Is quicksort a recursive sort algorithm?
Ans. Yes, both Quick and Merge Sort are based on divide-and-conquer algorithms. Quicksort also competes with merge sort, another recursive sort algorithm, but with the benefit of worst-case running time.
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