# An overview of the QuickSort algorithm (2023)

March 10, 2022

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(Video) A Complete Overview of Quicksort (Data Structures & Algorithms #11)

Sorting organizes items in a structured way. Quicksort is one of the most popular sorting algorithms in use.`nlogn`Compare the sorting of an array of n elements in a typical situation. Quicksort is based onDivide and conquer strategy.Let's look at the fast sort algorithm in this tutorial and see how it works.

Quicksort is a fast sorting algorithm that divides a large array of data into smaller subarrays.This implies that each iteration works by splitting the input into two components, sorting them, and recombining them.For large amounts of data, the technology is highly efficient due to its medium and optimal complexity.`O(n*login).`

Developed by Tony Hoare in 1961, it remains one of the most effective general-purpose sorting algorithms available today. It works by recursively sorting the sublists on either side of a given pivot and dynamically moving the list items around that pivot.

Therefore, the quick classification method can be summarized in three steps:

• To choose:Choose an element.
• To divide:Break up the problem set by moving smaller pieces to the left of the pivot and larger pieces to the right.
• Repeat and combine:Repeat the steps and combine the previously sorted matrices.

## Benefits of Quicksort

Let's look at some of the main benefits of using Quicksort:

• It works quickly and efficiently.
• It has the best time complexity compared to other ranking algorithms.
• Quick Sort has a spatial complexity of`the (enter)`, making it an excellent choice for situations where space is limited.

## Quicksort Limitations

Although QuickSort is the fastest algorithm, it has some drawbacks. Let's take a look at some of the disadvantages of Quicksort.

• This sorting technique is considered unstable because it does not preserve the initial order of key-value pairs.
• When the pivot is the largest or smallest, or when all components are the same size. Quicksort performance is severely impacted by these worst case scenarios.
• It is difficult to implement because it is a recursive process, especially when recursion is not available.

Let's look at an example to better understand the fast sort algorithm. In this example, the matrix(shown in the graphic below)contains unsorted values ​​that we will sort using quicksort.

(Video) Algorithms: Quicksort

## 1). Select pivot point

The process starts with selection.an element (known as a pivot)from the list; It can be any element. A pivot can be:

• every random item
• The first or last item.
• middle element

For this example, we used the last element,`4,`as our axis.

## two). array reordering

The objective here now is to reorganize the list so that all itemsless than the pivot are on the leftof this and allElements larger than the pivot are directed to the rightfrom that.

• HeThe pivot element is compared to all elementsstarting with the first index. If the element is greater than the pivot element, a second pointer is added.
• Compared to other itemsif an element smaller than the pivot element is found, the smaller element is replaced by the previously identified larger element.

Let's simplify the previous example,

• Every element that starts with`7`, is compared to the pivot (`4`). A second pointer is defined as`7`bom`7`is bigger than`4`.
• The next element, element`2`it is now compared to the pivot. As`2`It is less than`4`, is replaced by the largest number`7`what was found before.
• The payment`7`Y`2`They are exchanged. The pivot is now compared to the closest element,`1`which is less than`4`.
• ok one more time`7`is exchanged with`1`.
• The process continues until the penultimate element is reached,and at the end, the pivot element is replaced by the second pointer. here, number`4`(Pivot) is replaced by number`6`.

like elements`2`,`1`, Y`3`they are less than 4, they are on the left side of the pivot. The elements can be in any order:`"1", "2", "3" or "3", "1", "2" or "2", "3", "1"`. The only requirement is that all elements must be less than the pivot point. Also, on the right side, all components must be greater than the pivot, regardless of their order.

Simply put, the algorithm looks for any value that is less than the pivot. Values ​​less than pivot are placed on the left, while values ​​greater than pivot are placed on the right. Once the values ​​are reordered, the pivot is placed in its sorted position.

3). Share Subarrays

After we partition the array we can solve this problemtwo sub-problems. First,Sort array segmentto the left of the pivot, and then sort the array segment to the right of the pivot.

• In the same way that we rearranged the elements in step 2,We will select a pivot element for each of the left and right subparts individually.
• Now let's organize the sublist so that all elements are less than the pivot point that points to the left. element for example`3`is the largest of the three elements that satisfies the condition, so the element`3`is in an orderly position.
• In the same way, we will edit the sublist again and order the elements`2`Y`1`. We will stop the process when we are done with a single item.
• Repeat the same process for the sublist on the right.Subarrays are further subdivided until each subarray consists of a single element.
• Now the array is sorted at this point :)

## Fast Sort Algorithm

`//start -> start index, end --> end indexquicksort(array, start, end){if (start < end){pIndex = partition(A, start, end)Fast sort (A, start, pIndex-1)Quicksort(A,pIndex+1, fin)}}`

## divisionfunction algorithm

Subarrays are rearranged in a specific order using the partition method. You will find different ways to partition. Here we see one of the most used methods.

`partition(array, start, end){// Set the rightmost index as a pivotPivot = arr[End];i = (start - 1) // index of the smallest element and display it// Correct pivot position found so farfor (j = start; j <= end- 1; j++){// If the current element is less than the pivotif (arr[j] < Girar){I++; //Increase the index of the smallest elementSwap arr[i] and arr[j].}}interchange arr[i + 1] and arr[end])back (me + 1)}`

Let's look at quick sort programs written in the JavaScript and Python programming languages.

JavaScript

Let's start by creating a function that allows you to swap two components.

`Function Interchange (arr, i, j){ let temp = arr[i];matrix[i] = matrix[j];matrix[j] = temperature;}`

Now let's add a function that takes the last element (last value) as the pivot, moves all minor elements to the left of the pivot and all major elements to the right of the pivot, and places the pivot in the appropriate location in the .sorted array.

`function partition(arr, start, end) {// pivot pointlet pivot = arr[end];/* Index of a minor element that indicates the correct position of the pivot previously. */six i = (start - 1);for (chica j = inicio; j <= fin - 1; j++) {// If the current element is less than the pivotif (arr[j] < Girar) {you++;swap(arr, i, j);}}swap(arr, i + 1, Fin);return(i+1);}`

Then we add the main function that splits and sorts the elements.

`function quicksort(arr, start, end) {if (start < end) {// The partition index is represented by pi.let pi = partition(arr, start, end);// Sort the elements before and after the partition separatelyquicksort(arr, start, pi - 1);quicksort(arr, pi + 1, fim);}}`

Finally, let's add a function to print the array.

`function printArray(array, size) {for (let i = 0; i < size; i++)document.write(arr[i] + " ");document.write("");}// Let's start sorting the unsorted ones.let arr = [7, 2, 1, 6, 8, 5, 3, 4];let n = arr.length;document.write("Matriz original:" + arr);quicksort(arr, 0, n - 1);document.write("Sortiertes Array:"+arr);`

Here is the full (js) quick sort implementation code

(Video) Quick sort in 4 minutes

Python

Let's start by creating a function that will sort the first and last elements of an array.

`def find_pviot_index(A,inicio,fin):Pivots=A[End]p_index=startto iterate over range (start, end):and A[iter] <= Pivots:A[p_index],A[iter]=A[iter],A[p_index]p_index+=1A[p_index],A[end]=support point,A[p_index]return p_index`

Next, let's add the main function that QuickSort implements.

`def quick_sort(To,start,end):if start < end:pivot_index=find_pviot_index(A,inicio,fin)print("--------------",A)quick_sort(A,inicio,pivot_index-1)quick_sort(A,pivot_index+1,fin)`

Finally, let's add a function to print the array.

`A=List()n=int(input("Set of numbers to insert:"))for x in the range (0, n):num=int(input("Num eingeben:"))A.appendix(num)print("Original-Array:",A)quick_sort(A,0,n-1)print("Sort array:",A)`

Here is the complete code for implementing Quicksort in Python.

Let's look at quicksort's spatial and temporal complexity in best, average, and worst cases. In general, the time consumed by QuickSort can be written as follows.

`T(n) = T(k) + T(n-k-1) + O(n)`

Here,`T(k)`Y`T(n-k-1)`refer to two recursive calls while the last term`E)`refers to the partitioning process. The number of elements less than the pivot is denoted by`k`.

## time complexity

1). Best case complexity:If the partition algorithm always chooses the middle element or close to the middle element as the pivot, the best case scenario will occur. The time complexity of quicksort in the best case is`O (n*login)`. The following is the best case iteration.

`T(n) = 2T(n/2) + O(n)//Solution O(nRegister)`

two). Average case complexity:This occurs when the array elements are in an unordered order that doesn't grow or shrink correctly. The average time complexity of the Quicksort case is`O(n*login)`. The following is repetition in the average case.

`T(n) = T(n/9) + T(9n/10) + O(n)//Solution O(nRegister)`

3). Worst case complexity:The worst situation is when the partitioning algorithm chooses the largest or smallest element as the pivot element each time. The worst-case time complexity of Quicksort is`em 2)`. The following is the worst case iteration.

`T(n) = T(0) + T(n-1) + O(n)//O(n2) solution`

## space complexity

The space complexity for quicksort is`O(record n).`

The sort algorithm is used to find information and since the quick sort is the fastest, it is often used as a more efficient search approach.

• It is used where a stable classification is not required.
• Since it is tail recursive, any optimization call can be executed.
• It is useful in event-driven simulation and operations research.

QuickSort can have some drawbacks, but it is the fastest and most efficient sorting algorithm available. The quick sort has a`Or (enter)`Spatial complexity, making it an excellent choice for situations where space is limited.

Although the worst-case running time is always the same, Quicksort is generally faster than HeapSort`(begin session)`. Quicksort takes up less space than heapsort (due to the fact that a heap is an almost complete binary tree with pointers to it). So when it comes to sorting arrays, Quicksort is preferred.

QuickSort may have some drawbacks, but it is the fastest sorting algorithm out there. Quick Sort is an efficient algorithm that has proven itself in practice.

(Video) 5 1 Quicksort Overview 12 min

In this article, we learned what quicksort is, its advantages and disadvantages, and how to implement it. If you want a detailed explanation of an algorithm or a comparison of algorithms, feel free to comment below.

## FAQs

### What is the algorithm for quick sort? ›

Quicksort is the widely used sorting algorithm that makes n log n comparisons in average case for sorting an array of n elements. It is a faster and highly efficient sorting algorithm. This algorithm follows the divide and conquer approach.
...
2. Space Complexity.
Space ComplexityO(n*logn)
StableNO

How to do quick sort step by step? ›

Step 1 - Consider the first element of the list as pivot (i.e., Element at first position in the list). Step 2 - Define two variables i and j. Set i and j to first and last elements of the list respectively. Step 3 - Increment i until list[i] > pivot then stop.

What is Quick Sort write the algorithm and explain with suitable example? ›

Suppose the initial input array is: So after our first partition, the pivot element is at its correct place in the sorted array, with all its smaller elements to the left and greater to the right. Now QuickSort() will be called recursively for the subarrays {1,2} and {6,4,5} and continue till the array is sorted.

How does the quick find algorithm work? ›

The goal of this algorithm is to find if any two elements are connected. If not connected, then connect them.
...
We assume that:
1. Symmetric: If p is connected to q, then q is also connected to p.
2. Transitive: If p is connected to q and q is connected to r, p is connected to r as well.
3. Reflexive: p is connected to p.
Jan 13, 2020

What is the conclusion for quick sort algorithm? ›

Conclusion. Quick Sort method sorts the elements using the Divide and Conquer approach and has an average O(nLogn) complexity. It can be implemented in both recursive and iterative way. It is in-place, cache-friendly and also a tail-recursive algorithm.

What are the steps for sorting? ›

Sort by more than one column or row
1. Select any cell in the data range.
2. On the Data tab, in the Sort & Filter group, click Sort.
3. In the Sort dialog box, under Column, in the Sort by box, select the first column that you want to sort.
4. Under Sort On, select the type of sort. ...
5. Under Order, select how you want to sort.

What is the process of sorting process? ›

Sorting is the process of arranging data into meaningful order so that you can analyze it more effectively. For example, you might want to order sales data by calendar month so that you can produce a graph of sales performance. You can use Discoverer to sort data as follows: sort text data into alphabetical order.

How do you do sorting algorithms? ›

Start with a sorted list of 1 element on the left, and N-1 unsorted items on the right. Take the first unsorted item (element #2) and insert it into the sorted list, moving elements as necessary. We now have a sorted list of size 2, and N -2 unsorted elements. Repeat for all elements.

Why is quicksort the best algorithm? ›

There are certain reasons due to which quicksort is better: 1- Auxiliary Space: Quick sort is an in-place sorting algorithm. In-place sorting means no additional storage space is needed to perform sorting. Merge sort on the other hand requires a temporary array to merge the sorted arrays and hence it is not in-place.

Is quicksort the fastest sorting algorithm? ›

In practice, Quick Sort is usually the fastest sorting algorithm. Its performance is measured most of the time in O(N × log N). This means that the algorithm makes N × log N comparisons to sort N elements.

### Why quick sort algorithms are mostly used in applications? ›

The sorting algorithm is used for information searching and as Quicksort is the fastest algorithm so it is widely used as a better way of searching. It is used everywhere where a stable sort is not needed. Quicksort is a cache-friendly algorithm as it has a good locality of reference when used for arrays.

What is the objective of the searching algorithm? ›

In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the search space of a problem domain, with either discrete or continuous values.

What are the 5 basis of sorting? ›

Insertion, selection, bubble, merge, and quick sort.

What are the three basic sorting algorithms? ›

These sorting algorithms are the insertion sort, the bubble sort, and the selection sort.

What are the two basic types of sorting? ›

There are two broad types of sorting algorithms: integer sorts and comparison sorts. Comparison sorts compare elements at each step of the algorithm to determine if one element should be to the left or right of another element.

How do you explain sorting to a child? ›

Once a child is matching more than two objects, they are sorting. Sorting involves separating objects into groups according to their similarities, which means they are also noticing differences.

What are the two advantage of data sorting? ›

Systematic representation – sorting enables users to represent the data in a very systematic manner that enables fine presentation. Better understanding of data – when data is presented in a sorted and filtered manner then then data decoding and understanding becomes very easy.

What is the importance of sorting data? ›

Data sorting is any process that involves arranging the data into some meaningful order to make it easier to understand, analyze or visualize. When working with research data, sorting is a common method used for visualizing data in a form that makes it easier to comprehend the story the data is telling.

What is best sorting algorithm? ›

Quicksort. Quicksort is one of the most efficient sorting algorithms, and this makes of it one of the most used as well. The first thing to do is to select a pivot number, this number will separate the data, on its left are the numbers smaller than it and the greater numbers on the right.

What are four commonly used sorting algorithms? ›

When it comes to Computer Science, there are four main algorithms that you need to have in your arsenal. Bubble sort, selections sort, merge sort, and quickSort.

### Why is quicksort not stable? ›

If duplicate values are given as input, output will maintain given input order. Quick sort is not a stable algorithm because it swaps non-adjacent elements.

Which cases does quicksort perform best? ›

Quicksort's best case occurs when the partitions are as evenly balanced as possible: their sizes either are equal or are within 1 of each other.

When should we choose quicksort? ›

It's usually used when you need a hard upper limit to the time taken. Some more recent algorithms use quick sort, but attempt to recognize when it starts to degenerate, and switch to heap sort then.

What is the example of QuickSort? ›

Example of Quick Sort:

Comparing 44 to the right-side elements, and if right-side elements are smaller than 44, then swap it. As 22 is smaller than 44 so swap them. Now comparing 44 to the left side element and the element must be greater than 44 then swap them. As 55 are greater than 44 so swap them.

How much time does QuickSort take? ›

To sort an array of n distinct elements, quicksort takes O(n log n) time in expectation, averaged over all n! permutations of n elements with equal probability.

Why is QuickSort cache friendly? ›

Because it scans the array sequentially (and repeats on smaller segments). The most of its memory accesses take place in the cache.

Quicksort does well in theory and it is the best sorting technique in practice when comparisons are relatively cheap (such as in comparing integers or strings). The primary disadvantage with quicksort is that its absolute worst case is O( n ^2).

What is a pseudocode for quick sort? ›

Quick Sort Pseudocode

If an element is less than the pivot element then increment p and swap the elements at index p with the element at index i. Once all the elements are traversed, swap pivot with element present at p+1 as this will the same position as in the sorted array. Now return the pivot index.

What is this sorting algorithm? ›

A sorting algorithm is a method for reorganizing a large number of items into a specific order, such as alphabetical, highest-to-lowest value or shortest-to-longest distance. Sorting algorithms take lists of items as input data, perform specific operations on those lists and deliver ordered arrays as output.

What is the base case for quicksort? ›

The base cases are subarrays of fewer than two elements, just as in merge sort. In merge sort, you never see a subarray with no elements, but you can in quicksort, if the other elements in the subarray are all less than the pivot or all greater than the pivot.

### What are the advantages and disadvantages of quick sort algorithm? ›

Quicksort does well in theory and it is the best sorting technique in practice when comparisons are relatively cheap (such as in comparing integers or strings). The primary disadvantage with quicksort is that its absolute worst case is O( n ^2).

Is quicksort stable? ›

What is the main purpose of sorting? ›

What is sorting? Sorting is the process of arranging data into meaningful order so that you can analyze it more effectively. For example, you might want to order sales data by calendar month so that you can produce a graph of sales performance.

What are the benefits of sorting algorithms? ›

Sorting algorithms have two huge benefits: organizing the data faster so that it can be used and also reducing human errors. Business owners and managers are likely to use sorting algorithms every day without even knowing.

## Videos

1. Quick Sort - Computerphile
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2. The Quicksort Sorting Algorithm: Pick A Pivot, Partition, & Recurse
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3. 7.6 Quick Sort in Data Structure | Sorting Algorithm | DSA Full Course
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