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# QuickSort – Data Structure and Algorithm Tutorials

QuickSort is a sorting algorithm based on the Divide and Conquer algorithm that picks an element as a pivot and partitions the given array around the picked pivot by placing the pivot in its correct position in the sorted array.

## How does QuickSort work?

The key process in quickSort is a partition(). The target of partitions is to place the pivot (any element can be chosen to be a pivot) at its correct position in the sorted array and put all smaller elements to the left of the pivot, and all greater elements to the right of the pivot.

Partition is done recursively on each side of the pivot after the pivot is placed in its correct position and this finally sorts the array.

How Quicksort works

Recommended Practice

### Choice of Pivot:

There are many different choices for picking pivots.

### Partition Algorithm:

The logic is simple, we start from the leftmost element and keep track of the index of smaller (or equal) elements as i. While traversing, if we find a smaller element, we swap the current element with arr[i]. Otherwise, we ignore the current element.

Let us understand the working of partition and the Quick Sort algorithm with the help of the following example:

Consider: arr[] = {10, 80, 30, 90, 40}.

• Compare 10 with the pivot and as it is less than pivot arrange it accrodingly.

Partition in QuickSort: Compare pivot with 10

• Compare 80 with the pivot. It is greater than pivot.

Partition in QuickSort: Compare pivot with 80

• Compare 30 with pivot. It is less than pivot so arrange it accordingly.

Partition in QuickSort: Compare pivot with 30

• Compare 90 with the pivot. It is greater than the pivot.

Partition in QuickSort: Compare pivot with 90

• Arrange the pivot in its correct position.

Partition in QuickSort: Place pivot in its correct position

### Illustration of Quicksort:

As the partition process is done recursively, it keeps on putting the pivot in its actual position in the sorted array. Repeatedly putting pivots in their actual position makes the array sorted.

Follow the below images to understand how the recursive implementation of the partition algorithm helps to sort the array.

• Initial partition on the main array:

Quicksort: Performing the partition

• Partitioning of the subarrays:

Quicksort: Performing the partition

## C

 // C code to implement quicksort #include  // Function to swap two elementsvoid swap(int* a, int* b){    int t = *a;    *a = *b;    *b = t;} // Partition the array using the last element as the pivotint partition(int arr[], int low, int high){    // Choosing the pivot    int pivot = arr[high];     // Index of smaller element and indicates    // the right position of pivot found so far    int i = (low - 1);     for (int j = low; j <= high - 1; j++) {         // If current element is smaller than the pivot        if (arr[j] < pivot) {             // Increment index of smaller element            i++;            swap(&arr[i], &arr[j]);        }    }    swap(&arr[i + 1], &arr[high]);    return (i + 1);} // The main function that implements QuickSort// arr[] --> Array to be sorted,// low --> Starting index,// high --> Ending indexvoid quickSort(int arr[], int low, int high){    if (low < high) {         // pi is partitioning index, arr[p]        // is now at right place        int pi = partition(arr, low, high);         // Separately sort elements before        // partition and after partition        quickSort(arr, low, pi - 1);        quickSort(arr, pi + 1, high);    }} // Driver codeint main(){    int arr[] = { 10, 7, 8, 9, 1, 5 };    int N = sizeof(arr) / sizeof(arr[0]);     // Function call    quickSort(arr, 0, N - 1);    printf("Sorted array: \n");    for (int i = 0; i < N; i++)        printf("%d ", arr[i]);    return 0;}

## Java

 // Java implementation of QuickSortimport java.io.*; class GFG {     // A utility function to swap two elements    static void swap(int[] arr, int i, int j)    {        int temp = arr[i];        arr[i] = arr[j];        arr[j] = temp;    }     // This function takes last element as pivot,    // places the pivot element at its correct position    // in sorted array, and places all smaller to left    // of pivot and all greater elements to right of pivot    static int partition(int[] arr, int low, int high)    {        // Choosing the pivot        int pivot = arr[high];         // Index of smaller element and indicates        // the right position of pivot found so far        int i = (low - 1);         for (int j = low; j <= high - 1; j++) {             // If current element is smaller than the pivot            if (arr[j] < pivot) {                 // Increment index of smaller element                i++;                swap(arr, i, j);            }        }        swap(arr, i + 1, high);        return (i + 1);    }     // The main function that implements QuickSort    // arr[] --> Array to be sorted,    // low --> Starting index,    // high --> Ending index    static void quickSort(int[] arr, int low, int high)    {        if (low < high) {             // pi is partitioning index, arr[p]            // is now at right place            int pi = partition(arr, low, high);             // Separately sort elements before            // partition and after partition            quickSort(arr, low, pi - 1);            quickSort(arr, pi + 1, high);        }    }    // To print sorted array    public static void printArr(int[] arr)    {        for (int i = 0; i < arr.length; i++) {            System.out.print(arr[i] + " ");        }    }     // Driver Code    public static void main(String[] args)    {        int[] arr = { 10, 7, 8, 9, 1, 5 };        int N = arr.length;         // Function call        quickSort(arr, 0, N - 1);        System.out.println("Sorted array:");        printArr(arr);    }} // This code is contributed by Ayush Choudhary// Improved by Ajay Virmoti

## Python3

 # Python3 implementation of QuickSort  # Function to find the partition positiondef partition(array, low, high):     # Choose the rightmost element as pivot    pivot = array[high]     # Pointer for greater element    i = low - 1     # Traverse through all elements    # compare each element with pivot    for j in range(low, high):        if array[j] <= pivot:             # If element smaller than pivot is found            # swap it with the greater element pointed by i            i = i + 1             # Swapping element at i with element at j            (array[i], array[j]) = (array[j], array[i])     # Swap the pivot element with    # the greater element specified by i    (array[i + 1], array[high]) = (array[high], array[i + 1])     # Return the position from where partition is done    return i + 1  # Function to perform quicksortdef quicksort(array, low, high):    if low < high:         # Find pivot element such that        # element smaller than pivot are on the left        # element greater than pivot are on the right        pi = partition(array, low, high)         # Recursive call on the left of pivot        quicksort(array, low, pi - 1)         # Recursive call on the right of pivot        quicksort(array, pi + 1, high)  # Driver codeif __name__ == '__main__':    array = [10, 7, 8, 9, 1, 5]    N = len(array)     # Function call    quicksort(array, 0, N - 1)    print('Sorted array:')    for x in array:        print(x, end=" ") # This code is contributed by Adnan Aliakbar

## C#

 // C# implementation of QuickSort using System; class GFG {     // A utility function to swap two elements    static void swap(int[] arr, int i, int j)    {        int temp = arr[i];        arr[i] = arr[j];        arr[j] = temp;    }     // This function takes last element as pivot,    // places the pivot element at its correct position    // in sorted array, and places all smaller to left    // of pivot and all greater elements to right of pivot    static int partition(int[] arr, int low, int high)    {        // Choosing the pivot        int pivot = arr[high];         // Index of smaller element and indicates        // the right position of pivot found so far        int i = (low - 1);         for (int j = low; j <= high - 1; j++) {             // If current element is smaller than the pivot            if (arr[j] < pivot) {                 // Increment index of smaller element                i++;                swap(arr, i, j);            }        }        swap(arr, i + 1, high);        return (i + 1);    }     // The main function that implements QuickSort    // arr[] --> Array to be sorted,    // low --> Starting index,    // high --> Ending index    static void quickSort(int[] arr, int low, int high)    {        if (low < high) {             // pi is partitioning index, arr[p]            // is now at right place            int pi = partition(arr, low, high);             // Separately sort elements before            // and after partition index            quickSort(arr, low, pi - 1);            quickSort(arr, pi + 1, high);        }    }     // Driver Code    public static void Main()    {        int[] arr = { 10, 7, 8, 9, 1, 5 };        int N = arr.Length;         // Function call        quickSort(arr, 0, N - 1);        Console.WriteLine("Sorted array:");        for (int i = 0; i < N; i++)            Console.Write(arr[i] + " ");    }} // This code is contributed by gfgking

## Javascript

 // Function to partition the array and return the partition indexfunction partition(arr, low, high) {    // Choosing the pivot    let pivot = arr[high];       // Index of smaller element and indicates the right position of pivot found so far    let i = low - 1;       for (let j = low; j <= high - 1; j++) {        // If current element is smaller than the pivot        if (arr[j] < pivot) {            // Increment index of smaller element            i++;            [arr[i], arr[j]] = [arr[j], arr[i]]; // Swap elements        }    }       [arr[i + 1], arr[high]] = [arr[high], arr[i + 1]]; // Swap pivot to its correct position    return i + 1; // Return the partition index} // The main function that implements QuickSortfunction quickSort(arr, low, high) {    if (low < high) {        // pi is the partitioning index, arr[pi] is now at the right place        let pi = partition(arr, low, high);           // Separately sort elements before partition and after partition        quickSort(arr, low, pi - 1);        quickSort(arr, pi + 1, high);    }} // Driver codelet arr = [10, 7, 8, 9, 1, 5];let N = arr.length; // Function callquickSort(arr, 0, N - 1);console.log("Sorted array:");console.log(arr.join(" "));

## PHP



Output

Sorted array:
1 5 7 8 9 10

### Complexity Analysis of Quick Sort:

Time Complexity:

• Best Case: Ω (N log (N))
The best-case scenario for quicksort occur when the pivot chosen at the each step divides the array into roughly equal halves.
In this case, the algorithm will make balanced partitions, leading to efficient Sorting.
• Average Case: θ ( N log (N))
Quicksort’s average-case performance is usually very good in practice, making it one of the fastest sorting Algorithm.
• Worst Case: O(N2)
The worst-case Scenario for Quicksort occur when the pivot at each step consistently results in highly unbalanced partitions. When the array is already sorted and the pivot is always chosen as the smallest or largest element. To mitigate the worst-case Scenario, various techniques are used such as choosing a good pivot (e.g., median of three) and using Randomized algorithm (Randomized Quicksort ) to shuffle the element before sorting.
• Auxiliary Space: O(1), if we don’t consider the recursive stack space. If we consider the recursive stack space then, in the worst case quicksort could make O(N).