Dual pivot Quicksort

As we know, the single pivot quick sort takes a pivot from one of the ends of the array and partitioning the array, so that all elements are left to the pivot are less than or equal to the pivot, and all elements that are right to the pivot are greater than the pivot.
The idea of dual pivot quick sort is to take two pivots, one in the left end of the array and the second, in the right end of the array. The left pivot must be less than or equal to the right pivot, so we swap them if necessary. 
Then, we begin partitioning the array into three parts: in the first part, all elements will be less than the left pivot, in the second part all elements will be greater or equal to the left pivot and also will be less than or equal to the right pivot, and in the third part all elements will be greater than the right pivot. Then, we shift the two pivots to their appropriate positions as we see in the below bar, and after that we begin quicksorting these three parts recursively, using this method. 

Dual pivot quick sort is a little bit faster than the original single pivot quicksort. But still, the worst case will remain O(n^2) when the array is already sorted in an increasing or decreasing order. 

The space complexity is O(log n) in the average and best cases, and O(n) in the worst case.
An example: 

C++

// C++ program to implement dual pivot QuickSort
#include <iostream>
using namespace std;

int partition(int* arr, int low, int high, int* lp);

void swap(int* a, int* b)
{
    int temp = *a;
    *a = *b;
    *b = temp;
}

void DualPivotQuickSort(int* arr, int low, int high)
{
    if (low < high) {
        // lp means left pivot, and rp means right pivot.
        int lp, rp;
        rp = partition(arr, low, high, &lp);
        DualPivotQuickSort(arr, low, lp - 1);
        DualPivotQuickSort(arr, lp + 1, rp - 1);
        DualPivotQuickSort(arr, rp + 1, high);
    }
}

int partition(int* arr, int low, int high, int* lp)
{
    if (arr[low] > arr[high])
        swap(&arr[low], &arr[high]);

    // p is the left pivot, and q is the right pivot.
    int j = low + 1;
    int g = high - 1, k = low + 1, p = arr[low], q = arr[high];
    while (k <= g) {

        // if elements are less than the left pivot
        if (arr[k] < p) {
            swap(&arr[k], &arr[j]);
            j++;
        }

        // if elements are greater than or equal
        // to the right pivot
        else if (arr[k] >= q) {
            while (arr[g] > q && k < g)
                g--;
            swap(&arr[k], &arr[g]);
            g--;
            if (arr[k] < p) {
                swap(&arr[k], &arr[j]);
                j++;
            }
        }
        k++;
    }
    j--;
    g++;

    // bring pivots to their appropriate positions.
    swap(&arr[low], &arr[j]);
    swap(&arr[high], &arr[g]);

    // returning the indices of the pivots.
    *lp = j; // because we cannot return two elements
    // from a function.

    return g;
}

// Driver code
int main()
{
    int arr[] = { 24, 8, 42, 75, 29, 77, 38, 57 };
    DualPivotQuickSort(arr, 0, 7);
    cout << "Sorted array: ";
    for (int i = 0; i < 8; i++)
        cout << arr[i] << " ";
    cout << endl;
}

// This code is contributed by SHUBHAMSINGH10

C

// C program to implement dual pivot QuickSort
#include <stdio.h>

int partition(int* arr, int low, int high, int* lp);

void swap(int* a, int* b)
{
    int temp = *a;
    *a = *b;
    *b = temp;
}

void DualPivotQuickSort(int* arr, int low, int high)
{
    if (low < high) {
        // lp means left pivot, and rp means right pivot.
        int lp, rp;
        rp = partition(arr, low, high, &lp);
        DualPivotQuickSort(arr, low, lp - 1);
        DualPivotQuickSort(arr, lp + 1, rp - 1);
        DualPivotQuickSort(arr, rp + 1, high);
    }
}

int partition(int* arr, int low, int high, int* lp)
{
    if (arr[low] > arr[high])
        swap(&arr[low], &arr[high]);
    // p is the left pivot, and q is the right pivot.
    int j = low + 1;
    int g = high - 1, k = low + 1, p = arr[low], q = arr[high];
    while (k <= g) {

        // if elements are less than the left pivot
        if (arr[k] < p) {
            swap(&arr[k], &arr[j]);
            j++;
        }

        // if elements are greater than or equal
        // to the right pivot
        else if (arr[k] >= q) {
            while (arr[g] > q && k < g)
                g--;
            swap(&arr[k], &arr[g]);
            g--;
            if (arr[k] < p) {
                swap(&arr[k], &arr[j]);
                j++;
            }
        }
        k++;
    }
    j--;
    g++;

    // bring pivots to their appropriate positions.
    swap(&arr[low], &arr[j]);
    swap(&arr[high], &arr[g]);

    // returning the indices of the pivots.
    *lp = j; // because we cannot return two elements
    // from a function.

    return g;
}

// Driver code
int main()
{
    int arr[] = { 24, 8, 42, 75, 29, 77, 38, 57 };
    DualPivotQuickSort(arr, 0, 7);
    printf("Sorted array: ");
    for (int i = 0; i < 8; i++)
        printf("%d ", arr[i]);
    printf("\n");
    return 0;
}

Java

// Java program to implement
// dual pivot QuickSort
class GFG{

static void swap(int[] arr, int i, int j)
{
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}

static void dualPivotQuickSort(int[] arr,
                               int low, int high)
{
    if (low < high)
    {

        // piv[] stores left pivot and right pivot.
        // piv[0] means left pivot and
        // piv[1] means right pivot
        int[] piv;
        piv = partition(arr, low, high);

        dualPivotQuickSort(arr, low, piv[0] - 1);
        dualPivotQuickSort(arr, piv[0] + 1, piv[1] - 1);
        dualPivotQuickSort(arr, piv[1] + 1, high);
    }
}

static int[] partition(int[] arr, int low, int high)
{
    if (arr[low] > arr[high])
        swap(arr, low, high);

    // p is the left pivot, and q
    // is the right pivot.
    int j = low + 1;
    int g = high - 1, k = low + 1,
        p = arr[low], q = arr[high];

    while (k <= g)
    {

        // If elements are less than the left pivot
        if (arr[k] < p)
        {
            swap(arr, k, j);
            j++;
        }

        // If elements are greater than or equal
        // to the right pivot
        else if (arr[k] >= q)
        {
            while (arr[g] > q && k < g)
                g--;

            swap(arr, k, g);
            g--;

            if (arr[k] < p)
            {
                swap(arr, k, j);
                j++;
            }
        }
        k++;
    }
    j--;
    g++;

    // Bring pivots to their appropriate positions.
    swap(arr, low, j);
    swap(arr, high, g);

    // Returning the indices of the pivots
    // because we cannot return two elements
    // from a function, we do that using an array.
    return new int[] { j, g };
}

// Driver code
public static void main(String[] args)
{
    int[] arr = { 24, 8, 42, 75, 29, 77, 38, 57 };

    dualPivotQuickSort(arr, 0, 7);

    System.out.print("Sorted array: ");
    for (int i = 0; i < 8; i++)
        System.out.print(arr[i] + " ");

    System.out.println();
}
}

// This code is contributed by Gourish Sadhu

Python3

# Python3 program to implement
# dual pivot QuickSort
def dualPivotQuickSort(arr, low, high):

    if low < high:

        # lp means left pivot and rp
        # means right pivot
        lp, rp = partition(arr, low, high)

        dualPivotQuickSort(arr, low, lp - 1)
        dualPivotQuickSort(arr, lp + 1, rp - 1)
        dualPivotQuickSort(arr, rp + 1, high)

def partition(arr, low, high):

    if arr[low] > arr[high]:
        arr[low], arr[high] = arr[high], arr[low]

    # p is the left pivot, and q is the right pivot.
    j = k = low + 1
    g, p, q = high - 1, arr[low], arr[high]

    while k <= g:

        # If elements are less than the left pivot
        if arr[k] < p:
            arr[k], arr[j] = arr[j], arr[k]
            j += 1

        # If elements are greater than or equal
        # to the right pivot
        elif arr[k] >= q:
            while arr[g] > q and k < g:
                g -= 1

            arr[k], arr[g] = arr[g], arr[k]
            g -= 1

            if arr[k] < p:
                arr[k], arr[j] = arr[j], arr[k]
                j += 1

        k += 1

    j -= 1
    g += 1

    # Bring pivots to their appropriate positions.
    arr[low], arr[j] = arr[j], arr[low]
    arr[high], arr[g] = arr[g], arr[high]

    # Returning the indices of the pivots
    return j, g

# Driver code
arr = [ 24, 8, 42, 75, 29, 77, 38, 57 ]
dualPivotQuickSort(arr, 0, 7)

print('Sorted array: ', end = '')
for i in arr:
    print(i, end = ' ')

print()

# This code is contributed by Gourish Sadhu

C#

// C# program to implement
// dual pivot QuickSort
using System;

class GFG {

    static void swap(int[] arr, int i, int j)
{
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}


    static void dualPivotQuickSort(int[] arr,
                               int low, int high)
{
    if (low < high)
    {

        // piv[] stores left pivot and right pivot.
        // piv[0] means left pivot and
        // piv[1] means right pivot
        int[] piv;
        piv = partition(arr, low, high);

        dualPivotQuickSort(arr, low, piv[0] - 1);
        dualPivotQuickSort(arr, piv[0] + 1, piv[1] - 1);
        dualPivotQuickSort(arr, piv[1] + 1, high);
    }
}

static int[] partition(int[] arr, int low, int high)
{
    if (arr[low] > arr[high])
        swap(arr, low, high);

    // p is the left pivot, and q
    // is the right pivot.
    int j = low + 1;
    int g = high - 1, k = low + 1,
        p = arr[low], q = arr[high];

    while (k <= g)
    {

        // If elements are less than the left pivot
        if (arr[k] < p)
        {
            swap(arr, k, j);
            j++;
        }

        // If elements are greater than or equal
        // to the right pivot
        else if (arr[k] >= q)
        {
            while (arr[g] > q && k < g)
                g--;

            swap(arr, k, g);
            g--;

            if (arr[k] < p)
            {
                swap(arr, k, j);
                j++;
            }
        }
        k++;
    }
    j--;
    g++;

    // Bring pivots to their appropriate positions.
    swap(arr, low, j);
    swap(arr, high, g);

    // Returning the indices of the pivots
    // because we cannot return two elements
    // from a function, we do that using an array.
    return new int[] { j, g };
}

    // Driver code
    public static void Main()
    {
        int[] arr = { 24, 8, 42, 75, 29, 77, 38, 57 };

        dualPivotQuickSort(arr, 0, 7);

        Console.Write("Sorted array: ");
        for (int i = 0; i < 8; i++)
            Console.Write(arr[i] + " ");

    }
}

// This code is contributed by Pushpesh Raj

Javascript

<script>

// JavaScript program to implement
// dual pivot QuickSort

function swap(arr,i,j)
{
    let temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}

function dualPivotQuickSort(arr,low,high)
{
    if (low < high)
    {

        // piv[] stores left pivot and right pivot.
        // piv[0] means left pivot and
        // piv[1] means right pivot
        let piv = [];
        piv = partition(arr, low, high);

        dualPivotQuickSort(arr, low, piv[0] - 1);
        dualPivotQuickSort(arr, piv[0] + 1, piv[1] - 1);
        dualPivotQuickSort(arr, piv[1] + 1, high);
    }
}

function partition(arr,low,high)
{
    if (arr[low] > arr[high])
        swap(arr, low, high);

    // p is the left pivot, and q
    // is the right pivot.
    let j = low + 1;
    let g = high - 1, k = low + 1,
        p = arr[low], q = arr[high];

    while (k <= g)
    {

        // If elements are less than the left pivot
        if (arr[k] < p)
        {
            swap(arr, k, j);
            j++;
        }

        // If elements are greater than or equal
        // to the right pivot
        else if (arr[k] >= q)
        {
            while (arr[g] > q && k < g)
                g--;

            swap(arr, k, g);
            g--;

            if (arr[k] < p)
            {
                swap(arr, k, j);
                j++;
            }
        }
        k++;
    }
    j--;
    g++;

    // Bring pivots to their appropriate positions.
    swap(arr, low, j);
    swap(arr, high, g);

    // Returning the indices of the pivots
    // because we cannot return two elements
    // from a function, we do that using an array.
    return [ j, g ];
}

// Driver code

let arr = [ 24, 8, 42, 75, 29, 77, 38, 57 ];

dualPivotQuickSort(arr, 0, 7);

document.write("Sorted array: ");
for (let i = 0; i < 8; i++)
    document.write(arr[i] + " ");

document.write("</br>");

// This code is contributed by Shinjan Patra

</script>

Output:

Sorted array: 8 24 29 38 42 57 75 77 

Time Complexity: O(N^2)
Auxiliary Space: O(N)
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