Data Modelling & AI Data Structure & Algorithm

QuickSort using Random Pivoting

20 June 2025

1

In this article, we will discuss how to implement QuickSort using random pivoting. In QuickSort we first partition the array in place such that all elements to the left of the pivot element are smaller, while all elements to the right of the pivot are greater than the pivot. Then we recursively call the same procedure for left and right subarrays.
Unlike merge sort, we don’t need to merge the two sorted arrays. Thus Quicksort requires lesser auxiliary space than Merge Sort, which is why it is often preferred to Merge Sort. Using a randomly generated pivot we can further improve the time complexity of QuickSort.

We have discussed at two popular methods for partitioning the arrays-Hoare’s vs Lomuto partition scheme
It is advised that the reader has read that article or knows how to implement the QuickSort using either of the two partition schemes.

Algorithm for random pivoting using Lomuto Partitioning

partition(arr[], lo, hi) 
    pivot = arr[hi]
    i = lo     // place for swapping
    for j := lo to hi – 1 do
        if arr[j] <= pivot then
            swap arr[i] with arr[j]
            i = i + 1
    swap arr[i] with arr[hi]
    return i
partition_r(arr[], lo, hi)
    r = Random Number from lo to hi
    Swap arr[r] and arr[hi]
    return partition(arr, lo, hi)
quicksort(arr[], lo, hi)
    if lo < hi
        p = partition_r(arr, lo, hi)
        quicksort(arr, lo , p-1)
        quicksort(arr, p+1, hi)

Implementation using Lomuto Partitioning:

C++

// C++ implementation QuickSort 
// using Lomuto's partition Scheme.
#include <cstdlib>
#include <time.h>
#include <iostream>
using namespace std;
 
// This function takes last element
// as pivot, places
// the pivot element at its correct
// position in sorted array, and 
// places all smaller (smaller than pivot)
// to left of pivot and all greater 
// elements to right of pivot
int partition(int arr[], int low, int high)
{
    // pivot
    int pivot = arr[high]; 
   
    // Index of smaller element
    int i = (low - 1); 
 
    for (int j = low; j <= high - 1; j++) 
    {
        // If current element is smaller
        // than or equal to 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);
}
 
// Generates Random Pivot, swaps pivot with
// end element and calls the partition function
int partition_r(int arr[], int low, int high)
{
    // Generate a random number in between
    // low .. high
    srand(time(NULL));
    int random = low + rand() % (high - low);
 
    // Swap A[random] with A[high]
    swap(arr[random], arr[high]);
 
    return partition(arr, low, high);
}
 
/* The main function that implements
QuickSort
arr[] --> Array to be sorted,
low --> Starting index,
high --> Ending index */
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_r(arr, low, high);
 
        // Separately sort elements before
        // partition and after partition
        quickSort(arr, low, pi - 1);
        quickSort(arr, pi + 1, high);
    }
}
 
/* Function to print an array */
void printArray(int arr[], int size)
{
    int i;
    for (i = 0; i < size; i++)
        cout<<arr[i]<<" "; 
}
 
// Driver Code
int main()
{
    int arr[] = { 10, 7, 8, 9, 1, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);
     
    quickSort(arr, 0, n - 1);
    printf("Sorted array: \n");
    printArray(arr, n);
     
    return 0;
}

C

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
 
int partition(int arr[], int low, int high)
{
    int pivot = arr[low];
    int i = low - 1, j = high + 1;
 
    while (1) {
 
        do {
            i++;
        } while (arr[i] < pivot);
 
        do {
            j--;
        } while (arr[j] > pivot);
 
        if (i >= j)
            return j;
 
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
}
 
int partition_r(int arr[], int low, int high)
{
    srand(time(0));
    int random = low + rand() % (high - low);
 
    int temp = arr[random];
    arr[random] = arr[low];
    arr[low] = temp;
 
    return partition(arr, low, high);
}
 
void quickSort(int arr[], int low, int high)
{
    if (low < high) {
        int pi = partition_r(arr, low, high);
 
        quickSort(arr, low, pi);
        quickSort(arr, pi + 1, high);
    }
}
 
void printArray(int arr[], int n)
{
    for (int i = 0; i < n; i++)
        printf("%d ", arr[i]);
    printf("\n");
}
 
int main()
{
    int arr[] = { 10, 7, 8, 9, 1, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);
    quickSort(arr, 0, n - 1);
    printf("Sorted array: \n");
    printArray(arr, n);
    return 0;
}

Java

// Java program to illustrate
// Randomised Quick Sort 
import java.util.*; 
 
class RandomizedQsort 
{     
    // This Function helps in calculating
    // random numbers between low(inclusive)
    // and high(inclusive) 
    static void random(int arr[],int low,int high) 
    { 
     
        Random rand= new Random(); 
        int pivot = rand.nextInt(high-low)+low; 
         
        int temp1=arr[pivot];  
        arr[pivot]=arr[high]; 
        arr[high]=temp1; 
    } 
     
    /* This function takes last element as pivot, 
    places the pivot element at its correct 
    position in sorted array, and places all 
    smaller (smaller than pivot) to left of 
    pivot and all greater elements to right 
    of pivot */
    static int partition(int arr[], int low, int high) 
    { 
        // pivot is chosen randomly 
        random(arr,low,high);
        int pivot = arr[high]; 
     
 
        int i = (low-1); // index of smaller element 
        for (int j = low; j < high; j++) 
        { 
            // If current element is smaller than or 
            // equal to pivot 
            if (arr[j] < pivot) 
            { 
                i++; 
 
                // swap arr[i] and arr[j] 
                int temp = arr[i]; 
                arr[i] = arr[j]; 
                arr[j] = temp; 
            } 
        } 
 
        // swap arr[i+1] and arr[high] (or pivot) 
        int temp = arr[i+1]; 
        arr[i+1] = arr[high]; 
        arr[high] = temp; 
 
        return i+1; 
    } 
 
 
    /* The main function that implements QuickSort() 
    arr[] --> Array to be sorted, 
    low --> Starting index, 
    high --> Ending index */
    static void sort(int arr[], int low, int high) 
    { 
        if (low < high) 
        { 
            /* pi is partitioning index, arr[pi] is 
            now at right place */
            int pi = partition(arr, low, high); 
 
            // Recursively sort elements before 
            // partition and after partition 
            sort(arr, low, pi-1); 
            sort(arr, pi+1, high); 
        } 
    } 
 
    /* A utility function to print array of size n */
    static void printArray(int arr[]) 
    { 
        int n = arr.length; 
        for (int i = 0; i < n; ++i) 
            System.out.print(arr[i]+" "); 
        System.out.println(); 
    } 
 
    // Driver Code 
    public static void main(String args[]) 
    { 
        int arr[] = {10, 7, 8, 9, 1, 5}; 
        int n = arr.length; 
 
        sort(arr, 0, n-1); 
 
        System.out.println("Sorted array"); 
        printArray(arr); 
    } 
} 
 
// This code is contributed by Ritika Gupta.

Python3

# Python implementation QuickSort using 
# Lomuto's partition Scheme.
import random
 
'''
The function which implements QuickSort.
arr :- array to be sorted.
start :- starting index of the array.
stop :- ending index of the array.
'''
def quicksort(arr, start , stop):
    if(start < stop):
         
        # pivotindex is the index where 
        # the pivot lies in the array
        pivotindex = partitionrand(arr,\
                             start, stop)
         
        # At this stage the array is 
        # partially sorted around the pivot. 
        # Separately sorting the 
        # left half of the array and the
        # right half of the array.
        quicksort(arr , start , pivotindex-1)
        quicksort(arr, pivotindex + 1, stop)
 
# This function generates random pivot,
# swaps the first element with the pivot 
# and calls the partition function.
def partitionrand(arr , start, stop):
 
    # Generating a random number between the 
    # starting index of the array and the
    # ending index of the array.
    randpivot = random.randrange(start, stop)
 
    # Swapping the starting element of
    # the array and the pivot
    arr[start], arr[randpivot] = \
        arr[randpivot], arr[start]
    return partition(arr, start, stop)
 
'''
This function takes the first element as pivot, 
places the pivot element at the correct position 
in the sorted array. All the elements are re-arranged 
according to the pivot, the elements smaller than the
pivot is places on the left and the elements
greater than the pivot is placed to the right of pivot.
'''
def partition(arr,start,stop):
    pivot = start # pivot
     
    # a variable to memorize where the 
    i = start + 1
     
    # partition in the array starts from.
    for j in range(start + 1, stop + 1):
         
        # if the current element is smaller
        # or equal to pivot, shift it to the
        # left side of the partition.
        if arr[j] <= arr[pivot]:
            arr[i] , arr[j] = arr[j] , arr[i]
            i = i + 1
    arr[pivot] , arr[i - 1] =\
            arr[i - 1] , arr[pivot]
    pivot = i - 1
    return (pivot)
 
# Driver Code
if __name__ == "__main__":
    array = [10, 7, 8, 9, 1, 5]
    quicksort(array, 0, len(array) - 1)
    print(array)
 
# This code is contributed by soumyasaurav

C#

// C# program to illustrate
// Randomised Quick sort 
using System;
class RandomizedQsort 
{     
 
  /* This function takes last element as pivot, 
    places the pivot element at its correct 
    position in sorted array, and places all 
    smaller (smaller than pivot) to left of 
    pivot and all greater elements to right 
    of pivot */
  static int partition(int[] arr, int low, int high) 
  { 
 
    // pivot is chosen randomly 
    random(arr, low, high);
    int pivot = arr[high];
 
    int i = (low-1); // index of smaller element 
    for (int j = low; j < high; j++) 
    { 
 
      // If current element is smaller than or 
      // equal to pivot 
      if (arr[j] < pivot) 
      { 
        i++; 
 
        // swap arr[i] and arr[j] 
        int tempp = arr[i]; 
        arr[i] = arr[j]; 
        arr[j] = tempp; 
      } 
    } 
 
    // swap arr[i+1] and arr[high] (or pivot) 
    int tempp2 = arr[i + 1]; 
    arr[i + 1] = arr[high]; 
    arr[high] = tempp2; 
 
    return i + 1; 
  } 
 
  // This Function helps in calculating
  // random numbers between low(inclusive)
  // and high(inclusive) 
  static int random(int[] arr, int low, int high) 
  { 
 
    Random rand = new Random(); 
    int pivot = rand.Next() % (high - low) + low; 
 
    int tempp1 = arr[pivot];  
    arr[pivot] = arr[high]; 
    arr[high] = tempp1; 
 
    return partition(arr, low, high);
  } 
 
  /* The main function that implements Quicksort() 
    arr[] --> Array to be sorted, 
    low --> Starting index, 
    high --> Ending index */
  static void sort(int[] arr, int low, int high) 
  { 
    if (low < high) 
    { 
      /* pi is partitioning index, arr[pi] is 
            now at right place */
      int pi = partition(arr, low, high); 
 
      // Recursively sort elements before 
      // partition and after partition 
      sort(arr, low, pi - 1); 
      sort(arr, pi + 1, high); 
    } 
  } 
 
  /* A utility function to print array of size n */
  static void printArray(int[] arr) 
  { 
    int n = arr.Length; 
    for (int i = 0; i < n; ++i) 
      Console.Write(arr[i] + " "); 
    Console.WriteLine(); 
  } 
 
  // Driver Code 
  static public void Main ()
  {
    int[] arr = {10, 7, 8, 9, 1, 5}; 
    int n = arr.Length; 
 
    sort(arr, 0, n-1); 
 
    Console.WriteLine("sorted array"); 
    printArray(arr); 
  } 
}
 
//  This code is contributed by shubhamsingh10

Javascript

// JavaScript implementation QuickSort using 
// Lomuto's partition Scheme.
 
/*
The function which implements QuickSort.
arr :- array to be sorted.
start :- starting index of the array.
stop :- ending index of the array.
*/
function quicksort(arr, start, stop) {
  if (start < stop) {
 
    // pivotindex is the index where 
    // the pivot lies in the array
    let pivotindex = partitionrand(arr, start, stop);
 
    // At this stage the array is 
    // partially sorted around the pivot. 
    // Separately sorting the 
    // left half of the array and the
    // right half of the array.
    quicksort(arr, start, pivotindex - 1);
    quicksort(arr, pivotindex + 1, stop);
  }
}
 
// This function generates random pivot,
// swaps the first element with the pivot 
// and calls the partition function.
function partitionrand(arr, start, stop) {
 
  // Generating a random number between the 
  // starting index of the array and the
  // ending index of the array.
  let randpivot = Math.floor(Math.random() * (stop - start + 1)) + start;
 
  // Swapping the starting element of
  // the array and the pivot
  [arr[start], arr[randpivot]] = [arr[randpivot], arr[start]];
  return partition(arr, start, stop);
}
 
/*
This function takes the first element as pivot, 
places the pivot element at the correct position 
in the sorted array. All the elements are re-arranged 
according to the pivot, the elements smaller than the
pivot is places on the left and the elements
greater than the pivot is placed to the right of pivot.
*/
function partition(arr, start, stop) {
  let pivot = start; // pivot
 
  // a variable to memorize where the 
  let i = start + 1;
 
  // partition in the array starts from.
  for (let j = start + 1; j <= stop; j++) {
 
    // if the current element is smaller
    // or equal to pivot, shift it to the
    // left side of the partition.
    if (arr[j] <= arr[pivot]) {
      [arr[i], arr[j]] = [arr[j], arr[i]];
      i++;
    }
  }
  [arr[pivot], arr[i - 1]] = [arr[i - 1], arr[pivot]];
  pivot = i - 1;
  return pivot;
}
 
// Driver Code
let array = [10, 7, 8, 9, 1, 5];
quicksort(array, 0, array.length - 1);
console.log(array);

Output

Sorted array: 
1 5 7 8 9 10

Time Complexity: O(N*N)
Auxiliary Space: O(N) // due to recursive call stack

Algorithm for random pivoting using Hoare Partitioning

partition(arr[], lo, hi)
   pivot = arr[lo]
   i = lo - 1  // Initialize left index
   j = hi + 1  // Initialize right index
    
    while(True)
           // Find a value in left side greater than pivot
           do
              i = i + 1
           while arr[i] < pivot
        // Find a value in right side smaller than pivot
           do
              j = j - 1
           while arr[j] > pivot
           
           if i >= j then  
              return j
        else
               swap arr[i] with arr[j]
       end    while
   
partition_r(arr[], lo, hi)
    r = Random number from lo to hi
    Swap arr[r] and arr[lo]
    return partition(arr, lo, hi)
quicksort(arr[], lo, hi)
    if lo < hi
        p = partition_r(arr, lo, hi)
        quicksort(arr, lo, p)
        quicksort(arr, p+1, hi)

Implementation using Hoare’s Partitioning:

C++

// C++ implementation of QuickSort
// using Hoare's partition scheme
 
#include <cstdlib>
#include <iostream>
using namespace std;
 
// This function takes last element as 
// pivot, places the pivot element at
// its correct position in sorted
// array, and places all smaller 
// (smaller than pivot) to left of pivot
// and all greater elements to right
int partition(int arr[], int low, int high)
{
    int pivot = arr[low];
    int i = low - 1, j = high + 1;
 
    while (true) {
 
        // Find leftmost element greater than
        // or equal to pivot
        do {
            i++;
        } while (arr[i] < pivot);
 
        // Find rightmost element smaller than
        // or equal to pivot
        do {
            j--;
        } while (arr[j] > pivot);
 
        // If two pointers met
        if (i >= j)
            return j;
 
        swap(arr[i], arr[j]);
    }
}
 
// Generates Random Pivot, swaps pivot with
// end element and calls the partition function
// In Hoare partition the low element is selected
// as first pivot
int partition_r(int arr[], int low, int high)
{
    // Generate a random number in between
    // low .. high
    srand(time(NULL));
    int random = low + rand() % (high - low);
 
    // Swap A[random] with A[high]
    swap(arr[random], arr[low]);
 
    return partition(arr, low, high);
}
 
// The main function that implements QuickSort
// arr[] --> Array to be sorted,
// low  --> Starting index,
// high  --> Ending index
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_r(arr, low, high);
 
        // Separately sort elements before
        // partition and after partition
        quickSort(arr, low, pi);
        quickSort(arr, pi + 1, high);
    }
}
 
// Function to print an array
void printArray(int arr[], int n)
{
    for (int i = 0; i < n; i++)
        printf("%d ", arr[i]);
    printf("\n");
}
 
// Driver Code
int main()
{
    int arr[] = { 10, 7, 8, 9, 1, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);
    quickSort(arr, 0, n - 1);
    printf("Sorted array: \n");
    printArray(arr, n);
    return 0;
}

Java

/*
JAVA implementation of Randomize QuickSort
using Hoare's Partition
*/
import java.util.*;
 
class GFG
{
   
    // swap function
    static void swap(int[] arr, int i, int j)
    {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
 
    /*
    // partition function
    This function takes array, low and high index,
    swaps low with random index between low and high
    then places all elements less than pivot in the left
    of pivot and all elements greater than pivot to the
    right of pivot
    */
    static int partition(int[] arr, int low, int high)
    {
        // rIndex gives the random index between low and
        // high (both inclusive)
        int rIndex = (low) + (int)(Math.random() * (high - low + 1));
 
        swap(arr, low, rIndex); // swap low with random index
        int pivot = arr[low];
        int i = low - 1, j = high + 1;
 
        while (true) {
            // increase i while elements are less than pivot
            do {
                i++;
            } while (arr[i] < pivot);
 
            // decrease j while elements are greater than pivot
            do {
                j--;
            } while (arr[j] > pivot);
 
            if (i >= j) // when both pointers meet
                        // that means elements are at their
                        // correct place for now
                return j;
 
            swap(arr, i, j);
            // swap i and j, since both are not at their
            // correct index
        }
    }
 
    // recursive quick sort function
    static void quickSort(int[] arr, int low, int high)
    {
        if (low < high) {
            // find partition index
            int p = partition(arr, low, high);
            // sort before and after the pivot
            quickSort(arr, low, p);
            quickSort(arr, p + 1, high);
        }
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int[] arr = { 10, 7, 8, 9, 1, 5 };
        quickSort(arr, 0, arr.length - 1);
 
        System.out.println("Sorted array : ");
        System.out.print(Arrays.toString(arr));
    }
}
 
// This code is contributed by Anubhav Singh (singhanubhav)

Python3

# Python implementation QuickSort using 
# Hoare's partition Scheme.
 
import random
 
'''
The function which implements randomised
QuickSort, using Haore's partition scheme.
arr :- array to be sorted.
start :- starting index of the array.
stop :- ending index of the array.
'''
def quicksort(arr, start, stop):
    if(start < stop):
         
        # pivotindex is the index where
        # the pivot lies in the array
        pivotindex = partitionrand(arr,\
                              start, stop)
         
        # At this stage the array is 
        # partially sorted around the pivot. 
        # separately sorting the left half of 
        # the array and the right
        # half of the array.
        quicksort(arr , start , pivotindex)
        quicksort(arr, pivotindex + 1, stop)
 
# This function generates random pivot,
# swaps the first element with the pivot
# and calls the partition function.
def partitionrand(arr , start, stop):
 
    # Generating a random number between 
    # the starting index of the array and 
    # the ending index of the array.
    randpivot = random.randrange(start, stop)
 
    # Swapping the starting element of 
    # the array and the pivot
    arr[start], arr[randpivot] =\
        arr[randpivot], arr[start]
    return partition(arr, start, stop)
 
'''
This function takes the first element
as pivot, places the pivot element at
the correct position in the sorted array.
All the elements are re-arranged according
to the pivot, the elements smaller than 
the pivot is places on the left and 
the elements greater than the pivot is
placed to the right of pivot.
'''
def partition(arr,start,stop):
    pivot = start # pivot
    i = start - 1
    j = stop + 1
    while True:
        while True:
            i = i + 1
            if arr[i] >= arr[pivot]:
                break
        while True:
            j = j - 1
            if arr[j] <= arr[pivot]:
                break
        if i >= j:
            return j
        arr[i] , arr[j] = arr[j] , arr[i]
 
# Driver Code
if __name__ == "__main__":
    array = [10, 7, 8, 9, 1, 5]
    quicksort(array, 0, len(array) - 1)
    print(array)
 
# This code is contributed by soumyasaurav

C#

// C# implementation of QuickSort
// using Hoare's partition scheme
using System;
 
public class GFG {
    // Driver Code
 
    public static void Main()
    {
        int[] arr = { 10, 7, 8, 9, 1, 5 };
        int n = arr.Length;
        quickSort(arr, 0, n - 1);
        Console.WriteLine("Sorted array: ");
        printArray(arr, n);
    }
 
    // This function takes last element as
    // pivot, places the pivot element at
    // its correct position in sorted
    // array, and places all smaller
    // (smaller than pivot) to left of pivot
    // and all greater elements to right
    public static int partition(int[] arr, int low,
                                int high)
    {
        int pivot = arr[low];
        int i = low - 1, j = high + 1;
 
        // Find leftmost element greater than
        // or equal to pivot
        while (true) {
 
            do {
                i++;
            } while (arr[i] < pivot);
            // Find rightmost element smaller than
            // or equal to pivot
            do {
                j--;
            } while (arr[j] > pivot);
            // If two pointers met
 
            if (i >= j)
                return j;
 
            swap(arr, i, j);
        }
    }
 
    // Generates Random Pivot, swaps pivot with
    // end element and calls the partition function
    // In Hoare partition the low element is selected
    // as first pivot
    public static int partition_r(int[] arr, int low,
                                  int high)
    {
        // Generate a random number in between
        // low .. high
        Random rnd = new Random();
        int random = low + rnd.Next(high - low);
        // Swap A[random] with A[high]
        swap(arr, random, low);
 
        return partition(arr, low, high);
    }
 
    // The main function that implements QuickSort
    // arr[] --> Array to be sorted,
    // low  --> Starting index,
    // high  --> Ending index
    public 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_r(arr, low, high);
 
            // Separately sort elements before
            // partition and after partition
            quickSort(arr, low, pi);
            quickSort(arr, pi + 1, high);
        }
    }
 
    // Function to print an array
 
    public static void printArray(int[] arr, int n)
    {
        for (int i = 0; i < n; i++)
            Console.Write("{0} ", arr[i]);
        Console.Write("\n");
    }
 
    public static void swap(int[] arr, int i, int j)
    {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
}

Javascript

// javascript implementation of QuickSort
// using Hoare's partition scheme
 
// This function takes last element as 
// pivot, places the pivot element at
// its correct position in sorted
// array, and places all smaller 
// (smaller than pivot) to left of pivot
// and all greater elements to right
function partition(arr, low, high)
{
    let pivot = arr[low];
    let i = low - 1, j = high + 1;
 
    while (true) {
 
        // Find leftmost element greater than
        // or equal to pivot
        do {
            i++;
        } while (arr[i] < pivot);
 
        // Find rightmost element smaller than
        // or equal to pivot
        do {
            j--;
        } while (arr[j] > pivot);
 
        // If two pointers met
        if (i >= j)
            return j;
 
        let temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
}
 
// Generates Random Pivot, swaps pivot with
// end element and calls the partition function
// In Hoare partition the low element is selected
// as first pivot
function partition_r(arr,  low, high)
{
    // Generate a random number in between
    // low .. high
    let random = low + Math.random() * (high - low);
 
    // Swap A[random] with A[high]
    let temp = arr[random];
    arr[random] = arr[low];
    arr[low] = arr[random];
 
    return partition(arr, low, high);
}
 
// The main function that implements QuickSort
// arr[] --> Array to be sorted,
// low  --> Starting index,
// high  --> Ending index
function quickSort(arr, low, high)
{
    if (low < high) {
        // pi is partitioning index, 
        // arr[p] is now at right place
        let pi = partition_r(arr, low, high);
 
        // Separately sort elements before
        // partition and after partition
        quickSort(arr, low, pi);
        quickSort(arr, pi + 1, high);
    }
}
 
// Function to print an array
function printArray(arr, n)
{
    for (let i = 0; i < n; i++)
        process.stdout.write(arr[i] + " ");
}
 
// Driver Code
 
let arr = [ 10, 7, 8, 9, 1, 5 ];
let n = arr.length
quickSort(arr, 0, n - 1);
console.log("Sorted array: ");
printArray(arr, n);
 
// The code is contributed by Nidhi goel. 

Output

Sorted array: 
1 5 7 8 9 10

Time Complexity: O(N*N)
Auxiliary Space: O(N) // due to recursive call stack

Implementation using generateRandomPivot function :

Here is an implementation without using Hoare’s and Lomuto partition scheme

Implementation of QuickSort using random pivoting without partitioning:

C++

#include <iostream>
#include <cstdlib>
#include <ctime>
 
using namespace std;
 
// Function to swap two elements
void swap(int* a, int* b) {
    int temp = *a;
    *a = *b;
    *b = temp;
}
 
// Function to generate a random pivot index
int generateRandomPivot(int low, int high) {
    srand(time(NULL));
    return low + rand() % (high - low + 1);
}
 
// Function to perform QuickSort
void quickSort(int arr[], int low, int high) {
    if (low < high) {
        int pivotIndex = generateRandomPivot(low, high);
        int pivotValue = arr[pivotIndex];
 
        // Swap the pivot element with the last element
        swap(&arr[pivotIndex], &arr[high]);
 
        int i = low - 1;
 
        for (int j = low; j < high; j++) {
            if (arr[j] < pivotValue) {
                i++;
                swap(&arr[i], &arr[j]);
            }
        }
 
        // Swap the pivot element back to its final position
        swap(&arr[i+1], &arr[high]);
 
        // Recursively sort the left and right subarrays
        quickSort(arr, low, i);
        quickSort(arr, i+2, high);
    }
}
 
int main() {
    int arr[] = {5, 2, 7, 3, 1, 6, 4, 8};
    int n = sizeof(arr)/sizeof(arr[0]);
 
    cout << "Original array: ";
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
 
    quickSort(arr, 0, n-1);
 
    cout << "\nSorted array: ";
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
 
    return 0;
}

Java

import java.util.Random;
 
public class QuickSort {
 
    // Function to swap two elements in the array
    static void swap(int[] arr, int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
 
    // Function to generate a random pivot index
    static int generateRandomPivot(int low, int high) {
        Random random = new Random();
        return random.nextInt(high - low + 1) + low;
    }
 
    // Function to perform QuickSort
    static void quickSort(int[] arr, int low, int high) {
        if (low < high) {
            int pivotIndex = generateRandomPivot(low, high);
            int pivotValue = arr[pivotIndex];
 
            // Swap the pivot element with the last element
            swap(arr, pivotIndex, high);
 
            int i = low - 1;
 
            for (int j = low; j < high; j++) {
                if (arr[j] < pivotValue) {
                    i++;
                    swap(arr, i, j);
                }
            }
 
            // Swap the pivot element back to its final position
            swap(arr, i + 1, high);
 
            // Recursively sort the left and right subarrays
            quickSort(arr, low, i);
            quickSort(arr, i + 2, high);
        }
    }
 
    // Driver code
    public static void main(String[] args) {
        int[] arr = {5, 2, 7, 3, 1, 6, 4, 8};
        int n = arr.length;
 
        System.out.print("Original array: ");
        for (int num : arr) {
            System.out.print(num + " ");
        }
        System.out.println();
 
        quickSort(arr, 0, n - 1);
 
        System.out.print("Sorted array: ");
        for (int num : arr) {
            System.out.print(num + " ");
        }
        System.out.println();
    }
}

Python3

import random
 
# Function to swap two elements
def swap(arr, i, j):
    temp = arr[i]
    arr[i] = arr[j]
    arr[j] = temp
 
# Function to generate a random pivot index
def generateRandomPivot(low, high):
    return random.randint(low, high)
 
# Function to perform QuickSort
def quickSort(arr, low, high):
    if low < high:
        pivotIndex = generateRandomPivot(low, high)
        pivotValue = arr[pivotIndex]
 
        # Swap the pivot element with the last element
        swap(arr, pivotIndex, high)
 
        i = low - 1
 
        for j in range(low, high):
            if arr[j] < pivotValue:
                i += 1
                swap(arr, i, j)
 
        # Swap the pivot element back to its final position
        swap(arr, i+1, high)
 
        # Recursively sort the left and right subarrays
        quickSort(arr, low, i)
        quickSort(arr, i+2, high)
 
# Driver code
arr = [5, 2, 7, 3, 1, 6, 4, 8]
n = len(arr)
 
print("Original array:", arr)
 
quickSort(arr, 0, n-1)
 
print("Sorted array:", arr)

C#

using System;
 
class Program {
  // 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;
  }
 
  // Function to generate a random pivot index
  static int GenerateRandomPivot(int low, int high) {
    Random random = new Random();
    return low + random.Next(high - low + 1);
  }
 
  // Function to perform QuickSort
  static void QuickSort(int[] arr, int low, int high) {
    if (low < high) {
      int pivotIndex = GenerateRandomPivot(low, high);
      int pivotValue = arr[pivotIndex];
 
      // Swap the pivot element with the last element
      Swap(arr, pivotIndex, high);
 
      int i = low - 1;
 
      for (int j = low; j < high; j++) {
        if (arr[j] < pivotValue) {
          i++;
          Swap(arr, i, j);
        }
      }
 
      // Swap the pivot element back to its final position
      Swap(arr, i+1, high);
 
      // Recursively sort the left and right subarrays
      QuickSort(arr, low, i);
      QuickSort(arr, i+2, high);
    }
  }
 
  static void Main() {
    int[] arr = {5, 2, 7, 3, 1, 6, 4, 8};
    int n = arr.Length;
 
    Console.Write("Original array: ");
    for (int i = 0; i < n; i++) {
      Console.Write(arr[i] + " ");
    }
 
    QuickSort(arr, 0, n-1);
 
    Console.Write("\nSorted array: ");
    for (int i = 0; i < n; i++) {
      Console.Write(arr[i] + " ");
    }
  }
}

Javascript

// Function to swap two elements
function swap(arr, i, j) {
  let temp = arr[i];
  arr[i] = arr[j];
  arr[j] = temp;
}
 
// Function to generate a random pivot index
function generateRandomPivot(low, high) {
  return Math.floor(Math.random() * (high - low + 1)) + low;
}
 
// Function to perform QuickSort
function quickSort(arr, low, high) {
  if (low < high) {
    let pivotIndex = generateRandomPivot(low, high);
    let pivotValue = arr[pivotIndex];
 
    // Swap the pivot element with the last element
    swap(arr, pivotIndex, high);
 
    let i = low - 1;
 
    for (let j = low; j < high; j++) {
      if (arr[j] < pivotValue) {
        i++;
        swap(arr, i, j);
      }
    }
 
    // Swap the pivot element back to its final position
    swap(arr, i + 1, high);
 
    // Recursively sort the left and right subarrays
    quickSort(arr, low, i);
    quickSort(arr, i + 2, high);
  }
}
 
// Driver code
let arr = [5, 2, 7, 3, 1, 6, 4, 8];
let n = arr.length;
 
console.log("Original array: [" + arr.join(", ") + "]");
 
quickSort(arr, 0, n - 1);
 
console.log("Sorted array: [" + arr.join(", ") + "]");

Output

Original array: 5 2 7 3 1 6 4 8 
Sorted array: 1 2 3 4 5 6 7 8

Analysis of Randomized Quick Sort

Notes

Using random pivoting we improve the expected or average time complexity to O (N log N). The Worst-Case complexity is still O ( N^2 ).

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QuickSort using Random Pivoting

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