Skip to content
Related Articles

Related Articles

Improve Article

Quotient – Remainder Sort

  • Difficulty Level : Easy
  • Last Updated : 16 Jul, 2021
Geek Week

Quotient – Remainder Sort is a non-comparison based sorting algorithm. Steps to perform Quotient – Remainder sort as described below : 

  1. Find MIN and MAX of the array.
  2. Create an ROW*COL matrix consisting of 0s, where ROW = MAX/MIN+1 and COL = MIN.
  3. For each element in the input array, calculate quotient and remainder and store in the matrix[quotient][remainder]
  4. For each element in matrix, if element != 0, append element to sorted array

Examples:  

Input : 2 5 3 7 4 8   
MAX = 8, MIN = 2, ROW = 4, COL 2
matrix : 2 3  
         4 5  
         0 7  
         8 0
Output : 2 3 4 5 7 8

C++




// CPP program to implement Quotient - Remainder
// Sort
#include <algorithm>
#include <iostream>
using namespace std;
 
void QRsort(int arr[], int size)
{
    // max_element finds maximum element in an array
    int MAX = *max_element(arr, arr + size);
 
    // min_element finds minimum element in an array
    int MIN = *min_element(arr, arr + size);
 
    cout << "Maximum Element found is : " << MAX << endl;
    cout << "Minimum Element found is : " << MIN << endl;
 
    int COL = MIN;
    int ROW = MAX / MIN + 1;
 
    // Creating a ROW * COL matrix of all zeros
    int matrix[ROW][COL] = { 0 };
 
    for (int i = 0; i < size; i++) {
        int quotient = arr[i] / MIN;
        int remainder = arr[i] % MIN;
        matrix[quotient][remainder + 1] = arr[i];
    }
 
    int k = 0;
    for (int i = 0; i < ROW; i++) {
        for (int j = 0; j < COL; j++) {
            if (matrix[i][j] != 0) {
                arr[k++] = matrix[i][j];
            }
        }
    }
}
 
void printArray(int arr[], int size)
{
    for (int i = 0; i < size; i++)
        cout << arr[i] << " ";
    cout << endl;
}
 
int main()
{
    int arr[] = { 5, 3, 7, 4, 8, 2, 6 };
    int size = sizeof(arr) / sizeof(arr[0]);
    cout << "Initial Array : " << endl;
    printArray(arr, size);
 
    QRsort(arr, size);
 
    cout << "Array after sorting : " << endl;
    printArray(arr, size);
}

Java




// Java program to implement
// Quotient - Remainder Sort
import java.util.*;
 
class GFG
{
static void QRsort(int arr[], int size)
{
    // max_element finds maximum element in an array
    int MAX = Arrays.stream(arr).max().getAsInt();
 
    // min_element finds minimum element in an array
    int MIN = Arrays.stream(arr).min().getAsInt();
 
    System.out.println("Maximum Element found is : " + MAX);
    System.out.println("Minimum Element found is : " + MIN);
 
    int COL = MIN;
    int ROW = MAX / MIN + 1;
 
    // Creating a ROW * COL matrix of all zeros
    int[][] matrix = new int[ROW][COL];
 
    for (int i = 0; i < size; i++)
    {
        int quotient = arr[i] / MIN;
        int remainder = arr[i] % MIN;
        matrix[quotient][remainder] = arr[i];
    }
 
    int k = 0;
    for (int i = 0; i < ROW; i++)
    {
        for (int j = 0; j < COL; j++)
        {
            if (matrix[i][j] != 0)
            {
                arr[k++] = matrix[i][j];
            }
        }
    }
}
 
static void printArray(int arr[], int size)
{
    for (int i = 0; i < size; i++)
    {
        System.out.print(arr[i] + " ");
    }
    System.out.println();
}
 
// Driver Code
public static void main(String[] args)
{
    int arr[] = {5, 3, 7, 4, 8, 2, 6};
    int size = arr.length;
    System.out.println("Initial Array : ");
    printArray(arr, size);
 
    QRsort(arr, size);
 
    System.out.println("Array after sorting : ");
    printArray(arr, size);
}
}
 
// This code is contributed by Princi Singh

C#




// C# program to implement
// Quotient - Remainder Sort
using System;
using System.Linq;
 
class GFG
{
static void QRsort(int []arr, int size)
{
    // max_element finds maximum element in an array
    int MAX = arr.Max();
 
    // min_element finds minimum element in an array
    int MIN = arr.Min();
 
    Console.WriteLine("Maximum Element found is : " + MAX);
    Console.WriteLine("Minimum Element found is : " + MIN);
 
    int COL = MIN;
    int ROW = MAX / MIN + 1;
 
    // Creating a ROW * COL matrix of all zeros
    int[,] matrix = new int[ROW, COL];
 
    for (int i = 0; i < size; i++)
    {
        int quotient = arr[i] / MIN;
        int remainder = arr[i] % MIN;
        matrix[quotient, remainder] = arr[i];
    }
 
    int k = 0;
    for (int i = 0; i < ROW; i++)
    {
        for (int j = 0; j < COL; j++)
        {
            if (matrix[i, j] != 0)
            {
                arr[k++] = matrix[i, j];
            }
        }
    }
}
 
static void printArray(int []arr, int size)
{
    for (int i = 0; i < size; i++)
    {
        Console.Write(arr[i] + " ");
    }
    Console.WriteLine();
}
 
// Driver Code
public static void Main(String[] args)
{
    int []arr = {5, 3, 7, 4, 8, 2, 6};
    int size = arr.Length;
    Console.WriteLine("Initial Array : ");
    printArray(arr, size);
 
    QRsort(arr, size);
 
    Console.WriteLine("Array after sorting : ");
    printArray(arr, size);
}
}
 
// This code is contributed by Rajput-Ji
Output: 
Initial Array : 
5 3 7 4 8 2 6 
Maximum Element found is : 8
Minimum Element found is : 2
Array after sorting : 
2 3 4 5 6 7 8

 

References 
Abul Hasnat, Tanima Bhattacharyya, Atanu Dey, Santanu Halder, and Debotosh Bhattachajee, 2017. A Novel Sorting Algorithm using Quotient and Remainder, 
J. Eng. Applied Sci, 12 (Special Issue 7): 8016-8020, 2017, ISSN : 1816-949X

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.




My Personal Notes arrow_drop_up
Recommended Articles
Page :