Quotient – Remainder Sort

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 = MIN and COL = MAX/MIN + 1
  3. For each element in input array, calculate quotient and remainder and store in 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++

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// 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);
}

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Java

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// 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

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C#

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// 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

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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 Soring Algorithm using Quotient and Remainder,
J. Eng. Applied Sci, 12 (Special Issue 7): 8016-8020, 2017, ISSN : 1816-949X



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