# 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++

 // CPP program to implement Quotient - Remainder // Sort #include #include 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 Soring Algorithm using Quotient and Remainder,
J. Eng. Applied Sci, 12 (Special Issue 7): 8016-8020, 2017, ISSN : 1816-949X

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Improved By : princi singh, Rajput-Ji