Radix Sort

Radix sort is a non-comparative sorting algorithm. This sorting algorithm works on the integer keys by grouping digits which share the same position and value. The radix is the base of a number system. As we know that in the decimal system the radix or base is 10. So for sorting some decimal numbers, we need 10 positional boxes to store numbers.

The complexity of Radix Sort Technique

• Time Complexity: O(nk)
• Space Complexity: O(n+k)

Input and Output

Input:
The unsorted list: 802 630 20 745 52 300 612 932 78 187
Output:
Data before Sorting: 802 630 20 745 52 300 612 932 78 187
Data after Sorting: 20 52 78 187 300 612 630 745 802 932

Algorithm

radixSort(array, size, maxDigit)

Input − An array of data, and the total number in the array, digit count of max number

Output − Sorted array.

Begin
   define 10 lists as pocket
   for i := 0 to max -1 do
      m = 10^i+1
      p := 10^i
      for j := 0 to n-1 do
         temp := array[j] mod m
         index := temp / p
         pocket[index].append(array[j])
      done

      count := 0
      for j := 0 to radix do
         while pocket[j] is not empty
            array[count] := get first node of pocket[j] and delete it
            count := count +1
      done
   done
End

Example

#include<iostream>
#include<list>
#include<cmath>
using namespace std;

void display(int *array, int size) {
   for(int i = 0; i<size; i++)
      cout << array[i] << " ";
   cout << endl;
}

void radixSort(int *arr, int n, int max) {
   int i, j, m, p = 1, index, temp, count = 0;
   list<int> pocket[10]; //radix of decimal number is 10

   for(i = 0; i< max; i++) {
      m = pow(10, i+1);
      p = pow(10, i);

      for(j = 0; j<n; j++) {
         temp = arr[j]%m;
         index = temp/p;   //find index for pocket array
         pocket[index].push_back(arr[j]);
      }

      count = 0;
      for(j = 0; j<10; j++) {
         //delete from linked lists and store to array
         while(!pocket[j].empty()) {
            arr[count] = *(pocket[j].begin());
            pocket[j].erase(pocket[j].begin());
            count++;
         }
      }
   }
}

int main() {
   int n, max;
   cout << "Enter the number of elements: ";
   cin >> n;
   cout << "Enter the maximum digit of elements: ";
   cin >> max;
   int arr[n]; //create an array with given number of elements
   cout << "Enter elements:" << endl;

   for(int i = 0; i<n; i++) {
      cin >> arr[i];
   }

   cout << "Data before Sorting: ";
   display(arr, n);
   radixSort(arr, n, max);
   cout << "Data after Sorting: ";
   display(arr, n);
}

Output

Enter the number of elements: 10
Enter the maximum digit of elements: 3
Enter elements:
802 630 20 745 52 300 612 932 78 187
Data before Sorting: 802 630 20 745 52 300 612 932 78 187
Data after Sorting: 20 52 78 187 300 612 630 745 802 932