In this post we’ll see how to write Radix sort program in Java. Radix sort is in the league of __Counting Sort__ and __Bucket Sort__ which are O(n) sorting algorithms.

### How does Radix sort work

Radix sort works by doing the sorting in passes moving from least significant digit to most significant digit. In each pass you can use any stable sort to sort the numbers on the digit.

If you have an array **Arr** with the maximum element in array Arr having number of digits as d, then the working of Radix sort
is as shown below.

for i = 1 to d Use any stable sort (like counting sort) to sort Arr on digit d

Following image shows how Radix sort sorts an input array in each pass. Here the maximum number is 655 so number of passes is 3.

### Radix Sort Java program

Java program for Radix sort works on the following logic.

- Find the maximum number in the input array.
- Loop to iterate each digit of the maximum number starting from the least significant digit.
- Sort the array on that digit using Counting sort.

public class RadixSort { public static void main(String[] args) { int[] arr = {80, 406, 21, 655, 55, 4, 8, 91, 87, 6}; System.out.println("Original Array- " + Arrays.toString(arr)); radixSort(arr); System.out.println("Sorted array after Radix sort- " + Arrays.toString(arr)); } private static void radixSort(int[] arr){ int max = getMaxElement(arr); int position = 1; while(max/position > 0){ countingSort(arr, position); position *= 10; } } private static int getMaxElement(int[] arr){ int max = arr[0]; for(int i = 1; i < arr.length; i++){ if (arr[i] > max){ max = arr[i]; } } return max; } private static void countingSort(int[] arr, int position){ int n = arr.length; int[] output = new int[n]; int[] count = new int[n]; //count number of times each element appear for(int i = 0; i < arr.length; i++){ count[(arr[i]/position)%10]++; } // each element stores (element at current index+element // at previous index) to get the actual position of the element for(int i = 1; i < n; i++){ count[i] = count[i] + count[i-1]; } // for correct placement of the numbers start from the end for(int i = n-1; i >=0; i--){ output[count[(arr[i]/position)%10] - 1] = arr[i]; count[(arr[i]/position)%10]--; } // Copy output array to input to the input for // the next stage of counting sort for(int i = 0; i < output.length; i++){ arr[i] = output[i]; } System.out.println("Counting sort at this stage " + Arrays.toString(arr)); } }

__Output__

Original Array- [80, 406, 21, 655, 55, 4, 8, 91, 87, 6] Counting sort at this stage [80, 21, 91, 4, 655, 55, 406, 6, 87, 8] Counting sort at this stage [4, 406, 6, 8, 21, 655, 55, 80, 87, 91] Counting sort at this stage [4, 6, 8, 21, 55, 80, 87, 91, 406, 655] Sorted array after Radix sort- [4, 6, 8, 21, 55, 80, 87, 91, 406, 655]

### Performance of Radix Sort

If you are using Counting sort for sorting in each pass of Radix sort then time complexity of Radix sort is **O(d*(n+k))**.
Here O(n+k) is the time complexity of counting sort and d is the number of passes over number having d digits.

Auxiliary space requirement is (n+k). Count array takes k space and the output array of the same size as input array is also used while sorting. Thus the space complexity of Radix sort is O(n+k).

That's all for this topic **Radix Sort Program in Java**. If you have any doubt or any suggestions to make please drop a comment. Thanks!

>>>Return to Java Programs Page

__Related Topics__

**You may also like- **