Radix Sort - Python

Last Updated : 03 Mar, 2025

Radix Sort is a linear sorting algorithm that sorts elements by processing them digit by digit. It is an efficient sorting algorithm for integers or strings with fixed-size keys.

Rather than comparing elements directly, Radix Sort distributes the elements into buckets based on each digit’s value. By repeatedly sorting the elements by their significant digits, from the least significant to the most significant, Radix Sort achieves the final sorted order.

Working of Radix Sort Algorithm

To perform radix sort on the array [170, 45, 75, 90, 802, 24, 2, 66], we follow these steps:
Step 1: Find the largest element in the array, which is 802. It has three digits, so we will iterate three times, once for each significant place.
Step 2: Sort the elements based on the unit place digits (X=0). We use a stable sorting technique, such as counting sort, to sort the digits at each significant place. It’s important to understand that the default implementation of counting sort is unstable i.e. same keys can be in a different order than the input array. To solve this problem, We can iterate the input array in reverse order to build the output array. This strategy helps us to keep the same keys in the same order as they appear in the input array.
Sorting based on the unit place:
Perform counting sort on the array based on the unit place digits.
The sorted array based on the unit place is [170, 90, 802, 2, 24, 45, 75, 66].
Step 3: Sort the elements based on the tens place digits.
Sorting based on the tens place:
Perform counting sort on the array based on the tens place digits.
The sorted array based on the tens place is [802, 2, 24, 45, 66, 170, 75, 90].
Step 4: Sort the elements based on the hundreds place digits.
Sorting based on the hundreds place:
Perform counting sort on the array based on the hundreds place digits.
The sorted array based on the hundreds place is [2, 24, 45, 66, 75, 90, 170, 802].
Step 5: The array is now sorted in ascending order.
The final sorted array using radix sort is [2, 24, 45, 66, 75, 90, 170, 802].

Below is the implementation for the above illustrations:

Python

def countingSort(arr, exp1):         n = len(arr)         # The output array elements that will have sorted arr      output = [0] * (n)         # initialize count array as 0      count = [0] * (10)         # Store count of occurrences in count[]      for i in range(0, n):          index = (arr[i]/exp1)          count[int((index)%10)] += 1        # Change count[i] so that count[i] now contains actual      #  position of this digit in output array      for i in range(1,10):          count[i] += count[i-1]         # Build the output array      i = n-1     while i>=0:          index = (arr[i]/exp1)          output[ count[ int((index)%10) ] - 1] = arr[i]          count[int((index)%10)] -= 1         i -= 1        # Copying the output array to arr[],      # so that arr now contains sorted numbers      i = 0     for i in range(0,len(arr)):          arr[i] = output[i]   # Method to do Radix Sort def radixSort(arr):      # Find the maximum number to know number of digits     max1 = max(arr)      # Do counting sort for every digit. Note that instead     # of passing digit number, exp is passed. exp is 10^i     # where i is current digit number     exp = 1     while max1 // exp > 0:         countingSort(arr,exp)         exp *= 10  # Driver code  arr = [ 170, 45, 75, 90, 802, 24, 2, 66] radixSort(arr)  for i in range(len(arr)):     print(arr[i],end=" ")

Output

2 24 45 66 75 90 170 802

Time Complexity: O(n*d). Here d=10
Auxiliary Space: O(n)

Please refer complete article on Radix Sort for more details!

Java Program for Radix Sort

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Radix Sort - Python

Working of Radix Sort Algorithm

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