Python Data Structure and Algorithm Tutorial – Radix Sort Algorithm

Radix Sort Algorithm


In this tutorial, you will learn how radix sort works. Also, you will find working examples of radix sort in Python.

Radix sort is a sorting technique that sorts the elements by first grouping the individual digits of the same place value. Then, sort the elements according to their increasing/decreasing order.

Suppose, we have an array of 8 elements. First, we will sort elements based on the value of the unit place. Then, we will sort elements based on the value of the tenth place. This process goes on until the last significant place.

Let the initial array be [121, 432, 564, 23, 1, 45, 788]. It is sorted according to radix sort as shown in the figure below.

Radix Sort Working
Working of Radix Sort

Please go through the counting sort before reading this article because counting sort is used as an intermediate sort in radix sort.

How Radix Sort Works?

  1. Find the largest element in the array, i.e. max. Let X be the number of digits in maxX is calculated because we have to go through all the significant places of all elements.In this array [121, 432, 564, 23, 1, 45, 788], we have the largest number 788. It has 3 digits. Therefore, the loop should go up to hundreds place (3 times).
  2. Now, go through each significant place one by one.Use any stable sorting technique to sort the digits at each significant place. We have used counting sort for this.

    Sort the elements based on the unit place digits (X=0).

    Radix Sort working with Counting Sort as intermediate step
    Using counting sort to sort elements based on unit place
  3. Now, sort the elements based on digits at tens place.
    Radix Sort Step
    Sort elements based on tens place
  4. Finally, sort the elements based on the digits at hundreds place.
    Selection Sort Step
    Sort elements based on hundreds place

Radix Sort Algorithm

  d <- maximum number of digits in the largest element
  create d buckets of size 0-9
  for i <- 0 to d
    sort the elements according to ith place digits using countingSort

countingSort(array, d)
  max <- find largest element among dth place elements
  initialize count array with all zeros
  for j <- 0 to size
    find the total count of each unique digit in dth place of elements and
    store the count at jth index in count array
  for i <- 1 to max
    find the cumulative sum and store it in count array itself
  for j <- size down to 1
    restore the elements to array
    decrease count of each element restored by 1

Python Examples

/* Radix sort in Python */

/* Using counting sort to sort the elements in the basis of significant places */
def countingSort(array, place):
    size = len(array)
    output = [0] * size
    count = [0] * 10

    /* Calculate count of elements */
    for i in range(0, size):
        index = array[i] // place
        count[index % 10] += 1

    /* Calculate cummulative count */
    for i in range(1, 10):
        count[i] += count[i - 1]

    /* Place the elements in sorted order */
    i = size - 1
    while i >= 0:
        index = array[i] // place
        output[count[index % 10] - 1] = array[i]
        count[index % 10] -= 1
        i -= 1

    for i in range(0, size):
        array[i] = output[i]

/* Main function to implement radix sort */
def radixSort(array):
    /* Get maximum element */
    max_element = max(array)

    /* Apply counting sort to sort elements based on place value. */
    place = 1
    while max_element // place > 0:
        countingSort(array, place)
        place *= 10

data = [121, 432, 564, 23, 1, 45, 788]


Since radix sort is a non-comparative algorithm, it has advantages over comparative sorting algorithms.

For the radix sort that uses counting sort as an intermediate stable sort, the time complexity is O(d(n+k)).

Here, d is the number cycle and O(n+k) is the time complexity of counting sort.

Thus, radix sort has linear time complexity which is better than O(nlog n) of comparative sorting algorithms.

If we take very large digit numbers or the number of other bases like 32-bit and 64-bit numbers then it can perform in linear time however the intermediate sort takes large space.

This makes radix sort space inefficient. This is the reason why this sort is not used in software libraries.

Radix Sort Applications

Radix sort is implemented in

  • DC3 algorithm (Kärkkäinen-Sanders-Burkhardt) while making a suffix array.
  • places where there are numbers in large ranges.



Python Example for Beginners

Two Machine Learning Fields

There are two sides to machine learning:

  • Practical Machine Learning:This is about querying databases, cleaning data, writing scripts to transform data and gluing algorithm and libraries together and writing custom code to squeeze reliable answers from data to satisfy difficult and ill defined questions. It’s the mess of reality.
  • Theoretical Machine Learning: This is about math and abstraction and idealized scenarios and limits and beauty and informing what is possible. It is a whole lot neater and cleaner and removed from the mess of reality.

Data Science Resources: Data Science Recipes and Applied Machine Learning Recipes

Introduction to Applied Machine Learning & Data Science for Beginners, Business Analysts, Students, Researchers and Freelancers with Python & R Codes @ Western Australian Center for Applied Machine Learning & Data Science (WACAMLDS) !!!

Latest end-to-end Learn by Coding Recipes in Project-Based Learning:

Applied Statistics with R for Beginners and Business Professionals

Data Science and Machine Learning Projects in Python: Tabular Data Analytics

Data Science and Machine Learning Projects in R: Tabular Data Analytics

Python Machine Learning & Data Science Recipes: Learn by Coding

R Machine Learning & Data Science Recipes: Learn by Coding

Comparing Different Machine Learning Algorithms in Python for Classification (FREE)

Disclaimer: The information and code presented within this recipe/tutorial is only for educational and coaching purposes for beginners and developers. Anyone can practice and apply the recipe/tutorial presented here, but the reader is taking full responsibility for his/her actions. The author (content curator) of this recipe (code / program) has made every effort to ensure the accuracy of the information was correct at time of publication. The author (content curator) does not assume and hereby disclaims any liability to any party for any loss, damage, or disruption caused by errors or omissions, whether such errors or omissions result from accident, negligence, or any other cause. The information presented here could also be found in public knowledge domains.  

Google –> SETScholars