What is a radix sort in C and how is it implemented?

Table of Contents

• Introduction
• Understanding Radix Sort
  • How Radix Sort Works
• Implementation in C
• Practical Examples
  • Example 1: Sorting an Array of Integers
  • Example 2: Handling Large Datasets
• Conclusion

Introduction

Radix sort is a non-comparative sorting algorithm that sorts numbers by processing their individual digits. Unlike traditional comparison-based sorting algorithms, radix sort sorts numbers based on their digits' positional value. This guide will explain how radix sort works and provide a detailed implementation in C, along with practical examples.

Understanding Radix Sort

Radix sort operates by sorting numbers digit by digit. It can process digits starting from the least significant digit (LSD) or the most significant digit (MSD). The algorithm uses a stable subroutine, such as counting sort, to sort the digits at each position. This process is repeated for each digit position until the numbers are fully sorted.

How Radix Sort Works

1. Determine the Maximum Number of Digits: Identify the maximum number in the dataset to determine the number of iterations required for sorting.
2. Sort by Each Digit: Begin with the least significant digit and sort all numbers based on that digit using a stable sort. Move to the next digit and repeat until all digits are processed.
3. Use a Stable Sort: Radix sort relies on a stable sorting algorithm like counting sort for sorting digits. A stable sort maintains the relative order of elements with the same key.

Implementation in C

Here is a C implementation of radix sort using counting sort as the stable sorting algorithm:

Practical Examples

Example 1: Sorting an Array of Integers

In this example, data is sorted using radix sort. The sorted array will be printed.

Example 2: Handling Large Datasets

Radix sort is particularly useful for large datasets with integers, especially when the range of values (number of digits) is limited. Its time complexity is O(nk), where n is the number of elements and k is the number of digits in the largest number.

Conclusion

Radix sort is an efficient sorting algorithm for specific use cases, particularly when dealing with large datasets and numbers with a fixed number of digits. Implementing radix sort in C involves using counting sort to sort individual digits. Understanding and applying radix sort can enhance sorting performance and handle large volumes of data effectively.