Counting Sort vs. Radix Sort

Attribute	Counting Sort	Radix Sort
Algorithm type	Non-comparison based	Non-comparison based
Stable	Yes	Yes
Time complexity	O(n + k)	O(nk)
Space complexity	O(n + k)	O(n + k)
Sorting stability	Stable	Stable

Introduction

Counting Sort and Radix Sort are two popular sorting algorithms that are often used in computer science. While both algorithms are efficient in their own right, they have distinct differences in terms of their attributes and performance. In this article, we will compare the attributes of Counting Sort and Radix Sort to understand their strengths and weaknesses.

Counting Sort

Counting Sort is a non-comparison based sorting algorithm that works by counting the number of occurrences of each element in the input array. It then uses this information to place each element in its correct position in the output array. Counting Sort is efficient when the range of input elements is not significantly larger than the number of elements to be sorted. This algorithm has a time complexity of O(n + k), where n is the number of elements to be sorted and k is the range of input elements.

• Efficient for small range of input elements
• Time complexity of O(n + k)
• Non-comparison based sorting algorithm

Radix Sort

Radix Sort is a non-comparison based sorting algorithm that works by sorting the input elements based on their individual digits or bits. It processes the input elements digit by digit or bit by bit, starting from the least significant digit or bit to the most significant digit or bit. Radix Sort is efficient when the number of digits or bits in the input elements is relatively small. This algorithm has a time complexity of O(d * (n + k)), where d is the number of digits or bits in the input elements, n is the number of elements to be sorted, and k is the range of input elements.

• Efficient for small number of digits or bits
• Time complexity of O(d * (n + k))
• Non-comparison based sorting algorithm

Comparison of Attributes

Both Counting Sort and Radix Sort are non-comparison based sorting algorithms, which means they do not rely on comparing elements to each other during the sorting process. This makes them more efficient than comparison based sorting algorithms like Quick Sort or Merge Sort, especially when the range of input elements is small. However, Counting Sort is more suitable for sorting elements with a small range, while Radix Sort is more suitable for sorting elements with a small number of digits or bits.

Counting Sort has a time complexity of O(n + k), where n is the number of elements to be sorted and k is the range of input elements. This makes Counting Sort efficient when the range of input elements is not significantly larger than the number of elements to be sorted. On the other hand, Radix Sort has a time complexity of O(d * (n + k)), where d is the number of digits or bits in the input elements. This makes Radix Sort efficient when the number of digits or bits in the input elements is relatively small.

Another difference between Counting Sort and Radix Sort is their stability. Counting Sort is a stable sorting algorithm, which means that it preserves the relative order of equal elements in the input array. This makes Counting Sort suitable for sorting elements that have multiple occurrences with the same value. On the other hand, Radix Sort is not inherently stable, but it can be modified to be stable by using a stable sorting algorithm as a subroutine.

Conclusion

In conclusion, Counting Sort and Radix Sort are both efficient non-comparison based sorting algorithms that have distinct attributes and performance characteristics. Counting Sort is more suitable for sorting elements with a small range, while Radix Sort is more suitable for sorting elements with a small number of digits or bits. Understanding the differences between these two algorithms can help in choosing the most appropriate sorting algorithm for a given problem.