Implemented Radix Sort Algorithm

[Ramy-Badr-Ahmed]

Description:

This pull request introduces an implementation of the Radix Sort algorithm with support for different bases.

Definition:

• Radix Sort is a non-comparison-based sorting algorithm that sorts numbers by processing individual digits.
• The Algorithm is efficient for sorting integers and other values with a fixed number of digits or characters.
• It sorts numbers by processing individual digits. It works by performing Counting Sort on each digit, starting from the least significant digit to the most significant digit.
• Time Complexity: O(d * (n + k)), where n is the number of elements, d is the number of digits, and k is the range of digits.
• Compared to the comparison-based sorting algorithms (Implemented Merge Sort Algorithm #7, Implemented Heap Sort Algorithm #8, Implemented Quick Sort Algorithm #10), Radix Sort is non-comparison-based; it can be more efficient for sorting integers with a fixed number of digits (when the number of digits is small compared to the number of elements).
• Radix Sort is more efficient than Gnome Sort (O(n^2)) Implemented Gnome Sort Algorithm #9 for larger datasets.

Implementation Details:

radix_sort.f90: Contains the radix_sort_module with:

radix_sort: A subroutine that sorts the input array using the Radix Sort algorithm.
counting_sort: A subroutine that performs Counting Sort based on the digit represented by exp.

The module has been enhanced to support sorting based on different numeral systems (bases). The radix_sort subroutine can now be used with different bases, such as base 2, 10, and 16.

Example Usage:

example_usage_radix_sort.f90: Includes three test programs demonstrating the radix_sort subroutine from the radix_sort_module with different bases:

Base 10:
    Array: [170, 45, 75, 90, 802, 24, 2, 66, 15, 40]
    Output: Sorted array in base 10.

Base 2:
    Array: [1010, 1101, 1001, 1110, 0010, 0101, 1111, 0110, 1000, 0001]
    Output: Sorted binary array, represented in decimal.

Base 16:
    Array: [0xAB, 0x1F, 0x3D, 0xFF, 0x10, 0x05, 0xD3, 0x2A, 0xB4, 0x00]
    Output: Sorted hexadecimal array, represented in decimal.

The program sorts the sample arrays in their respective bases and prints the results.

Additional Test Cases:

tests_radix_sort.f90: A test program that includes a variety of test cases to validate the radix_sort implementation.

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Reference

The Algorithm Design Manual, Latest edition

[Ramy-Badr-Ahmed]

Hi @SatinWukerORIG ,
Looking forward to your review 🙂

[Ramy-Badr-Ahmed]

Added more test cases for the radix_sort module.

[SatinWukerORIG]

Great implementation and test cases. The comments are also very detailed.
I can merge it and then refactor the directory structure. Then you can put examples, tests, and modules under different folders as mentioned in issue #13!

[Ramy-Badr-Ahmed]

Great implementation and test cases. The comments are also very detailed. I can merge it and then refactor the directory structure. Then you can put examples, tests, and modules under different folders as mentioned in issue #13!

Thanks, Satin!
Sure 👍