Add Self-Dividing Numbers algorithm in R

[Siddhram]

Overview

This PR introduces a comprehensive and well-documented implementation of the Self-Dividing Numbers problem in R, featuring efficient digit extraction and divisibility checking.

A self-dividing number is a number that is divisible by every digit it contains and does not contain the digit 0 (since division by zero is undefined).
The algorithm efficiently examines each number in a given range by extracting its digits and validating divisibility.

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Features

• Optimized O(m × log₁₀(n)) algorithm
  • For each number in the given range, extract digits using modulo (%) and division (/)
  • Skip immediately if any digit is 0 or if original_number %% digit != 0
  • Return TRUE only if all digits divide the number evenly
• Multiple implementation variants:
  • is_self_dividing_number() — Checks an individual number
  • self_dividing_numbers() — Finds all self-dividing numbers in range [left, right]
  • self_dividing_numbers_vectorized() — Vectorized version for improved performance
  • analyze_number_digits() — Debug helper for visualizing digit breakdown
• Comprehensive input validation and error handling
• Extensive test suite covering edge cases and performance benchmarks
• Consistent roxygen2 documentation matching other scripts in the mathematics module

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Complexity

• Time Complexity: O(m × log₁₀(n))
  where m = right - left + 1, and log₁₀(n) is the number of digits in each number.
• Space Complexity: O(m) — for storing the result list.

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Directory

• Updated DIRECTORY.md
  Added "Self Dividing Numbers" entry under Mathematics

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Demonstration

Run the script to execute built-in examples and validations:

PowerShell

Rscript "mathematics/self_dividing_numbers.r"