Add Decode Ways dynamic programming solutions in R

[Siddhram]

This PR introduces a complete and well-documented implementation of the Decode Ways problem in R.

Overview

The implementation provides solutions for counting the number of ways to decode a numeric string. It includes a classic tabulation approach and two O(1)-space variants (forward and backward), along with concise examples and explanatory comments.

Features

• Three approaches:
  • Tabulation DP: O(n) time, O(n) space
  • Forward O(1) DP: uses two rolling states (Fibonacci-style)
  • Backward O(1) DP: iterates from right to left
• Proper handling of zeros ("0" invalid unless part of "10" or "20")
• Helper function for two-digit validity (11–19, 21–26)
• Embedded examples printing results from all three methods
• Consistent structure and comments with other dynamic_programming scripts

Complexity

• Time Complexity: O(n)
• Space Complexity:
  • O(1) for forward/backward DP
  • O(n) for tabulation

Directory

• Updated DIRECTORY.md to list “Decode Ways” under Dynamic Programming

Demonstration

Run the script to execute built-in examples:

From Windows command line:

Rscript "R/dynamic_programming/decode_ways.r"