Add Longest Common Subsequence (LCS) dynamic programming algorithm

- Implement complete LCS solution with O(m*n) time complexity
- Include space-optimized O(min(m,n)) version for large inputs
- Add path reconstruction to return actual LCS string
- Support for both string and array sequences
- Multiple LCS finding for cases with multiple solutions
- Create new Dynamic Programming category
- Comprehensive examples including DNA analysis and file diff simulation

Author: piyushkumar0707

DIRECTORY.md

@@ -33,6 +33,9 @@
   * [K Folds](https://github.com/TheAlgorithms/R/blob/HEAD/data_preprocessing/k_folds.r)
   * [Lasso](https://github.com/TheAlgorithms/R/blob/HEAD/data_preprocessing/lasso.r)
 
+## Dynamic Programming
+  * [Longest Common Subsequence](https://github.com/TheAlgorithms/R/blob/HEAD/dynamic_programming/longest_common_subsequence.r)
+
 ## Mathematics
   * [Amicable Numbers](https://github.com/TheAlgorithms/R/blob/HEAD/mathematics/amicable_numbers.r)
   * [Armstrong Number](https://github.com/TheAlgorithms/R/blob/HEAD/mathematics/armstrong_number.r)