Add dp algorithms

[hamadasyr]

This module implements two classic Dynamic Programming strategies to solve the Longest Common Subsequence (LCS) problem:

Top-Down (Memoization):
Uses recursion with caching to avoid redundant subproblem computations. The recursive function stores results in a dictionary to ensure efficiency.

Bottom-Up (Tabulation):
Builds a 2D table iteratively, where each cell stores the LCS length for prefixes of the two input strings.

Additionally, the module provides a function to reconstruct the actual LCS string by backtracking through the DP table.

Each function is modular, readable, and thoroughly commented, demonstrating best practices in applying DP for string problems.