Refactor memoized knapsack implementation to remove global state

[anikchand461]

Feature description

The current memoized knapsack implementation relies on a global DP table, which reduces code clarity and reusability. This PR proposes a cleaner implementation using Python’s functools.lru_cache to eliminate global state and improve readability. The updated version will follow repository standards, include type hints, and provide doctests.

[Bhavik3103]

Hi @anikchand461,

I would like to work on this issue.

I’m planning to refactor the current memoized knapsack implementation by replacing the global DP table with Python’s functools.lru_cache. This will help eliminate global state, improve readability, and make the solution more modular and easier to test.