Barcelona | OCT-2025-2 | Iheb Hamdi | Sprint 2 |Improve with cahces| Module-Complexity - #4

Summary

• Memoize fibonacci with a dict cache threaded through recursive calls, turning exponential recursion into linear time.
• Rewrite ways_to_make_change as bottom-up DP, using a ways list as the cache (ways[amount] = ways to make that amount with the coins considered so far). Avoids both the original's near-quadratic blowup and a Python recursion-depth crash hit while prototyping a memoized-recursive version for large totals (e.g. total=9176).
• No @cache decorator used, per exercise constraints.