WestMidlands| SDC NOV 2025 |Sara Tahir| Sprint 2 | Improve with caches

[SaraTahir28]

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Changelist

Improved the performance of both the fibonacci and making_change functions by adding caching (memoisation) to avoid recalculating the same subproblems.

Questions

I dont have any questions.

[cjyuan]

Array creation is a relatively costly operation.

From line 42, we know coins can only be one of the following 9 arrays:

[200, 100, 50, 20, 10, 5, 2, 1]
[100, 50, 20, 10, 5, 2, 1]
[50, 20, 10, 5, 2, 1]
...
[1]
[]

We could further improve the performance if we can

• avoid repeatedly creating the same sub-arrays at line 42 (e.g. use another cache), and
• create key as (total, a_unique_integer_identifying_the_subarray) instead of as (total, tuple of coins)
  • There are only a small number of different subarrays. We can easily assign each subarray a unique integer.

[SaraTahir28]

1. Thanks for the suggestion . I’ve updated the implementation so I no longer slice the coins list. Instead, I pass a start_index through the recursion, which avoids creating new subarrays entirely.
2. I also switched the cache key to (total, start_index) rather than (total, tuple(coins)). This gives each of the 9 possible sub‑arrays a unique integer “identity” automatically, without needing a separate mapping
3. This keeps the logic the same but removes the repeated list allocations and makes the memoisation faster and cheaper.

[cjyuan]

Changes look good.