London | 26-JUL-SDC |Ping Wang | Sprint 2 | Improve caches CYF-1182

[pathywang]

Self checklist

• I have titled my PR with Region | Cohort | FirstName LastName | Sprint | Assignment Title
• My changes meet the requirements of the task
• I have tested my changes
• My changes follow the style guide

Task code

CYF-1182

Changelist

. Updated the Fibonacci function to use the existing cache dictionary, avoiding repeated calculations and
improving performance through memoisation.

• Optimized ways_to_make_change by replacing coin-list slicing with a coin index.
• Updated memoization to use (total, coin_index) as the cache key, avoiding repeated tuple creation.
• Used recursive cases to count combinations by either skipping the current coin or using it again.

[cjyuan]

This variable is not used anywhere in this file.

[pathywang]

Thank, i deleted it now while cache variable is never used in fibronacci function

[cjyuan]

Wouldn't deleting it beat the purpose of this exercise?

[pathywang]

Thank you for pointing out. I've kept the original Fibonacci implementation and updated it to use the existing cache dictionary. How do you think?

[cjyuan]

Array and tuple creations are relatively costly operations.

From lines 27 and 35, 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 35 (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.

[pathywang]

Thanks for the feedback! I updated the implementation to use a coin index instead of creating sliced lists. The memoization cache now uses (total, coin_index) as its key, avoiding repeated tuple and list creation while preserving the logic for counting combinations.

[cjyuan]

Sounds good.

I don't see any new commits on GitHub yet.

[pathywang]

Do apologize, i forgot to commit and push. i just did it

[cjyuan]

Changes look good.

[cjyuan]

Why use tuple instead of list?

[pathywang]

Thank you for asking.I changed the coin denominations to a tuple because they are fixed and do not need to be modified. The main optimization was replacing list slicing with a coin index, avoiding the creation of new lists during recursive calls. The cache now uses (total, coin_index) as its key.