Sheffield | 25-SDC-Nov | Sheida Shabankari | Sprint 2 |improve with caches

[sheida-shab]

• 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

PR summary :

Add manual caching to speed up recursive Fibonacci and ways_to_make_change functions.

• Use dictionaries to store results of already computed subproblems.
• In Fibonacci, store fibonacci(n) values to avoid recalculating them.
• In ways_to_make_change, use a key (total, tuple(coins)) to remember results for each combination of total and remaining coins.
• All recursive calls share the same cache to reuse previous results, without using @cache.
• These changes reduce repeated calculations and make the functions much faster for large inputs.

[cjyuan]

Why not use {} as the default value for cache?

[cjyuan]

Array creation is a relatively costly operation.

From line 34, 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 41 (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.