Glasgow | 25-SDC-Nov | Nataliia Volkova | Sprint 2 | improve_with_caches

[Nataliia74]

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Changelist

Improve code with caches 11

[cjyuan]

When total == 1 or len(coins) == 1 is true, the result may not be 1 if the last coin is not 1 (e.g. the initial list of coins given is different)

On the other hand, when len(coins) == 1, there is simple way to determine if the current total (any value) can be made by the coin value.

[Nataliia74]

Hello CJ Yuan, I understood that I can have 2 possible results, not just 1. So, the best founded solution is not to use recursion, but simple math to check if the total is divisible by that left type coin.

[cjyuan]

What do you mean by 2 possible results? 0 or 1?

Yes, this approach:

simple math to check if the total is divisible by that left type coin

[Nataliia74]

Hello CJ Yuan, I mean 0 or 1. In this case, a better approach is to use math.

[cjyuan]

Array creation is a relatively costly operation.

From line 41, 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.

[Nataliia74]

Eliminated slicing, which is costly and creates a new array every recursion, and also many duplicates; the tuple conversion was costly as well. Changed by exchanging the tuple at the index an array.

[cjyuan]

Changes look good.

[cjyuan]

Should you need to avoid introducing variables in the global scope, you can consider:

• Declare them in ways_to_make_change()
• Define ways_to_make_change_helper() as an inner function of ways_to_make_change(). Inner function can access the variables in the outer scope.