London | 25-SDC-Nov | Aida Eslamimoghadam | Sprint 2 | Add caching to improve performance#144
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aydaeslami wants to merge 2 commits into
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London | 25-SDC-Nov | Aida Eslamimoghadam | Sprint 2 | Add caching to improve performance#144aydaeslami wants to merge 2 commits into
aydaeslami wants to merge 2 commits into
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aydaeslami
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cjyuan
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| @@ -26,7 +27,11 @@ def ways_to_make_change_helper(total: int, coins: List[int]) -> int: | |||
| if total_from_coins == total: | |||
| ways += 1 | |||
| else: | |||
| intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:]) | |||
| ways += intermediate | |||
| ways += ways_to_make_change_helper( | |||
| total - total_from_coins, | |||
| coins=coins[coin_index + 1:] | |||
| ) | |||
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Array and tuple creations are relatively costly operations.
From lines 6 and 32, 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 32 (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.
cjyuan
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Thanks a million @cjyuan for your suggestion, I updated the solution to use start_index instead of creating coin sub-arrays, and changed the cache key to total, start_index to avoid unnecessary array and tuple creation. |
aydaeslami
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cjyuan
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| def ways_to_make_change_helper(total: int, coins: List[int]) -> int: | ||
| key = (total, tuple(coins)) | ||
| def ways_to_make_change_helper(total: int, start_index: int) -> int: | ||
| key = (total, start_index) |
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Why not pass the coin list through the parameter (in addition to passing start_index) so that the function can be reused for different coin list?
When we pass a list to a function, we are only passing its reference -- the cost is negligible.
| ways = 0 | ||
| for coin_index in range(len(coins)): | ||
| coin = coins[coin_index] | ||
| for coin_index in range(start_index, len(COINS)): |
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This loop is actually redundant. Subsequent coins will be considered in the recursive function calls anyway.
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Changelist
Added caching (memoisation) to avoid repeated calculations and improve performance of recursive functions.