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London | 26-Jul-SDC | Shaghayegh Far| Sprint 2 | Improve Code with Caches - #257
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shaghayeghfar
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cjyuan
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Oct 15, 2026
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+21
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+42
| key = (total, tuple(coins)) | ||
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| if key in cache: | ||
| return cache[key] | ||
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| ways = 0 | ||
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| for coin_index in range(len(coins)): | ||
| coin = coins[coin_index] | ||
| count_of_coin = 1 | ||
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| while coin * count_of_coin <= total: | ||
| total_from_coins = coin * count_of_coin | ||
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| 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[coin_index + 1:], | ||
| cache, | ||
| ) |
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Array and tuple creations are relatively costly operations.
We could observe that 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 40 (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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Learners, PR Template
Self checklist
Task code
CYF-1182
Changelist
Improved Fibonacci and making-change solutions by using caching to avoid repeated calculations and improve performance.