ZA | 25-SDC-July | Luke Manyamazi | Sprint 2 | Imrove With Caches #59
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Luke-Manyamazi
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cjyuan
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Jan 25, 2026
Comment on lines
24
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46
| cache_key = (total, tuple(coins)) | ||
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| # Check if we already computed this combination | ||
| if cache_key in change_cache: | ||
| return change_cache[cache_key] | ||
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| # Base cases | ||
| if total == 0: | ||
| return 1 # One way to make 0: use no coins | ||
| if len(coins) == 0: | ||
| return 0 # No coins left but still need to make total > 0 | ||
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| ways = 0 | ||
| for coin_index in range(len(coins)): | ||
| coin = coins[coin_index] | ||
| count_of_coin = 1 | ||
| while coin * count_of_coin <= total: | ||
| total_from_coins = coin * count_of_coin | ||
| 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 |
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From line 45, we can figure out coins can only be one of the following 9 lists:
[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-lists at line 45, and
- create key as
(total, a_value_identifiying_one_of_the_sublists)instead of as(total, tuple(coins))
I don't think this exercise expects trainees to optimize the code to this level. So change is optional.
cjyuan
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