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mervereis
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the
Needs Review
cjyuan
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Oct 14, 2026
Comment on lines
+17
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+29
| key = (total, tuple(coins)) | ||
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| if key in cache: | ||
| return cache[key] | ||
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| coin = coins[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 | ||
| count_of_coin += 1 | ||
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| for count in range(total // coin + 1): | ||
| remaining = total - count * coin | ||
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| ways += ways_to_make_change_helper(remaining, coins[1:]) |
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Array and tuple creations are relatively costly operations.
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 29 (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.
Author
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Thanks, that’s a good point. I’ve replaced the repeated coin-list slicing with a single COINS tuple and pass a coin_index to identify each suffix. The cache key is now (total, coin_index), avoiding the repeated tuple construction as well. @cjyuan
cjyuan
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cjyuan
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Oct 15, 2026
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cjyuan
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Changes look good.
Note: You should also add the "Needs review" label when you PR is ready to be re-reviewed.
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