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West Midlands | 25-SDC-July | Gabriel Deng | Sprint 2 | Improve with caches #71

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West Midlands | 25-SDC-July | Gabriel Deng | Sprint 2 | Improve with caches #71

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13 changes: 11 additions & 2 deletions Sprint-2/improve_with_caches/fibonacci/fibonacci.py
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Original file line number Diff line number Diff line change
@@ -1,4 +1,13 @@
cache = {}

def fibonacci(n):
if n in cache:
return cache[n]

if n <= 1:
return n
return fibonacci(n - 1) + fibonacci(n - 2)
result = n
else:
result = fibonacci(n - 1) + fibonacci(n - 2)

cache[n] = result
return result
9 changes: 9 additions & 0 deletions Sprint-2/improve_with_caches/making_change/making_change.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,8 @@
from typing import List


cache = {}

def ways_to_make_change(total: int) -> int:
"""
Given access to coins with the values 1, 2, 5, 10, 20, 50, 100, 200, returns a count of all of the ways to make the passed total value.
Expand All @@ -14,6 +16,11 @@ def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
"""
Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
"""
# Create a cache key from total and coins tuple
cache_key = (total, tuple(coins))
if cache_key in cache:
return cache[cache_key]

if total == 0 or len(coins) == 0:
return 0

Expand All @@ -29,4 +36,6 @@ def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
ways += intermediate
count_of_coin += 1
Comment on lines 20 to 38
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@cjyuan cjyuan Jan 23, 2026

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From line 36, 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 36, 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.


cache[cache_key] = ways
return ways