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London | 25-SDC-Nov | Aida Eslamimoghadam | Sprint 2 | Add caching to improve performance #144

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London | 25-SDC-Nov | Aida Eslamimoghadam | Sprint 2 | Add caching to improve performance #144

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9 changes: 8 additions & 1 deletion Sprint-2/improve_with_caches/fibonacci/fibonacci.py
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Original file line number Diff line number Diff line change
@@ -1,4 +1,11 @@
cache = {}

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

if n in cache:
return cache[n]

cache[n] = fibonacci(n - 1) + fibonacci(n - 2)
return cache[n]
29 changes: 17 additions & 12 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
@@ -1,20 +1,21 @@
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.

For instance, there are two ways to make a value of 3: with 3x 1 coins, or with 1x 1 coin and 1x 2 coin.
"""
return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])


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.
"""
if total == 0 or len(coins) == 0:
key = (total, tuple(coins))

if key in cache:
return cache[key]

if total == 0:
return 1

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

ways = 0
Expand All @@ -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:]
)
Comment on lines 10 to +33
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@cjyuan cjyuan Mar 2, 2026

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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.

count_of_coin += 1
return ways

cache[key] = ways
return ways