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Sheffield | 25-SDC-Nov | Sheida Shabankari | Sprint 2 |improve with caches #112

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Sheffield | 25-SDC-Nov | Sheida Shabankari | Sprint 2 |improve with caches #112

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e93e7c9
Add memoisation to fibonacci using default cache dictionary
sheida-shab Feb 16, 2026
55157fa
Add manual caching to ways_to_make_change to speed up recursive calls
sheida-shab Feb 17, 2026
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16 changes: 14 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 +1,16 @@
def fibonacci(n):
def fibonacci(n,fib_memo={}):
# fib_memo is a default mutable dictionary used to cache computed Fibonacci values
# This allows memoisation: results are stored and reused across recursive calls

if n <= 1:
return n
return fibonacci(n - 1) + fibonacci(n - 2)
if n in fib_memo:
# Return cached value if already computed
return fib_memo[n]
else:
result=fibonacci(n - 1) + fibonacci(n - 2)

# Store computed value in cache
fib_memo[n]=result

return result
12 changes: 9 additions & 3 deletions Sprint-2/improve_with_caches/making_change/making_change.py
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@cjyuan cjyuan Feb 22, 2026

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Array creation is a relatively costly operation.

From line 34, 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 41 (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.

Original file line number Diff line number Diff line change
Expand Up @@ -10,13 +10,18 @@ def ways_to_make_change(total: int) -> int:
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:
def ways_to_make_change_helper(total: int, coins: List[int],cache=None) -> int:
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@cjyuan cjyuan Feb 22, 2026

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Why not use {} as the default value for cache?

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@sheida-shab sheida-shab Feb 23, 2026

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If I use {} as the default value, the cache is shared between all function calls .
Not only between recursive calls, but between every call to the function in the whole program.

This happens because default arguments in Python are created once, when the function is defined.

If I use None instead, then every time ways_to_make_change is called,
a new cache dictionary is created.

At the same time, all recursive calls share that same cache,
which is exactly what we want for memoisation .

"""
Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
"""
if total == 0 or len(coins) == 0:
return 0

if cache is None:
cache={}
key=(total,tuple(coins))
if key in cache:
return cache[key]

ways = 0
for coin_index in range(len(coins)):
coin = coins[coin_index]
Expand All @@ -26,7 +31,8 @@ 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:])
intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:],cache=cache)
ways += intermediate
count_of_coin += 1
cache[key]=ways
return ways