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London | 26-SDC-Mar | Ebrahim Beiati-Asl | Sprint 2 | improve_with_caches #156

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London | 26-SDC-Mar | Ebrahim Beiati-Asl | Sprint 2 | improve_with_caches #156

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10 changes: 8 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 +1,10 @@
def fibonacci(n):
def fibonacci(n, cache=None):
if cache is None:
cache = {}
if n in cache:
return cache[n]
if n <= 1:
return n
return fibonacci(n - 1) + fibonacci(n - 2)
else:
cache[n] = fibonacci(n - 1, cache) + fibonacci(n - 2, cache)
return cache[n]
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@cjyuan cjyuan May 17, 2026

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Could also consider using inner function:

def fibonacci(n):
    cache = {}          # Accessible in fib_helper()
    def fib_helper(n):
       ... 

    return fib_helper(n);

or just declare cache in the global scope since the values in the cache are still valid in subsequent call to fibonacci(n).

37 changes: 22 additions & 15 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
@@ -1,4 +1,4 @@
from typing import List
from typing import List, Tuple, Dict


def ways_to_make_change(total: int) -> int:
Expand All @@ -7,26 +7,33 @@ def ways_to_make_change(total: int) -> int:

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])
coins = [200, 100, 50, 20, 10, 5, 2, 1]
cache: Dict[Tuple[int, int], int] = {}
return ways_to_make_change_helper(total, coins, 0, cache)


def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
def ways_to_make_change_helper(
total: int, coins: List[int], coin_index: int, cache: Dict[Tuple[int, int], int]
) -> int:
"""
Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
"""
if total == 0 or len(coins) == 0:
if total == 0:
return 1
if total < 0 or coin_index == len(coins):
return 0

Comment on lines +23 to 25
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@cjyuan cjyuan May 17, 2026

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Note: When coin_index == len(coins) - 1, there is a quicker way to determine if the number of ways is 0 or 1 without involving cache lookup.

key = (total, coin_index)
if key in cache:
return cache[key]

coin = coins[coin_index]
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
count = 0
while count * coin <= total:
remaining = total - count * coin
ways += ways_to_make_change_helper(remaining, coins, coin_index + 1, cache)
count += 1

cache[key] = ways
return ways
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