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NW | 26-SDC-Mar | TzeMing Ho | Sprint 2 | improve with caches #171

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NW | 26-SDC-Mar | TzeMing Ho | Sprint 2 | improve with caches #171

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759b0e0
completed fibonacci exercise
TzeMingHo Jun 18, 2026
d8e4cca
completed making_change.py
TzeMingHo Jun 19, 2026
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13 changes: 9 additions & 4 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 +1,9 @@
def fibonacci(n):
if n <= 1:
return n
return fibonacci(n - 1) + fibonacci(n - 2)
def fibonacci(n, cache=None):
if cache == None:
cache={0:0, 1:1}
if n in cache:
return cache[n]
else:
value = fibonacci(n - 1, cache) + fibonacci(n - 2, cache)
cache[n] = value
return value
37 changes: 23 additions & 14 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
Expand Up @@ -7,26 +7,35 @@ 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])
return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1], coin_index = 0, cache = None)


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 = 0, cache: dict = None) -> int:
"""
Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
"""
if total == 0 or len(coins) == 0:
if cache == None:
cache = {}

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

if total == 0:
return 1

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

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

remaining_value = total - coins[coin_index]

taken_the_coin = ways_to_make_change_helper(remaining_value, coins, coin_index, cache)

left_the_coin = ways_to_make_change_helper(total, coins, coin_index + 1, cache)

ways = taken_the_coin + left_the_coin

cache[current_key] = ways
return ways
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