diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc6671..27617629 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,13 @@ +cache = { + 0: 0, + 1: 1 +} + def fibonacci(n): + if n in cache: + return cache[n] if n <= 1: return n - return fibonacci(n - 1) + fibonacci(n - 2) + result = fibonacci(n - 1) + fibonacci(n - 2) + cache[n] = result + return result diff --git a/Sprint-2/improve_with_caches/making_change/making_change.py b/Sprint-2/improve_with_caches/making_change/making_change.py index 255612e5..7488c933 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -1,5 +1,6 @@ from typing import List - +cache = {} +all_coins = [200, 100, 50, 20, 10, 5, 2, 1] def ways_to_make_change(total: int) -> int: """ @@ -7,26 +8,38 @@ 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, 0) -def ways_to_make_change_helper(total: int, coins: List[int]) -> int: +def ways_to_make_change_helper(total: int, start_index: int) -> int: """ Helper function for ways_to_make_change to avoid exposing the coins parameter to callers. """ - if total == 0 or len(coins) == 0: - return 0 + key = (total, start_index) + if key in cache: + return cache[key] + + if total == 0: + return 1 + + if start_index >= len(all_coins): + return 0 + ways = 0 - for coin_index in range(len(coins)): - coin = coins[coin_index] + for coin_index in range(start_index, len(all_coins)): + coin = all_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 + intermediate = ways_to_make_change_helper( + total - total_from_coins, + coin_index + 1 + ) + ways += intermediate + count_of_coin += 1 + cache[key] = ways return ways