diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc6671..b25b936c 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,15 @@ + +cache = {} + + 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..de42d91e 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -1,32 +1,47 @@ + from typing import List 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. + cache = {} + coins = [200, 100, 50, 20, 10, 5, 2, 1] + + return ways_to_make_change_helper(total, coins, cache) - 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], cache: dict +) -> int: + if total == 0: + return 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: + if len(coins) == 0: return 0 + key = (total, tuple(coins)) + + if key in cache: + return cache[key] + 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 + ways += ways_to_make_change_helper( + total - total_from_coins, + coins[coin_index + 1:], + cache, + ) + count_of_coin += 1 + + cache[key] = ways return ways