diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..9e3c76f 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,14 @@ +cache = {} + + def fibonacci(n): + if n in cache: + return cache[n] + if n <= 1: - return n - return fibonacci(n - 1) + fibonacci(n - 2) + result = n + else: + 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 255612e..babd7e3 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 +1,37 @@ from typing import List +CACHE = {} +COINS = [200, 100, 50, 20, 10, 5, 2, 1] + + 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. - 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]) + CACHE.clear() + return ways_to_make_change_helper(total, 0) -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: +def ways_to_make_change_helper(total: int, coin_index: int) -> int: + if total == 0: + return 1 + if coin_index >= len(COINS) or total < 0: return 0 + + # Optimization: if this is the last coin, check if total is divisible by it + if coin_index == len(COINS) - 1: + return 1 if total % COINS[coin_index] == 0 else 0 + + key = (total, coin_index) + 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 - count_of_coin += 1 + coin = COINS[coin_index] + count_of_coin = 0 + + while coin * count_of_coin <= total: + ways += ways_to_make_change_helper(total - (coin * count_of_coin), coin_index + 1) + count_of_coin += 1 + + CACHE[key] = ways return ways