diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..143fb5b 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,12 @@ +memo = {} + def fibonacci(n): + if n in memo: + return memo[n] + if n <= 1: return n - return fibonacci(n - 1) + fibonacci(n - 2) + result = fibonacci(n - 1) + fibonacci(n - 2) + memo[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..8f412e0 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 +1,51 @@ -from typing import List +from typing import List, Dict, Tuple + +# Pre-create only +_BASE_COINS: List[int] = [200, 100, 50, 20, 10, 5, 2, 1] + +cache: Dict[Tuple[int, int], int] = {} 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.clear() + # suffix_id == 0 identifies [200, 100, 50, 20, 10, 5, 2, 1] + return ways_to_make_change_helper(total, start_index: 0) - 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, start_index: int) -> 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 start_index >= len(_BASE_COINS): return 0 + coin = _BASE_COINS[start_index] + + if start_index == len(_BASE_COINS) - 1: + return 1 if total % coin == 0 else 0 + + key = (total, start_index) + if key in cache: + return cache[key] + ways = 0 - for coin_index in range(len(coins)): - coin = coins[coin_index] + + for coin_index in range(start_index, len(_BASE_COINS)): + coin = _BASE_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, + coin_index + 1 + ) + count_of_coin += 1 + + cache[key] = ways return ways