diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..398c865 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,12 @@ -def fibonacci(n): +def fibonacci(n, memo=None): if n <= 1: return n - return fibonacci(n - 1) + fibonacci(n - 2) + + if memo is None: + memo = {} + + if n in memo: return memo[n] + + memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo) + return memo[n] + 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..406fe67 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -1,4 +1,4 @@ -from typing import List +from typing import List, Tuple, Dict def ways_to_make_change(total: int) -> int: @@ -10,23 +10,24 @@ def ways_to_make_change(total: int) -> int: 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]) -> int: +def ways_to_make_change_helper(total: int, coins: List[int], memo: Dict[Tuple[int, int], int] = None) -> int: """ Helper function for ways_to_make_change to avoid exposing the coins parameter to callers. + Uses memoization to optimize repeated subproblems. """ - if total == 0 or len(coins) == 0: + if memo is None: + memo = {} + key = (total, len(coins)) + if key in memo: + return memo[key] + if total == 0: + return 1 + if total < 0 or len(coins) == 0: 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 + coin = coins[0] + for count_of_coin in range(0, total // coin + 1): + remaining = total - coin * count_of_coin + ways += ways_to_make_change_helper(remaining, coins[1:], memo) + memo[key] = ways return ways