diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..10faf71 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,10 @@ -def fibonacci(n): - if n <= 1: - return n - return fibonacci(n - 1) + fibonacci(n - 2) +def fibonacci(n, cache=None): + if cache is None: + cache = {0: 0, 1: 1} + + if n in cache: + return cache[n] + + cache[n] = fibonacci(n - 1, cache) + fibonacci(n - 2, cache) + + return cache[n] \ No newline at end of file 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..872bd10 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 +1,44 @@ from typing import List +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. + 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. """ - return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1]) + cache = {} + def helper(total: int, start_index: int) -> int: + key = (total, start_index) -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: - 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 - return ways + if key in cache: + return cache[key] + + if total == 0 or start_index >= len(COINS): + return 0 + + ways = 0 + + for coin_index in range(start_index, 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: + ways += helper( + total - total_from_coins, + coin_index + 1 + ) + + count_of_coin += 1 + + cache[key] = ways + return ways + + return helper(total, 0) \ No newline at end of file