diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc6671..8e897cb7 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,13 @@ -def fibonacci(n): - if n <= 1: - return n - return fibonacci(n - 1) + fibonacci(n - 2) +fib_cache = {} +def fibonacci(n: int) -> int: + if n == 0: + return 0 + if n == 1: + return 1 + + if n in fib_cache: + return fib_cache[n] + + fib_cache[n] = fibonacci(n - 1) + fibonacci(n - 2) + + return fib_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 255612e5..c466ad00 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -2,31 +2,36 @@ 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. + + return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1], coin_index = 0, cache = None) - 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], coin_index: int = 0, cache: dict = None) -> int: + if cache == None: + cache = {} -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: + current_key = (total, coin_index) + if current_key in cache: + return cache[current_key] + + if total == 0: + return 1 + + if coin_index == len(coins) - 1: + return 1 if total % coins[coin_index] == 0 else 0 + + if total < 0 or coin_index >= len(coins): 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 + + remaining_value = total - coins[coin_index] + + taken_the_coin = ways_to_make_change_helper(remaining_value, coins, coin_index, cache) + + left_the_coin = ways_to_make_change_helper(total, coins, coin_index + 1, cache) + + ways = taken_the_coin + left_the_coin + + cache[current_key] = ways + return ways \ No newline at end of file