diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc6671..8fdd80f7 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,11 @@ +cache = { + 0: 0, + 1: 1 +} + def fibonacci(n): - if n <= 1: - return n - return fibonacci(n - 1) + fibonacci(n - 2) + if n in cache: + return cache[n] + + cache[n] = fibonacci(n - 1) + fibonacci(n - 2) + 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 255612e5..32c075bb 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 +1,5 @@ -from typing import List +COINS = (200, 100, 50, 20, 10, 5, 2, 1) +cache = {} def ways_to_make_change(total: int) -> int: @@ -7,26 +8,32 @@ def ways_to_make_change(total: int) -> int: 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]) + return ways_to_make_change_helper(total, 0) -def ways_to_make_change_helper(total: int, coins: List[int]) -> int: +def ways_to_make_change_helper(total: int, coin_index: int) -> int: """ Helper function for ways_to_make_change to avoid exposing the coins parameter to callers. """ - if total == 0 or len(coins) == 0: + key = (total, coin_index) + + if key in cache: + return cache[key] + + if total == 0: + return 1 + + 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 + coin = COINS[coin_index] + + # Option 1: Skip this coin and move to the next denomination. + ways = ways_to_make_change_helper(total, coin_index + 1) + + # Option 2: Use this coin and consider it again. + if coin <= total: + ways += ways_to_make_change_helper(total - coin, coin_index) + + cache[key] = ways return ways