diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..d55d190 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,11 @@ +fibonacci_cache = {} + def fibonacci(n): + if(n) in fibonacci_cache: + return fibonacci_cache[n] if n <= 1: return n - return fibonacci(n - 1) + fibonacci(n - 2) + + result = fibonacci(n - 1) + fibonacci(n - 2) + fibonacci_cache[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..1670605 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 Dict, List, Tuple def ways_to_make_change(total: int) -> int: @@ -7,26 +7,34 @@ 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]) + cache: Dict[Tuple[int, int], int] = {} # Initialize cache + return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1], cache, 0) -def ways_to_make_change_helper(total: int, coins: List[int]) -> int: +def ways_to_make_change_helper(total: int, coins: List[int], cache: Dict[Tuple[int, int], 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: + if total == 0: + return 1 + if total < 0 or coin_index >= len(coins): return 0 + + + # Check cache + key = (total, coin_index) + if key in cache: + return cache[key] 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] + count_of_coin = 1 + while coin * count_of_coin <= total: + remaining = total - coin * count_of_coin + ways += ways_to_make_change_helper(remaining, coins, cache, coin_index + 1) + count_of_coin += 1 + + ways += ways_to_make_change_helper(total, coins, cache, coin_index + 1) + + cache[key] = ways # Store result in cache return ways