diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..808f363 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): + +def fibonacci(n: int, fib_cache: dict[int, int] = {0: 0, 1: 1}) -> int: if n <= 1: return n - return fibonacci(n - 1) + fibonacci(n - 2) + #check if already calc this num. + if n in fib_cache: + return fib_cache[n] + # if not in cache, calculate it, store it, and return + fib_cache[n] = fibonacci(n - 1) + fibonacci(n - 2) + return fib_cache[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..2b67747 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 +1,41 @@ -from typing import List - +from typing import List, Tuple, Dict +change_cache: Dict[Tuple[int, int], int] = {} 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. """ - return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1]) + return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1],0) -def ways_to_make_change_helper(total: int, coins: List[int]) -> int: +def ways_to_make_change_helper(total: int, coins: List[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 is 0, we found exactly 1 valid way to make change + if total == 0: + return 1 + + #If total becomes negative or we run out of coins, this way failed + 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 + # Cache check + cache_key = (total, coin_index) + if cache_key in change_cache: + return change_cache[cache_key] + + current_coin = coins[coin_index] + + # 1 use the current coin and stay on the same coin index + # 2 skip the current coin and move to the next coin index + ways = ( + ways_to_make_change_helper(total - current_coin, coins, coin_index) + + ways_to_make_change_helper(total, coins, coin_index + 1) + ) + # store the result in the cache before the return + change_cache[cache_key] = ways return ways