diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..143fb5b 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,12 @@ +memo = {} + def fibonacci(n): + if n in memo: + return memo[n] + if n <= 1: return n - return fibonacci(n - 1) + fibonacci(n - 2) + result = fibonacci(n - 1) + fibonacci(n - 2) + memo[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..c060549 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 +1,57 @@ -from typing import List +from typing import List, Dict, Tuple -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. +# Pre-create only 8 possible "coins" arrays +_BASE_COINS: List[int] = [200, 100, 50, 20, 10, 5, 2, 1] +COIN_SUFFIXES: List[Tuple[int, ...]] = [tuple(_BASE_COINS[i:]) for i in range(len(_BASE_COINS))] - 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] = {} + +def ways_to_make_change(total: int) -> int: + cache.clear() + # suffix_id == 0 identifies [200, 100, 50, 20, 10, 5, 2, 1] + return ways_to_make_change_helper(total, suffix_id=0) -def ways_to_make_change_helper(total: int, coins: List[int]) -> int: +def ways_to_make_change_helper(total: int, suffix_id: int) -> int: """ - Helper function for ways_to_make_change to avoid exposing the coins parameter to callers. + suffix_id uniquely identifies the subarray coins = COIN_SUFFIXES[suffix_id] + where suffix_id in [0..7]. """ - if total == 0 or len(coins) == 0: + key = (total, suffix_id) + if key in cache: + return cache[key] + + coins = COIN_SUFFIXES[suffix_id] + + # Keep behavior close to original, but fix the standard base case: + if total == 0: + return 1 + if len(coins) == 0: return 0 + if len(coins) == 1: + cache[key] = 1 if (total % coins[0] == 0) else 0 + 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 + # Instead of slicing coins[coin_index+1:], move the suffix_id forward. + # suffix_id is the start index of `coins` in the base list, so: + next_suffix_id = suffix_id + coin_index + 1 + if next_suffix_id < len(COIN_SUFFIXES): + ways += ways_to_make_change_helper(total - total_from_coins, suffix_id=next_suffix_id) + count_of_coin += 1 + + cache[key] = ways return ways