diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc6671..0e8669a6 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,14 @@ def fibonacci(n): - if n <= 1: - return n - return fibonacci(n - 1) + fibonacci(n - 2) + cache = {} + + def fib(n): + if n <= 1: + return n + + if n in cache: + return cache[n] + + cache[n] = fib(n - 1) + fib(n - 2) + return cache[n] + + return fib(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..bdb97a4d 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 +1,53 @@ + from typing import List +# Define coin values globally +COIN_VALUES = [200, 100, 50, 20, 10, 5, 2, 1] + 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. + Given coin values of 1, 2, 5, 10, 20, 50, 100, and 200, + return the number of ways to make the given total. """ - return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1]) + memo = {} + return change_helper(total, 0, memo) -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: +def change_helper(amount: int, index: int, memo: dict) -> int: + """Helper function to calculate the number of ways.""" + + key = (amount, index) + + if key in memo: + return memo[key] + + if amount == 0: + return 1 + + if index >= len(COIN_VALUES): 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 + result = 0 + + for position in range(index, len(COIN_VALUES)): + value = COIN_VALUES[position] + quantity = 1 + + while value * quantity <= amount: + current_sum = value * quantity + + if current_sum == amount: + result += 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 = change_helper( + amount - current_sum, + position + 1, + memo + ) + result += remaining + + quantity += 1 + + memo[key] = result + return result