From 759b0e0f7e6b71dd4f8e79a5711379da7935e149 Mon Sep 17 00:00:00 2001 From: TzeMingHo Date: Thu, 18 Jun 2026 14:40:40 +0100 Subject: [PATCH 1/2] completed fibonacci exercise --- Sprint-2/improve_with_caches/fibonacci/fibonacci.py | 13 +++++++++---- 1 file changed, 9 insertions(+), 4 deletions(-) diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..8be0462 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,9 @@ -def fibonacci(n): - if n <= 1: - return n - return fibonacci(n - 1) + fibonacci(n - 2) +def fibonacci(n, cache=None): + if cache == None: + cache={0:0, 1:1} + if n in cache: + return cache[n] + else: + value = fibonacci(n - 1, cache) + fibonacci(n - 2, cache) + cache[n] = value + return value From d8e4ccaf51eff6018122da4822ea98ac3720d10a Mon Sep 17 00:00:00 2001 From: TzeMingHo Date: Fri, 19 Jun 2026 20:56:28 +0100 Subject: [PATCH 2/2] completed making_change.py --- .../making_change/making_change.py | 37 ++++++++++++------- 1 file changed, 23 insertions(+), 14 deletions(-) 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..b1fff42 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -7,26 +7,35 @@ 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, [200, 100, 50, 20, 10, 5, 2, 1], coin_index = 0, cache = None) -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 = 0, cache: dict = None) -> int: """ Helper function for ways_to_make_change to avoid exposing the coins parameter to callers. """ - if total == 0 or len(coins) == 0: + if cache == None: + cache = {} + + current_key = (total, coin_index) + if current_key in cache: + return cache[current_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 + + remaining_value = total - coins[coin_index] + + taken_the_coin = ways_to_make_change_helper(remaining_value, coins, coin_index, cache) + + left_the_coin = ways_to_make_change_helper(total, coins, coin_index + 1, cache) + + ways = taken_the_coin + left_the_coin + + cache[current_key] = ways return ways