From 95027fb1a89446d1ac946050d0c661eb9afce3da Mon Sep 17 00:00:00 2001 From: eyuell21 Date: Tue, 14 Oct 2025 11:41:38 +0100 Subject: [PATCH 1/4] Added memoization to the existing code. --- Sprint-2/improve_with_caches/fibonacci/fibonacci.py | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..1f02dea 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,8 @@ -def fibonacci(n): +def fibonacci(n, memo={}): + if n in memo: + return memo[n] if n <= 1: return n - return fibonacci(n - 1) + fibonacci(n - 2) + + memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo) + return memo[n] From bce4a775f14698e070b0d6b703405588d0a7cfbe Mon Sep 17 00:00:00 2001 From: eyuell21 Date: Fri, 23 Jan 2026 12:09:27 +0000 Subject: [PATCH 2/4] Refactor ways_to_make_change to include memoization for improved performance --- .../making_change/making_change.py | 27 +++++++++++++------ 1 file changed, 19 insertions(+), 8 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..1305e45 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -1,5 +1,4 @@ -from typing import List - +from typing import List, Dict, Tuple def ways_to_make_change(total: int) -> int: """ @@ -7,26 +6,38 @@ 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]) + memo: Dict[Tuple[int, int], int] = {} + return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1], memo) -def ways_to_make_change_helper(total: int, coins: List[int]) -> int: +def ways_to_make_change_helper(total: int, coins: List[int], memo: Dict[Tuple[int, int], int]) -> int: """ Helper function for ways_to_make_change to avoid exposing the coins parameter to callers. + Uses memoization to cache results for (total, coin_index). """ - if total == 0 or len(coins) == 0: - return 0 + if total == 0: + return 1 + if total < 0 or not coins: + return 0 + + key = (total, len(coins)) + if key in memo: + return memo[key] ways = 0 + coin_index = 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: + remainder = total - total_from_coins + if remainder == 0: ways += 1 else: - intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:]) + intermediate = ways_to_make_change_helper(remainder, coins[coin_index + 1:], memo) ways += intermediate count_of_coin += 1 + + memo[key] = ways return ways From 93806b63d82915ead40913200fe77e53070ee88b Mon Sep 17 00:00:00 2001 From: eyuell21 Date: Fri, 23 Jan 2026 12:32:39 +0000 Subject: [PATCH 3/4] Improved code by pre-computing. --- .../common_prefix/common_prefix.py | 20 +++++++++++++------ 1 file changed, 14 insertions(+), 6 deletions(-) diff --git a/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py b/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py index f4839e7..96b633e 100644 --- a/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py +++ b/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py @@ -1,18 +1,26 @@ from typing import List -def find_longest_common_prefix(strings: List[str]): +def find_longest_common_prefix(strings: List[str]) -> str: """ find_longest_common_prefix returns the longest string common at the start of any two strings in the passed list. In the event that an empty list, a list containing one string, or a list of strings with no common prefixes is passed, the empty string will be returned. """ + if len(strings) < 2: + return "" + + # PRE-COMPUTE by sorting strings once + strings = sorted(strings) + longest = "" - for string_index, string in enumerate(strings): - for other_string in strings[string_index+1:]: - common = find_common_prefix(string, other_string) - if len(common) > len(longest): - longest = common + + #compare only strings that are next to eacotherr in sorted order + for i in range(len(strings) - 1): + common = find_common_prefix(strings[i], strings[i + 1]) + if len(common) > len(longest): + longest = common + return longest From 1c6540aab3f854167c4475c3679d06ed21795a10 Mon Sep 17 00:00:00 2001 From: eyuell21 Date: Fri, 23 Jan 2026 15:53:52 +0000 Subject: [PATCH 4/4] Refactor ways_to_make_change for clarity and consistency in memoization --- .../improve_with_caches/making_change/making_change.py | 10 ++++------ 1 file changed, 4 insertions(+), 6 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 1305e45..30f07f0 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -6,8 +6,9 @@ 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. """ + coins = [200, 100, 50, 20, 10, 5, 2, 1] memo: Dict[Tuple[int, int], int] = {} - return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1], memo) + return ways_to_make_change_helper(total, coins, memo) def ways_to_make_change_helper(total: int, coins: List[int], memo: Dict[Tuple[int, int], int]) -> int: @@ -25,18 +26,15 @@ def ways_to_make_change_helper(total: int, coins: List[int], memo: Dict[Tuple[in return memo[key] ways = 0 - coin_index = 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 - remainder = total - total_from_coins + remainder = total - coin * count_of_coin if remainder == 0: ways += 1 else: - intermediate = ways_to_make_change_helper(remainder, coins[coin_index + 1:], memo) - ways += intermediate + ways += ways_to_make_change_helper(remainder, coins[coin_index + 1:], memo) count_of_coin += 1 memo[key] = ways