From 51b891b09014d82a860bb498092bc0ceaacf242f Mon Sep 17 00:00:00 2001 From: Jamal Laqdiem Date: Mon, 13 Jul 2026 19:26:26 +0100 Subject: [PATCH 1/4] feat: optomise fibonacci using manual dictionary memoization --- Sprint-2/improve_with_caches/fibonacci/fibonacci.py | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc6671..d4acd305 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,10 @@ +fib_cache = {} def fibonacci(n): 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] From 66cfc3438988732d783b7dc8a7d7570f7fb857b9 Mon Sep 17 00:00:00 2001 From: Jamal Laqdiem Date: Mon, 13 Jul 2026 20:10:54 +0100 Subject: [PATCH 2/4] feat: optimize change helper with index-based recursion and caching --- .../making_change/making_change.py | 43 +++++++++++-------- 1 file changed, 26 insertions(+), 17 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 255612e5..2b677477 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 From 88578a27417cbae8bf338f204bf118ac3a08548d Mon Sep 17 00:00:00 2001 From: Jamal Laqdiem Date: Mon, 13 Jul 2026 20:20:24 +0100 Subject: [PATCH 3/4] fix: remove the globale scope and use a default argument in the function signature --- Sprint-2/improve_with_caches/fibonacci/fibonacci.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index d4acd305..808f363d 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,5 +1,5 @@ -fib_cache = {} -def fibonacci(n): + +def fibonacci(n: int, fib_cache: dict[int, int] = {0: 0, 1: 1}) -> int: if n <= 1: return n #check if already calc this num. From f0b11c00503d56e99c6fd8cb3ca95f8c61295c0c Mon Sep 17 00:00:00 2001 From: Jamal Laqdiem Date: Fri, 16 Oct 2026 18:01:30 +0100 Subject: [PATCH 4/4] refactor: optimize recursion with single loop and last-coin shortcut. --- .../making_change/making_change.py | 25 +++++++++++-------- 1 file changed, 15 insertions(+), 10 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 2b677477..670da7b2 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -14,28 +14,33 @@ def ways_to_make_change_helper(total: int, coins: List[int], coin_index: int) -> """ Helper function for ways_to_make_change to avoid exposing the coins parameter to callers. """ - - #If total is 0, we found exactly 1 valid way to make change + + # If total is 0, we found 1 valid way if total == 0: return 1 - #If total becomes negative or we run out of coins, this way failed + # If total becomes negative or we ran out of coins, 0 ways if total < 0 or coin_index >= len(coins): return 0 + # shortcut if only one coin is left + if coin_index == len(coins) - 1: + return 1 if total % coins[coin_index] == 0 else 0 + # Cache check cache_key = (total, coin_index) if cache_key in change_cache: return change_cache[cache_key] + ways = 0 current_coin = coins[coin_index] + + # One level of loop to try taking 0, 1, 2... of the current coin + current_total = 0 + while current_total <= total: + ways += ways_to_make_change_helper(total - current_total, coins, coin_index + 1) + current_total += current_coin - # 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 + # Store the result in the cache before returning change_cache[cache_key] = ways return ways