From 51b891b09014d82a860bb498092bc0ceaacf242f Mon Sep 17 00:00:00 2001
From: Jamal Laqdiem <jlaqdiem@gmail.com>
Date: Mon, 13 Jul 2026 19:26:26 +0100
Subject: [PATCH 1/3] 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 60cc667..d4acd30 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 <jlaqdiem@gmail.com>
Date: Mon, 13 Jul 2026 20:10:54 +0100
Subject: [PATCH 2/3] 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 255612e..2b67747 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 <jlaqdiem@gmail.com>
Date: Mon, 13 Jul 2026 20:20:24 +0100
Subject: [PATCH 3/3] 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 d4acd30..808f363 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.