CodeYourFuture · fatmaevin · Mar 3, 2026 · Jun 10, 2026 · cjyuan · Jun 11, 2026
diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
@@ -1,4 +1,15 @@
+memo = {}
+
 def fibonacci(n):
+
+    if n in memo:
+        return memo[n]
+
     if n <= 1:
-        return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+        result = n
+    else:
+        # Recursive
+        result = fibonacci(n - 1) + fibonacci(n - 2)
+
+    memo[n] = result
+    return result
diff --git a/Sprint-2/improve_with_caches/making_change/making_change.py b/Sprint-2/improve_with_caches/making_change/making_change.py
@@ -7,26 +7,37 @@ 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])
+
+    coins = [200, 100, 50, 20, 10, 5, 2, 1]
+    memo = {}
+    return ways_to_make_change_helper(total, coins, 0, memo)
 
 
-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, memo:dict) -> 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 == 0 :
+
+        return 1
+    if coin_index == len(coins):
         return 0
+
+    key = (total, coin_index)
+
+    if key in memo:
+        return memo[key]
 
     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
+
+    coin = coins[coin_index]
+    count_of_coin = 0
+
+    while count_of_coin * coin <= total:
+        remaining = total - count_of_coin * coin
+        ways += ways_to_make_change_helper(remaining, coins, coin_index + 1, memo)
+        count_of_coin += 1
+
+    memo[key] = ways
+
     return ways