correction

Author: pathywang

Sprint-2/improve_with_caches/fibonacci/fibonacci.py

@@ -1,8 +1,3 @@
-cache = {
-    0: 0,
-    1: 1
-}
-
 def fibonacci(n):
     if n <= 1:
         return n

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,4 +1,4 @@
-from typing import List
+COINS = (200, 100, 50, 20, 10, 5, 2, 1)
 cache = {}
 
 
@@ -8,34 +8,32 @@ 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, 0)
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+def ways_to_make_change_helper(total: int, coin_index: int) -> int:
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
     """
-    key = (total, tuple(coins))
+    key = (total, coin_index)
 
     if key in cache:
         return cache[key]
 
-    if total == 0 or len(coins) == 0:
+    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
+    coin = COINS[coin_index]
+
+    # Option 1: Skip this coin and move to the next denomination.
+    ways = ways_to_make_change_helper(total, coin_index + 1)
+
+    # Option 2: Use this coin and consider it again.
+    if coin <= total:
+        ways += ways_to_make_change_helper(total - coin, coin_index)
 
     cache[key] = ways
     return ways
-