Refactor ways_to_make_change to use a fixed COINS tuple and simplify parameters

Author: mervereis

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,32 +1,30 @@
-from typing import List
-
+COINS = (200, 100, 50, 20, 10, 5, 2, 1)
 cache = {}
 
 def ways_to_make_change(total: int) -> int:
-    coins = [200, 100, 50, 20, 10, 5, 2, 1]
-    return ways_to_make_change_helper(total, coins)
+    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:
     if total == 0:
         return 1
 
-    if total < 0 or len(coins) == 0:
+    if total < 0 or coin_index == len(COINS):
         return 0
 
-    key = (total, tuple(coins))
+    key = (total, coin_index)
 
     if key in cache:
         return cache[key]
 
-    coin = coins[0]
+    coin = COINS[coin_index]
 
     ways = 0
 
     for count in range(total // coin + 1):
         remaining = total - count * coin
 
-        ways += ways_to_make_change_helper(remaining, coins[1:])
+        ways += ways_to_make_change_helper(remaining, coin_index + 1)
 
     cache[key] = ways