Optimize making_change: move base checks before cache lookup and add last-coin shortcut

Author: RahwaZeslusHaile

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,33 +1,37 @@
 from typing import List
 
 
-cache = {}
-coins = [200, 100, 50, 20, 10, 5, 2, 1]
+CACHE = {}
+COINS = [200, 100, 50, 20, 10, 5, 2, 1]
 
 
 def ways_to_make_change(total: int) -> int:
 
-    cache.clear()
+    CACHE.clear()
     return ways_to_make_change_helper(total, 0)
 
 
 def ways_to_make_change_helper(total: int, coin_index: int) -> int:
-    key = (total, coin_index)
-    if key in cache:
-        return cache[key]
-    
     if total == 0:
         return 1
-    if coin_index >= len(coins) or total < 0:
+    if coin_index >= len(COINS) or total < 0:
         return 0
+    
+    # Optimization: if this is the last coin, check if total is divisible by it
+    if coin_index == len(COINS) - 1:
+        return 1 if total % COINS[coin_index] == 0 else 0
+    
+    key = (total, coin_index)
+    if key in CACHE:
+        return CACHE[key]
 
     ways = 0
-    coin = coins[coin_index]
+    coin = COINS[coin_index]
     count_of_coin = 0
 
     while coin * count_of_coin <= total:
         ways += ways_to_make_change_helper(total - (coin * count_of_coin), coin_index + 1)
         count_of_coin += 1
 
-    cache[key] = ways
+    CACHE[key] = ways
     return ways