Update 2 making_change.py

Author: RihannaP

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,45 +1,57 @@
-from typing import List
-cache = {}
-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.
-    """
-  
+from typing import List, Dict, Tuple
+
+# Pre-create only 8 possible "coins" arrays
+_BASE_COINS: List[int] = [200, 100, 50, 20, 10, 5, 2, 1]
+COIN_SUFFIXES: List[Tuple[int, ...]] = [tuple(_BASE_COINS[i:]) for i in range(len(_BASE_COINS))]
+
+cache: Dict[Tuple[int, int], int] = {}
+
+def ways_to_make_change(total: int) -> int:
     cache.clear()
-    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])
+    # suffix_id == 0 identifies [200, 100, 50, 20, 10, 5, 2, 1]
+    return ways_to_make_change_helper(total, suffix_id=0)
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+def ways_to_make_change_helper(total: int, suffix_id: int) -> int:
     """
-    Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
+    suffix_id uniquely identifies the subarray coins = COIN_SUFFIXES[suffix_id]
+    where suffix_id in [0..7].
     """
-    key = (total, tuple(coins))
-
+    key = (total, suffix_id)
     if key in cache:
         return cache[key]
-    
-    if total == 0 or len(coins) == 0:
+
+    coins = COIN_SUFFIXES[suffix_id]
+
+    # Keep behavior close to original, but fix the standard base case:
+    if total == 0:
+        return 1
+    if len(coins) == 0:
         return 0
-    
+
     if len(coins) == 1:
-        if total % coins[0] == 0:
-            return 1
-        else:
-            return 0
-        
+        cache[key] = 1 if (total % coins[0] == 0) else 0
+        return cache[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
+                # Instead of slicing coins[coin_index+1:], move the suffix_id forward.
+                # suffix_id is the start index of `coins` in the base list, so:
+                next_suffix_id = suffix_id + coin_index + 1
+                if next_suffix_id < len(COIN_SUFFIXES):
+                    ways += ways_to_make_change_helper(total - total_from_coins, suffix_id=next_suffix_id)
+
             count_of_coin += 1
+
     cache[key] = ways
     return ways