Improve efficiency with cached results

Author: RomanSanaye

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,19 +1,28 @@
 from typing import List
 
-
+# ===============> change function <============
 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.
     """
-    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])
-
+    # Initialize a cache dictionary
+    cache = {}
+    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1], cache)
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+# =================> change helper function <==============
+def ways_to_make_change_helper(total: int, coins: List[int], cache: dict) -> int:
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
     """
+    # Create unique key for this subproblem
+    cache_key = (total, tuple(coins))
+
+    # Return cached result if already calculated
+    if cache_key in cache:
+        return cache[cache_key]
+
     if total == 0 or len(coins) == 0:
         return 0
 
@@ -26,7 +35,10 @@ def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
             if total_from_coins == total:
                 ways += 1
             else:
-                intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
+                intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:], cache=cache)
                 ways += intermediate
             count_of_coin += 1
+
+    # Save result before returning
+    cache[cache_key] = ways
     return ways