Add memoisation to making change

Author: Zobeir-Rigi

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,32 +1,47 @@
 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.
+    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.
     """
-    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])
+    cache.clear()
+    return ways_to_make_change_helper(
+        total,
+        [200, 100, 50, 20, 10, 5, 2, 1]
+    )
 
 
 def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
-    """
-    Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
-    """
+    key = (total, tuple(coins))
+
+    if key in cache:
+        return cache[key]
+
     if total == 0 or len(coins) == 0:
         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
+                ways += ways_to_make_change_helper(
+                    total - total_from_coins,
+                    coins[coin_index + 1:]
+                )
+
             count_of_coin += 1
-    return ways
+
+    cache[key] = ways
+    return ways