refactor ways_to_make_change function to improve caching

Author: Droid-An

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,42 +1,25 @@
-from typing import List
-
-
 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.
+    cache = {}
+    coins = (200, 100, 50, 20, 10, 5, 2, 1)
 
-    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])
+    def helper(remaining: int, start: int) -> int:
+        if remaining == 0:
+            return 1
+        if remaining < 0 or start == len(coins):
+            return 0
 
+        key = (remaining, start)
+        if key in cache:
+            return cache[key]
 
-cache = {}
+        coin = coins[start]
+        ways = 0
 
+        max_count = remaining // coin
+        for count in range(max_count + 1):
+            ways += helper(remaining - count * coin, start + 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.
-    """
-    if total == 0 or len(coins) == 0:
-        return 0
+        cache[key] = ways
+        return ways
 
-    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:
-                key = (total - total_from_coins, tuple(coins[coin_index + 1 :]))
-                if key not in cache:
-                    cache[key] = ways_to_make_change_helper(
-                        total - total_from_coins, coins=coins[coin_index + 1 :]
-                    )
-                    intermediate = cache[key]
-                else:
-                    intermediate = cache[key]
-                ways += intermediate
-            count_of_coin += 1
-    return ways
+    return helper(total, 0)

Sprint-2/improve_with_caches/making_change/making_change_test.py

@@ -2,6 +2,7 @@
 
 from making_change import ways_to_make_change
 
+
 class MakingChangeTest(unittest.TestCase):
     def test_1(self):
         # 1x 1p
@@ -27,5 +28,6 @@ def test_17(self):
     def test_9176(self):
         self.assertEqual(ways_to_make_change(9176), 628431158425225)
 
+
 if __name__ == "__main__":
     unittest.main()