making change

Author: ZabihollahNamazi

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,32 +1,12 @@
-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.
-
-    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 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
-
-    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
-            count_of_coin += 1
-    return ways
+    coins = [1, 2, 5, 10, 20, 50, 100, 200]
+    
+    dp = [0] * (total + 1)
+    
+    dp[0] = 1
+    
+    for coin in coins:
+        for i in range(coin, total + 1):
+            dp[i] += dp[i - coin]
+            
+    return dp[total]