added coin change 2 solution

dynamic_programming/coin_change_II.py

@@ -0,0 +1,21 @@
+from typing import List
+
+class Solution:
+    def change(self, amount: int, coins: List[int]) -> int:
+        cache = {}
+        def dfs(i,a):
+            if a == amount:
+                return 1
+            if a > amount:
+                return 0
+            if i == len(coins):
+                return 0
+            if (i,a) in cache:
+                return cache[(i,a)]
+            cache[(i,a)] = dfs(i,a + coins[i]) +dfs(i+1, a)
+            return cache[(i,a)]
+        return dfs(0,0)
+
+sol = Solution()
+# for example
+print(sol.change(5, [1,2,5]))  # Output: 4