Create 518-coin-change-2.py

Author: neetcode-gh

518-coin-change-2.py

@@ -0,0 +1,51 @@
+class Solution:
+    def change(self, amount: int, coins: List[int]) -> int:
+        # MEMOIZATION
+        # Time: O(n*m) 
+        # Memory: O(n*m)
+        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)
+        
+        
+        # DYNAMIC PROGRAMMING
+        # Time: O(n*m) 
+        # Memory: O(n*m)
+        dp = [[0] * (len(coins) + 1) for i in range(amount + 1)]
+        dp[0] = [1] * (len(coins) + 1)
+        for a in range(1, amount + 1):
+            for i in range(len(coins) - 1, -1, -1):
+                dp[a][i] = dp[a][i + 1]
+                if a - coins[i] >= 0:
+                    dp[a][i] += dp[a - coins[i]][i]
+        return dp[amount][0]
+        
+        
+        # DYNAMIC PROGRAMMING
+        # Time: O(n*m) 
+        # Memory: O(n) where n = amount
+        dp = [0] * (amount + 1)
+        dp[0] = 1
+        for i in range(len(coins) - 1, -1, -1):
+            nextDP = [0] * (amount + 1)
+            nextDP[0] = 1
+            
+            for a in range(1, amount + 1):
+                nextDP[a] =  dp[a]
+                if a - coins[i] >= 0:
+                    nextDP[a] += nextDP[a - coins[i]] 
+            dp = nextDP
+        return dp[amount]