Python solution for max sum in DSA450

Author: dsrao711

DSA 450 GFG/max_sum.py

@@ -0,0 +1,57 @@
+
+#https://practice.geeksforgeeks.org/problems/maximum-sum-problem2211/1/
+
+# Approach 1 - Memoization 
+
+from functools import lru_cache
+
+class Solution:
+    @lru_cache(maxsize = 1000)
+    def maxSum(self, n): 
+        # code here 
+        if(n == 0 or n == 1):
+            return n
+        else:
+            return max( (self.maxSum(n//2) + self.maxSum(n//3) + self.maxSum(n//4))  , n )
+
+
+
+#{ 
+#  Driver Code Starts
+#Initial Template for Python 3
+
+if __name__ == '__main__': 
+    t = int(input())
+    for _ in range(t):
+        n = int(input())
+        ob = Solution()
+        print(ob.maxSum(n))
+# } Driver Code Ends
+
+
+#Approach 2 - Bottom Up approach 
+
+
+    def maxSum(self, n): 
+        # code here
+        dp = [0]*(n+1)
+        dp[0] = 0
+        if(n >= 1):
+            dp[1] = 1
+            for i in range(2 , n+1):
+                dp[i] = max((dp[int(i/2)] + dp[int(i/3)] + dp[int(i/4)]) , i)
+                
+        return dp[n]
+
+
+#{ 
+#  Driver Code Starts
+#Initial Template for Python 3
+
+if __name__ == '__main__': 
+    t = int(input())
+    for _ in range(t):
+        n = int(input())
+        ob = Solution()
+        print(ob.maxSum(n))
+# } Driver Code Ends