added maximum path sum (#28)

Author: Rudra407

C++/Binary-Tree-Maximum-Path-Sum.cpp

@@ -0,0 +1,47 @@
+/**
+ * Definition for a binary tree node.
+ * struct TreeNode {
+ *     int val;
+ *     TreeNode *left;
+ *     TreeNode *right;
+ *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
+ *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
+ *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
+ * };
+ *
+ * Runtime : 40ms
+ * Memory : 28.5 MB
+ * 
+ *
+ */
+class Solution {
+public:
+    
+    int solve(TreeNode* root, int &ans)
+    {
+        if(root == NULL)
+            return 0;
+   	
+	# to traverse left and right childs     
+        int l = solve(root->left, ans);
+        int r = solve(root->right, ans);
+        
+	/* to find max sum including root_val and left and child subtree
+	   max sum or just including root val if result from subtree is -  		   negative
+	*/ 
+        int temp = max(max(l,r)+root->val, root->val);
+
+	/* in case max sum does not include main root and 
+	   forms maximum sum path through sub tree
+	*/
+        int res = max(temp, root->val+l+r);
+        ans = max(res,ans);
+        return temp;
+    }
+    int maxPathSum(TreeNode* root) {
+     int ans = INT_MIN;
+        solve(root,ans);
+        return ans;
+        
+    }
+};

README.md

@@ -147,6 +147,8 @@ Check out ---> [Sample PR](https://github.com/codedecks-in/LeetCode-Solutions/pu
 | 129 | [Sum Root to Leaf Numbers](https://leetcode.com/problems/sum-root-to-leaf-numbers/)               | [Java](./Java/sum-root-to-leaf-numbers.java)               | _O(n)_    | _O(logn)_ | Medium     | Binary Tree, Depth First Search                |      |
 | 307 | [Range Sum Query - Mutable](https://leetcode.com/problems/range-sum-query-mutable/)               | [Java](./Java/Range-Sum-Query-Mutable.java)                | _O(logn)_ | _O(n)_    | Medium     | Segment Tree                                   |      |
 | 919 | [Complete Binary Tree Inserter](https://leetcode.com/problems/complete-binary-tree-inserter/)     | [Java](./Java/complete-binary-tree-inserter.java)          | _O(n)_    | _O(n)_    | Medium     | Tree                                           |      |
+| 124 | [Binary Tree Maximum Path Sum](https://leetcode.com/problems/binary-tree-maximum-path-sum/)     | [C++](./C++/Binary-Tree-Maximum-Path-Sum.cpp)          | _O(n)_    | _O(n)_    | Hard     | Tree                                           |      |
+
 
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