feat: add Binary Tree Maximum Path Sum (#1179)

* add leetcode Binary Tree Maximum Path Sum

* Update leetcode/src/124.c

Co-authored-by: Taj <tjgurwara99@users.noreply.github.com>

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: Taj <tjgurwara99@users.noreply.github.com>

leetcode/DIRECTORY.md

@@ -46,6 +46,7 @@
 | 112  | [Path Sum](https://leetcode.com/problems/path-sum/)                                                                             | [C](./src/112.c)  | Easy       |
 | 118  | [Pascal's Triangle](https://leetcode.com/problems/pascals-triangle/)                                                            | [C](./src/118.c)  | Easy       |
 | 121  | [Best Time to Buy and Sell Stock](https://leetcode.com/problems/best-time-to-buy-and-sell-stock/)                               | [C](./src/121.c)  | Easy       |
+| 124  | [Binary Tree Maximum Path Sum](https://leetcode.com/problems/binary-tree-maximum-path-sum/description/)                         | [C](./src/124.c)  | Hard       |
 | 125  | [Valid Palindrome](https://leetcode.com/problems/valid-palindrome/)                                                             | [C](./src/125.c)  | Easy       |
 | 136  | [Single Number](https://leetcode.com/problems/single-number/)                                                                   | [C](./src/136.c)  | Easy       |
 | 141  | [Linked List Cycle](https://leetcode.com/problems/linked-list-cycle/)                                                           | [C](./src/141.c)  | Easy       |

leetcode/src/124.c

@@ -0,0 +1,36 @@
+/**
+ * Definition for a binary tree node.
+ * struct TreeNode {
+ *     int val;
+ *     struct TreeNode *left;
+ *     struct TreeNode *right;
+ * };
+ */
+
+#define max(a,b) (((a)>(b))?(a):(b))
+
+int recursiveSolve(struct TreeNode* node, int* result){
+    if (node == NULL){
+        return 0;
+    }
+
+    int leftSum = max(recursiveSolve(node->left, result), 0);
+    int rightSum = max(recursiveSolve(node->right, result), 0);
+
+    // Check if it's possible to make a maximum path from left right and current node
+    int maxValueNode = node->val + leftSum + rightSum;
+    *result = max(maxValueNode, *result);
+
+    // Choose the max sum val path 
+    return node->val + max(leftSum, rightSum);
+}
+
+// Depth First Search
+// Runtime: O(n), n - the number of nodes in tree.
+// Space: O(1)
+int maxPathSum(struct TreeNode* root){
+    const int LOWER_BOUND = -2147483648
+    int result = LOWER_BOUND;
+    recursiveSolve(root, &result);
+    return result;
+}