1373 - Maximum Sum BST in Binary Tree.

Hard

Given a binary tree root, return the maximum sum of all keys of any sub-tree which is also a Binary Search Tree (BST).

Assume a BST is defined as follows:

• The left subtree of a node contains only nodes with keys less than the node's key.

• The right subtree of a node contains only nodes with keys greater than the node's key.

• Both the left and right subtrees must also be binary search trees.

Example 1:

Input: root = 1,4,3,2,4,2,5,null,null,null,null,null,null,4,6

Output: 20

Explanation: Maximum sum in a valid Binary search tree is obtained in root node with key equal to 3.

Example 2:

Input: root = 4,3,null,1,2

Output: 2

Explanation: Maximum sum in a valid Binary search tree is obtained in a single root node with key equal to 2.

Example 3:

Input: root = -4,-2,-5

Output: 0

Explanation: All values are negatives. Return an empty BST.

Constraints:

• The number of nodes in the tree is in the range <code>1, 4 * 10⁴</code>.

• <code>-4 * 10⁴<= Node.val <= 4 * 10⁴</code>