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Maximum Sum BST in a Binary Tree

Bloomberg LP● HardNEW GRADONSITE INTERVIEW

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Problem statement

Given the root of a binary tree, find the maximum sum of node values among all subtrees that are valid binary search trees.

A valid BST has every left-subtree value strictly smaller than its root and every right-subtree value strictly larger. Return 0 when every valid non-empty BST subtree has a negative sum.

Function

maxSumBST(root: TreeNode) → int

Examples

Example 1

root = [1,4,3,2,4,2,5,null,null,null,null,null,null,4,6]return = 20

The subtree rooted at 3 is a BST with sum 20.

Example 2

root = [4,3,null,1,2]return = 2

The leaf with value 2 is the best valid BST subtree.

Example 3

root = [-4,-2,-5]return = 0

All valid BST sums are negative, so zero is returned.

Constraints

The tree contains between 0 and 5000 nodes.
-10000 ≤ Node.val ≤ 10000.