> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/1373-maximum-sum-bst-in-binary-tree.md).

# 1373. Maximum Sum BST in Binary Tree

<https://leetcode.com/problems/maximum-sum-bst-in-binary-tree>

## Description

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:**

![](https://assets.leetcode.com/uploads/2020/01/30/sample_1_1709.png)

```
**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:**

![](https://assets.leetcode.com/uploads/2020/01/30/sample_2_1709.png)

```
**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.
```

**Example 4:**

```
**Input:** root = [2,1,3]
**Output:** 6
```

**Example 5:**

```
**Input:** root = [5,4,8,3,null,6,3]
**Output:** 7
```

**Constraints:**

* The number of nodes in the tree is in the range `[1, 4 * 104]`.
* `-4 * 104 <= Node.val <= 4 * 104`

## ac

```java
```