# [LeetCode] Largest BST Subtree

## Largest BST Subtree

Given a binary tree, find the largest subtree which is a Binary Search Tree (BST), where largest means subtree with largest number of nodes in it.

## Note:

A subtree must include all of its descendants.
Here's an example:

``````    10
/ \
5  15
/ \   \
1   8   7``````

The Largest BST Subtree in this case is the highlighted one.
The return value is the subtree's size, which is 3.

## Hint:

You can recursively use algorithm similar to 98. Validate Binary Search Tree at each node of the tree, which will result in O(nlogn) time complexity.

Can you figure out ways to solve it with O(n) time complexity?

## Solution

``````public class Solution {
public int largestBSTSubtree(TreeNode root) {
if (root == null) return 0;
if (isValidBST(root)) return largestBSTSubtree(root.left)+largestBSTSubtree(root.right)+1;
else return Math.max(largestBSTSubtree(root.left), largestBSTSubtree(root.right));
}
public boolean isValidBST(TreeNode root) {
if (root == null) return true;
return dfs(root, Long.MIN_VALUE, Long.MAX_VALUE);
}
public boolean dfs(TreeNode root, long min, long max) {
if (root == null) return true;
if (root.val <= min || root.val >= max) return false;
return dfs(root.left, min, root.val) && dfs(root.right, root.val, max);
}
}

``````