# [LeetCode] 333. Largest BST Subtree

## Problem

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.

``````Example:

Input: [10,5,15,1,8,null,7]

10
/ \
5  15
/ \   \
1   8   7

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

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

## Solution

First try:

``````class Solution {
public int largestBSTSubtree(TreeNode root) {
if (root == null) return 0;
if (isBST(root)) return largestBSTSubtree(root.left)+largestBSTSubtree(root.right)+1;
return Math.max(largestBSTSubtree(root.left), largestBSTSubtree(root.right));
}
private boolean isBST(TreeNode root) {
if (root == null) return true;
if (root.left != null && findMax(root.left) >= root.val) return false;
if (root.right != null && findMin(root.right) <= root.val) return false;
if (isBST(root.left) && isBST(root.right)) return true;
return false;
}
private int findMax(TreeNode root) {
while (root.right != null) root = root.right;
return root.val;
}
private int findMin(TreeNode root) {
while (root.left != null) root = root.left;
return root.val;
}
}``````

Optimized:

``````class Solution {
public int largestBSTSubtree(TreeNode root) {
if (root == null) return 0;
if (isBST(root, null, null)) return largestBSTSubtree(root.left)+largestBSTSubtree(root.right)+1;
return Math.max(largestBSTSubtree(root.left), largestBSTSubtree(root.right));
}
private boolean isBST(TreeNode root, Integer min, Integer max) {
if (root == null) return true;
if (min != null && min >= root.val) return false;
if (max != null && max <= root.val) return false;
if (isBST(root.left, min, root.val) && isBST(root.right, root.val, max)) return true;
return false;
}
}``````

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