333. Largest BST Subtree节点数最多的bst子树

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.

本来以为是生成left,right这样。没想到用math.max比较一下就行了
还有个很好用的用traverse写的bst validation

复习时不会的地方：countNode不用left =， right =，直接返回1+left+right就行了

参考：https://leetcode.com/problems/largest-bst-subtree/discuss/78896/Clean-and-easy-to-understand-Java-Solution

public int largestBSTSubtree(TreeNode root) {
    if (root == null) return 0;
    if (root.left == null && root.right == null) return 1;
    if (isValid(root, null, null)) return countNode(root);
    return Math.max(largestBSTSubtree(root.left), largestBSTSubtree(root.right));
}

public boolean isValid(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;
    return isValid(root.left, min, root.val) && isValid(root.right, root.val, max);
}

public int countNode(TreeNode root) {
    if (root == null) return 0;
    if (root.left == null && root.right == null) return 1;
    return 1 + countNode(root.left) + countNode(root.right);
}