Validate Binary Search Tree

Given a binary tree, determine if it is a valid 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.

题目要求判断一颗树是不是二叉搜索数，有关二叉搜索树的性质在这里就不在赘述了。我们采用递归的思想，借助两个变量max，和min，从根节点开始，递归比较每一颗子树，对于左子树的递归我们让max等于子树root的值，对于右子树我们让min等于子树root的值。代码如下：

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public boolean isValidBST(TreeNode root) {
        return isValid(root, null, null);
    }
    
    public boolean isValid(TreeNode root, Integer min, Integer max) {
        if(root == null) return true;
        if(min != null && root.val <= min) return false;
        if(max != null && root.val >= max) return false;
        return isValid(root.left, min, root.val) && isValid(root.right, root.val, max);
    }
}