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.
• Example 1

    2
   / \
  1   3

Binary tree

[2,1,3]

, return true. Example 2:

    1
   / \
  2   3

Binary tree

[1,2,3], return false.

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

    }

}

/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */

public class Solution {
    /**
     * @param root: The root of binary tree.
     * @return: True if the binary tree is BST, or false
     */
    private class ResultType{
        boolean isValid;
        TreeNode maxNode;
        TreeNode minNode;
        private ResultType(boolean valid) {
            this.isValid = valid;
            maxNode = null;
            minNode = null;
        }
    }
    public boolean isValidBST(TreeNode root) {
        // write your code here
        if (root == null) {
            return true;
        }
        ResultType res = helper(root);
        return res.isValid;
    }
    public ResultType helper(TreeNode root) {
        if (root == null) {
            return new ResultType(true);
        }
        ResultType left = helper(root.left);
        ResultType right = helper(root.right);
        if (!left.isValid || !right.isValid) {
            return new ResultType(false); 
        }
        //valid -> value 
        if (left.maxNode != null && left.maxNode.val >= root.val) {
            return new ResultType(false);  
        }
        if (right.minNode != null && right.minNode.val <= root.val) {
            return new ResultType(false);  
        }
        ResultType res = new ResultType(true);
        res.minNode = left.minNode != null ? left.minNode : root;
        res.maxNode = right.maxNode != null ? right.maxNode : root;

        return res;

    }
}