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.

根据定义http://en.wikipedia.org/wiki/Binary_search_tree

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.
The left and right subtree each must also be a binary search tree.
Each node can have up to two successor nodes.
There must be no duplicate nodes.
A unique path exists from the root to every other node.

左子树小于节点小于右子树，并且不能有重复出现的值。做法是我们每次比较左右节点和根节点的值，只要有一个节点不满足条件就返回FALSE

we compare the left, right node key with root key. If any of the condition cannot match the requirement, we return False.

# Definition for a  binary tree node
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    # @param root, a tree node
    # @return a boolean
    def testnode(self,root,minval,maxval):
        if root==None:
            return True
        if root.val>maxval or root.val<minval:
            return False
        return self.testnode(root.left,minval,root.val-1) and self.testnode(root.right,root.val+1,maxval)
    def isValidBST(self, root):
        
        minval=-3147483648
        maxval=3147483648
        return self.testnode(root,minval,maxval)

Validate Binary Search Tree Leetcode Python