# @Time    : 2019/4/24 23:33
# @Author  : shakespere
# @FileName: Validate Binary Search Tree.py
'''
98. Validate Binary Search Tree
Medium
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:

Input:
    2
   / \
  1   3
Output: true
Example 2:

    5
   / \
  1   4
     / \
    3   6
Output: false
Explanation: The input is: [5,1,4,null,null,3,6]. The root node's value
             is 5 but its right child's value is 4.
'''


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

class Solution(object):
    def isValidBST(self, root):
        """
        :type root: TreeNode
        :rtype: bool
        """
        return self.valid(root, float('-INF'), float('INF'))

    def valid(self, root, min, max):
        if not root: return True
        if root.val >= max or root.val <= min:
            return False
        return self.valid(root.left, min, root.val) and self.valid(root.right, root.val, max)


# @Time    : 2019/4/24 23:33
# @Author  : shakespere
# @FileName: Validate Binary Search Tree.py
'''
98. Validate Binary Search Tree
Medium
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:

Input:
    2
   / \
  1   3
Output: true
Example 2:

    5
   / \
  1   4
     / \
    3   6
Output: false
Explanation: The input is: [5,1,4,null,null,3,6]. The root node's value
             is 5 but its right child's value is 4.
'''


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

class Solution(object):
    def isValidBST(self, root):
        """
        :type root: TreeNode
        :rtype: bool
        """
        return self.valid(root, float('-INF'), float('INF'))

    def valid(self, root, min, max):
        if not root: return True
        if root.val >= max or root.val <= min:
            return False
        return self.valid(root.left, min, root.val) and self.valid(root.right, root.val, max)


# @Time    : 2019/4/24 23:33 # @Author  : shakespere # @FileName: Validate Binary Search Tree.py 98. Validate Binary Search Tree
 Medium
 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:
 
 Input:
     2
    / \
   1   3
 Output: true
 Example 2:
 
     5
    / \
   1   4
      / \
     3   6
 Output: false
 Explanation: The input is: [5,1,4,null,null,3,6]. The root node's value
              is 5 but its right child's value is 4. # Definition for a binary tree node. # class TreeNode(object): #     def __init__(self, x): #         self.val = x #         self.left = None #         self.right = None :type root: TreeNode
         :rtype: bool