LeetCode98. Validate Binary Search Tree

题目：

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.

思路：

要判定一棵树是二叉搜索树，需要判定两点，一个是当前节点的值小于右子树的最小值，大于左子树的最大值；一个是其左右子树仍满足这个性质。

这与“判定一棵树是否是平衡二叉树”问题类似，于是想到一种自底向上的解法，依次判定左右子树是否为二叉搜素树，并向上传递左右子树的最小值、最大值及是否为二叉搜索树。代码如下：

class Solution(object):
    def isValidBST(self, root):
        """
        :type root: TreeNode
        :rtype: bool
        """
        if not root:
            return True
        _i, _j, res = self.checkValid(root)
        return res

    def checkValid(self, root):
        max_val, min_val = root.val, root.val
        if root.left:
            left_max, left_min, left_res = self.checkValid(root.left)
            if not left_res or left_max >= root.val:
                return 0, 0, False
            min_val = left_min
        if root.right:
            right_max, right_min, right_res = self.checkValid(root.right)
            if not right_res or right_min <= root.val:
                return 0, 0, False
            max_val = right_max
        return max_val, min_val, True

但这种传递显得比较乱，要写的代码比较长，因此使用另一个方式，自顶向下的判断，并将判断结果自底向上传递。代码如下，会简洁一些：

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

    def checkValid(self, root, min_val, max_val):
        if not root:
            return True
        if root.val <= min_val or root.val >= max_val:
            return False
        return (self.checkValid(root.left, min_val, root.val) and self.checkValid(root.right, root.val, max_val))

另， float('+inf')表示正无穷的这种用法也比较有趣。