首页 > 代码库 > LeetCode 98. Validate Binary Search Tree

LeetCode 98. Validate Binary Search Tree

原题

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.

 

解题思路

思路一:

  • 先将二叉树进行中序遍历,接着判断遍历的数据是否为递增的即可(较简单)

 

思路二:

  • 采用二叉搜索树的定义来解题(较难)
  • 难点:每个节点都得跟两个数进行比较,它必须在这两个数的范围之内,其中一个是它的父节点,另外一个是它的某个祖先节点
  • 这个树是从上往下遍历的,遍历到每个节点时,都要把它限定在一个已知的范围内,不管他下面的节点,只根据他上面的节点来找出这个范围
  • 这里我采用继承的方法,首先定义根节点的范围为正负无穷大,节点每一个左节点的最大值为它的父节点,最小值继承它父节点的最小值(右节点相似),由此就可以构造出一个递归程序。

技术分享

技术分享

 

 

完整代码

思路一

# Definition for a binary tree node.# class TreeNode(object):#     def __init__(self, x):#         self.val = x#         self.left = None#         self.right = None# 先将二叉搜索树进行中序遍历,接着判断是否满足规则class Solution(object):    def isValidBST(self, root):        """        :type root: TreeNode        :rtype: bool        """        self.ret = []        self.helper(root)        for i in xrange(1, len(self.ret)):            if self.ret[i] <= self.ret[i-1]:                return False        return True            def helper(self, node):        if node == None:            return         self.helper(node.left)        self.ret.append(node.val)        self.helper(node.right)

  

 

思路二

# Definition for a binary tree node.# class TreeNode(object):#     def __init__(self, x):#         self.val = x#         self.left = None#         self.right = Noneclass Solution(object):    def isValidBST(self, root):        """        :type root: TreeNode        :rtype: bool        """        return self.helper(root, -float("inf"), float("inf"))            def helper(self, node, low, high):        if node == None:            return True        if node.val <= low or node.val >= high:            return False        return self.helper(node.left, low, node.val) and self.helper(node.right, node.val, high)

  

LeetCode 98. Validate Binary Search Tree