leetcode#98. Validate Binary Search Tree

Description

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.

Code

# 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        """        if root == None:            return True        elif root.left != None and root.left.val >= root.val:            return False        elif root.right != None and root.right.val <= root.val:            return False        else:            return self.recur(root.left, float("-inf"), root.val) and self.recur(root.right, root.val, float("inf"))    def recur(self, node, Min, Max):        if node == None:            return True        elif node.val <= Min or node.val >= Max:            return False        else:            return self.recur(node.left, Min, node.val) and self.recur(node.right, node.val, Max)

用最大最小值的方法限定后续的节点值，始终将后续的节点值限制在一定的区间内，同时避免了每次判断节点值时得从根节点开始判断。缺点时最大最小值是个特例，当节点中有值为inf或-inf时该算法失效。

Code2(author:jakwings)

class Solution {public:    bool isValidBST(TreeNode* root) {        TreeNode* prev = NULL;        return validate(root, prev);    }    bool validate(TreeNode* node, TreeNode* &prev) {        if (node == NULL) return true;        if (!validate(node->left, prev)) return false;        if (prev != NULL && prev->val >= node->val) return false;        prev = node;        return validate(node->right, prev);    }};

注意这里的prev为引用调用，所以prev的值一直在改变，总的来说code2不仅仅可以用于判断BST，它可以用于所有前序遍历的操作中，值得学习。

Conclusion

学习了一种通用的树遍历方法，值得记下来