LeetCode.98 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:

2
/ \
1   3

Binary tree

[2,1,3]

, return true.
Example 2:

1
/ \
2   3

Binary tree

[1,2,3]

, return false.
分析：

/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
class Solution {
public boolean isValidBST(TreeNode root) {
//给定二叉树，判定其是否满足左子树均小于根节点，右字数大于等于根节点
//思路：使用递归实现，注意记录上下限，来判别该节点是否满足规则。
return backtrace(root,Long.MAX_VALUE,Long.MIN_VALUE);
}

//递归实现
public boolean backtrace(TreeNode root,long up,long down){
//通过上下限来限制其递归
if(root==null) return true;
if(!(root.val>down&&root.val<up)){
//不满足情况
return false;
}
//递归对左右子树进行判别
if(backtrace(root.left,(long)root.val,down)&&backtrace(root.right,up,(long)root.val)){
return true;
}
return false;
}
}