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;
    }
}