LeetCode - Validate Binary Search Tree

验证二叉搜索树的有效性

最新推荐文章于 2025-09-12 17:31:31 发布

weixin_33910460

最新推荐文章于 2025-09-12 17:31:31 发布

阅读量60

点赞数

文章标签：数据结构与算法

本文介绍了一种检查给定二叉树是否为有效二叉搜索树的方法。通过递归方式确认节点值是否符合BST定义，并采用类似中序遍历的方式确保节点值递增，从而实现对二叉搜索树的有效验证。

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.

思路：

1) 递归，两边夹

package bst;

public class ValidateBinarySearchTree {

    public boolean isValidBST(TreeNode root) {
        return isValidBST(root, false, Integer.MIN_VALUE, false, Integer.MAX_VALUE);
    }
    
    private boolean isValidBST(TreeNode root, boolean reachMin, int min, boolean reachMax, int max) {
        if (root == null) return true;
        int value = root.val;
        if (value < min || value > max) return false;
        
        if (!reachMin && value == Integer.MIN_VALUE) {
            if (root.left != null) return false;
            return isValidBST(root.right, true, value, reachMax, max);            
        } else if (!reachMax && value == Integer.MAX_VALUE) {
            if (root.right != null) return false;            
            return isValidBST(root.left, reachMin, min, true, value);
        } else if (value > min && value < max) { 
            return isValidBST(root.left, reachMin, min, reachMax, value) && 
                    isValidBST(root.right, reachMin, value, reachMax, max);        
        }
        
        return false;
    }
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub

    }

}

2) 类似于中序遍历

package bst;

public class ValidateBinarySearchTree {

    private boolean firstNode = true;
    
    private int lastValue = 0;
    
    public boolean isValidBST(TreeNode root) {
        if (root == null) return true;
        if (!isValidBST(root.left)) return false;
        
        if (!firstNode && root.val <= lastValue) return false;
        firstNode = false;
        lastValue = root.val;
        
        if (!isValidBST(root.right)) return false;
        
        return true;
    }
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub

    }

}