> For the complete documentation index, see [llms.txt](https://shuati.gitbook.io/crack-lintcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://shuati.gitbook.io/crack-lintcode/linkedin/validate-binary-search-tree.md).

# Validate Binary Search Tree

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:**

```
Input:
    2
   / \
  1   3
Output: true
```

**Example 2:**

```
    5
   / \
  1   4
     / \
    3   6
Output: false
Explanation: The input is: [5,1,4,null,null,3,6]. The root node's value
             is 5 but its right child's value is 4.
```

时间  o(n),空间 o(n)

```java
/**
 * 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) {
        if(root == null)
            return true;
        
        Stack<TreeNode> stack = new Stack<>();
        TreeNode pre = null;
        while(root!= null || !stack.isEmpty()){
            while(root!= null){
                stack.push(root);
                root = root.left;
            }
            
            root = stack.pop();
            if(pre != null && root.val <= pre.val) return false;
            
            pre = root;
            root = root.right;
            
        }
        
        return true;
    }
}
```

分治法，更快， time space 最糟是o(n), space o(n), 注意 node val的值可能比int大

```java
/**
 * 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) {
        if(root == null)
            return true;
        
        
        return helper(root, Long.MIN_VALUE,Long.MAX_VALUE);
    }
    
    public boolean helper(TreeNode root, long min, long max){
        if(root== null)
            return true;
        
        if(root.val <= min || root.val >= max)
            return false;
        
        return helper(root.left, min, Math.min(root.val, max)) && helper(root.right, Math.max(root.val,min),max);
    }
}
```


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