[leetcode]98. Validate Binary Search Tree验证二叉搜索树

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.

Solution1: DFS

根据BST的性质：左子树<根<右子树

要特别留心，对于input的root，没有办法给定一个确定的范围。所以初始化为null

    5  (min, max)                             5 :in(min,max)?

   / \                                /   / return true             \ \ return false

  1   4                           1 update(min, 5), in (min, 5)?    4 update(5, 4), in (5,4)?

code

 /**

  * 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) {

                            /*why using null, null? 因为对于root，没有办法确定范围*/

        return helper(root, null, null);

     }

                                   /* 因为上面定义的是null，这里initialize就应该是Integer而不是int*/

     private boolean helper(TreeNode root, Integer min, Integer max) {

         // base case

         if (root == null)return true;

         // based on BST attribute

         if ((min != null && root.val <= min) || (max != null && root.val >= max))

             return false;

         // dfs

         Boolean left = helper(root.left, min, root.val);

         Boolean right = helper(root.right, root.val, max);

         return  left && right;

     }

 }

复杂度

Time: O(n) : visit each node

Space: O(h): h is the deepest height of such tree

巴特西

[leetcode]98. Validate Binary Search Tree验证二叉搜索树

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