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:

1. The left subtree of a node contains only nodes with keys less than the node's key.
2. The right subtree of a node contains only nodes with keys greater than the node's key.
3. 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.

Tips:

Recursive: 设一个min一个max，如果root <= min或者 root >= max就返回false。

Iterative：就中序遍历呗, cost O(logN) space

Code：

Recursive:

public class Solution {
    public boolean isValidBST(TreeNode root) {
        return isValid(root, null, null);
    }

    public boolean isValid(TreeNode root, Integer min, Integer max) {
        if(root == null) return true;
        if(min != null && root.val <= min) return false;
        if(max != null && root.val >= max) return false;
        return isValid(root.left, min, root.val) && isValid(root.right, root.val, max);
    }
}

Iterative:

public boolean isValidBST (TreeNode root){
       Stack<TreeNode> stack = new Stack<TreeNode> ();
       TreeNode cur = root ;
       TreeNode pre = null ;           
       while (!stack.isEmpty() || cur != null) {               
           if (cur != null) {
               stack.push(cur);
               cur = cur.left ;
           } else {                   
               TreeNode p = stack.pop() ;
               if (pre != null && p.val <= pre.val) {                       
                   return false ;
               }                   
               pre = p ;                       
               cur = p.right ;
           }
       }
       return true ; 
   }

另一种比较直观的recursive：

class Solution {
    public boolean isValidBST(TreeNode root) {
        return check(root, Integer.MIN_VALUE, Integer.MAX_VALUE);
    }

    private boolean check(TreeNode root, int min, int max) {
        if (root == null) {
            return true;
        }
        if (root.val < min || root.val > max) {
            return false;
        }
        if (root.val == Integer.MIN_VALUE && root.left != null) {
            return false;
        }
        if (root.val == Integer.MAX_VALUE && root.right != null) {
            return false;
        }
        return check(root.left, min, root.val - 1) && check(root.right, root.val + 1, max);
    }
}