Validate Binary Search Tree 检测一个BST是否有效@LeetCode

思路：用上下限限定来递归
一开始想到了递归，但没想到用上下限的办法，而用多加一个parent作参数，结果非常麻烦。改成用上下限后代码很简洁清晰。

package Level3;

import Utility.TreeNode;

/**
* 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.
confused what "{1,#,2,3}" means? > read more on how binary tree is serialized on OJ.

OJ's Binary Tree Serialization:
The serialization of a binary tree follows a level order traversal, where '#' signifies a path terminator where no node exists below.

Here's an example:
1
/ \
2 3
/
4
\
5
The above binary tree is serialized as "{1,2,3,#,#,4,#,#,5}".
*
*/
public class S98 {

public static void main(String[] args) {
TreeNode root = new TreeNode(3);
TreeNode p1 = new TreeNode(1);
TreeNode p2 = new TreeNode(5);
TreeNode p3 = new TreeNode(0);
TreeNode p4 = new TreeNode(2);
TreeNode p5 = new TreeNode(4);
TreeNode p6 = new TreeNode(6);

root.left = p1;
root.right = p2;
p1.left = p3;
p1.right = p4;
p2.left = p5;
p2.right = p6;
System.out.println(isValidBST(root));
}

public static boolean isValidBST(TreeNode root) {
return rec(root, Integer.MIN_VALUE, Integer.MAX_VALUE);
}

// 用最小值和最大值，来限定子树的范围
public static boolean rec(TreeNode root, int min, int max){
if(root == null){
return true;
}

// 不在范围内
if(root.val <= min || root.val >= max){
return false;
}

// 检查左右子树的合法性并更新上下限
return rec(root.left, min, root.val) && rec(root.right, root.val, max);
}

}


/**
* Definition for binary tree
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
public class Solution {
public boolean isValidBST(TreeNode root) {
return isBSTRec(root, Integer.MIN_VALUE, Integer.MAX_VALUE);
}

public boolean isBSTRec(TreeNode root, int left, int right) {
if(root == null) {
return true;
}
if(root.val <= left || root.val >= right) {
return false;
}

return isBSTRec(root.left, left, root.val) && isBSTRec(root.right, root.val, right);
}
}