Leetcode 98. Validate Binary Search Tree

原题：
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:

2
/ \
1   3

Binary tree

[2,1,3]

, return true.
Example 2:

1
/ \
2   3

Binary tree

[1,2,3]

, return false.

解决方法：
一棵树是BST，遵循规则：

- 左边子树的值一定小于根节点；

- 右边子树的值一定大于根节点；

- 左右子树都是BST。

根据这个特性，我们只需把最大最小值传入到函数中进行限定判断即可：根节点的值是左边子树的最大值，是右边子树的最小值。

代码：

bool isValidBST(TreeNode* root, TreeNode* minValue, TreeNode* maxValue){
if (!root)
return true;

if ( (minValue && root->val <= minValue->val) || (maxValue && root->val >= maxValue->val) )
return false;

return isValidBST(root->left, minValue, root) && isValidBST(root->right, root, maxValue);
}

bool isValidBST(TreeNode* root) {
return isValidBST(root, NULL, NULL);
}