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.
A single node tree is a BST

​http://www.lintcode.com/en/problem/validate-binary-search-tree/#​

1.需要两个值maxValue, minValue 来记录当前节点应该的取值范围。

/**
* Definition of TreeNode:
* class TreeNode {
* public:
* int val;
* TreeNode *left, *right;
* TreeNode(int val) {
* this->val = val;
* this->left = this->right = NULL;
* }
* }
*/
class Solution {
public:
/**
* @param root: The root of binary tree.
* @return: True if the binary tree is BST, or false
*/
bool helper(TreeNode *node,long minVal,long maxVal){
if(node==NULL){
return true;
}

if(node->val<=minVal || node->val>=maxVal){
return false;
}

return helper(node->left,minVal,node->val) & helper(node->right,node->val,maxVal);
}

bool isValidBST(TreeNode *root) {
// write your code here
return helper(root,LONG_MIN,LONG_MAX);
}
};

2.判断中序遍历是否有序

这里写代码片/**
* Definition of TreeNode:
* class TreeNode {
* public:
* int val;
* TreeNode *left, *right;
* TreeNode(int val) {
* this->val = val;
* this->left = this->right = NULL;
* }
* }
*/
class Solution {
public:
/**
* @param root: The root of binary tree.
* @return: True if the binary tree is BST, or false
*/
bool helper(TreeNode *root, long & pre){

if(root==NULL){
return true;
}

if(helper(root->left,pre)==false){
return false;
}

if(root->val<=pre){
return false;
}else{
pre=root->val;
}

if(helper(root->right,pre)==false){
return false;
}

return true;
}

bool isValidBST(TreeNode *root) {
// write your code here

long pre=LONG_MIN;

return helper(root,pre);
}
};

参考:
​​​http://www.acmerblog.com/validate-binary-search-treeleetcode-6194.html​​​