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.

 

Analyse: 

1. Using upper bound(INT_MAX) and lower bound(INT_MIN).

NA: Because if the root is INT_MAX / INT_MIN, it will cause error.

There is a chancy method: we can set the upper bound higher and the lower bound smaller. And let the arguments be long long int type.

Runtime: 12ms.

2. Use inorder traversal to get the inorder sequence, then check whether it's ascending. 

　 Runtime: 16ms.

 1 /**
 2  * Definition for a binary tree node.
 3  * struct TreeNode {
 4  *     int val;
 5  *     TreeNode *left;
 6  *     TreeNode *right;
 7  *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 8  * };
 9  */
10 class Solution {
11 public:
12     bool isValidBST(TreeNode* root) {
13         if(!root) return true;
14         
15         vector<int> result;
16         inorder(root, result);
17         for(int i = 1; i < result.size(); i++){
18             if(result[i] <= result[i - 1]) return false;
19         }
20         return true;
21     }
22     void inorder(TreeNode* root, vector<int>& result){
23         if(root->left) inorder(root->left, result);
24         result.push_back(root->val);
25         if(root->right) inorder(root->right, result);
26     }
27 };

3. For every node, check its left subtree nodes whether are all smaller than it and check its right subtree nodes whether are all larger than it.

    Runtime: 20ms.

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    bool isValidBST(TreeNode* root) {
        if(!root) return true;
        if(!root->left && !root->right) return true;
        
        if(validLeft(root->left, root->val) && validRight(root->right, root->val)){
            return isValidBST(root->left) && isValidBST(root->right);
        }
        else return false;
    }
    bool validLeft(TreeNode* root, int max){
        if(!root) return true;
        if(root->val >= max) return false;
        return validLeft(root->left, max) && 
               validLeft(root->right, max); //make sure every node in left subtree is smaller than the root value
    }
    bool validRight(TreeNode* root, int min){
        if(!root) return true;
        if(root->val <= min) return false;
        return validRight(root->left, min) &&
               validRight(root->right, min); //make sure every node in the right subtree is larger than the root value
    }
};