Given a Binary Tree, the task is to check whether the given binary tree is Binary Search Tree or not.
A binary search tree (BST) is a node-based binary tree data structure which has the following properties.
- 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.
From the above properties it naturally follows that:
We have already discussed different approaches to solve this problem in the previous article.
In this article, we will discuss a simple yet efficient approach to solve the above problem.
The idea is to use Inorder traversal and keep track of the previously visited node’s value. Since the inorder traversal of a BST generates a sorted array as output, So, the previous element should always be less than or equals to the current element.
While doing In-Order traversal, we can keep track of previously visited Node’s value by passing an integer variable using reference to the recursive calls. If the value of the currently visited node is less than the previous value, then the tree is not BST.
Below is the implementation of the above approach:
Time Complexity: O(N)
Auxiliary Space: O(1)
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
- Check whether a binary tree is a full binary tree or not | Iterative Approach
- Check for Symmetric Binary Tree (Iterative Approach)
- Iterative approach to check if a Binary Tree is Perfect
- Iterative approach to check for children sum property in a Binary Tree
- Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)
- Find the closest element in Binary Search Tree | Space Efficient Method
- Check if a binary tree is subtree of another binary tree using preorder traversal : Iterative
- Get level of a node in binary tree | iterative approach
- Construct Binary Tree from Ancestor Matrix | Top Down Approach
- Largest value in each level of Binary Tree | Set-2 (Iterative Approach)
- Deepest right leaf node in a binary tree | Iterative approach
- Sum of nodes at maximum depth of a Binary Tree | Iterative Approach
- Print All Leaf Nodes of a Binary Tree from left to right | Set-2 ( Iterative Approach )
- Construct Binary Tree from given Parent Array representation | Iterative Approach
- Deepest left leaf node in a binary tree | iterative approach
- Iterative Approach to check if two Binary Trees are Isomorphic or not
- Check whether a given binary tree is skewed binary tree or not?
- Check whether a binary tree is a full binary tree or not
- Check if a binary tree is subtree of another binary tree | Set 2
- Check if a binary tree is subtree of another binary tree | Set 1
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.