# Program to check if Tree is Binary Search Tree C++

Hello all, today we will write a program to check if given Binary Tree is Binary Search Tree C++ or not. So let’s start with what properties a tree must satisfy so that it is a Binary Search Tree.

### How to identify a Binary Search Tree:

The tree satisfies the binary search tree property, which states that the key in each node must be greater than or equal to any key stored in the left sub-tree, and less than or equal to any key stored in the right sub-tree.

### How code works:

• Perform a simple inorder traversal and keep the previous value of the node.
• If the current node is smaller than the previous node then it is not a binary search tree
• Otherwise it is a Binary search Tree.

Checkout the program to implement Binary Search Tree C++

## Program to check if Tree is Binary Search Tree C++:

```#include <iostream>
#include <cstdlib>
#include <climits>
using namespace std;

//Node Declaration
struct node
{
int data;
node* left;
node* right;
};

int isBSTUtil(node* node, int min, int max);

//Returns true if the given tree is a binary search tree
int isBST(node* node)
{
return(isBSTUtil(node, INT_MIN, INT_MAX));
}

// Returns true if the given tree is a BST and its values are >= min and <= max.

int isBSTUtil(struct node* node, int min, int max)

{
if (node==NULL)
return 1;
if (node->data < min || node->data > max)
return 0;
return isBSTUtil(node->left, min, node->data - 1) &&
isBSTUtil(node->right, node->data + 1, max);
}

// allocates a new node with the data and NULL left and right pointers.

node* newNode(int data)
{
node* nod = new node;
nod->data = data;
nod->left = NULL;
nod->right = NULL;
return nod;
}

int main()
{
node *root = newNode(4);
root->left = newNode(2);
root->right = newNode(5);
root->left->left = newNode(1);
root->left->right = newNode(3);

if (isBST(root))
cout<<"The Given Binary Tree is a BST"<<endl;
else
cout<<"The Given Binary Tree is not a BST"<<endl;
return 0;
}```

## OUTPUT:

```\$ g++ binary_bst.cpp
\$ a.out

The Given Binary Tree is a BST

------------------
(program exited with code: 1)