C++ Program to Check Whether a Given Tree is Binary Search Tree

Binary Search Tree is a binary tree data structure in which we have 3 properties

• The left subtree of a binary search tree of a node contains only nodes with keys lesser than the node’s key.

• The right subtree of a binary search tree node contains only nodes with keys greater than the node’s key.

• The left and right trees of a subtree each must also be a binary search tree.

Algorithm

Begin
   function BSTUtill()
      If node is equals to NULL then
         Returns 1.
      If data of node is less than minimum or greater than
      maximum data then
         Return 0.
      Traverse left and right sub-trees recursively. 
End.

Example Code

 Live Demo

#include <iostream>
#include <cstdlib>
#include <climits>
using namespace std;
struct n {
   int d;
   n* l;
   n* r;
};
int BSTUtil(n* node, int min, int max);
int isBST(n* node) {
   return(BSTUtil(node, INT_MIN, INT_MAX));
}
int BSTUtil(struct n* node, int min, int max) {
   if (node==NULL)
      return 1;
   if (node->d < min || node->d > max)
      return 0;
      return BSTUtil(node->l, min, node->d - 1) && BSTUtil(node->r, node->d + 1, max);
}
n* newN(int d) {
   n* nod = new n;
   nod->d = d;
   nod->l = NULL;
   nod->r = NULL;
   return nod;
}
int main() {
   n *root = newN(7);
   root->l = newN(6);
   root->r = newN(10);
   root->l->l = newN(2);
   root->l->r = newN(4);
   if (isBST(root))
      cout<<"The Given Tree is a BST"<<endl;
   else
      cout<<"The Given Tree is not a BST"<<endl;
      n *root1 = newN(10);
      root1->l = newN(6);
      root1->r = newN(11);
      root1->l->l = newN(2);
      root1->l->r = newN(7);
   if (isBST(root1))
      cout<<"The Given Tree is a BST"<<endl;
   else
      cout<<"The Given Tree is not a BST"<<endl;
      return 0;
}

Output

The Given Tree is not a BST
The Given Tree is a BST