From the definition of BST, it may seem that for a binary tree to be BST, it’s enough to check for each node if the node on its left is smaller & node on its right is greater. But this is actually the wrong approach since it will give wrong output for many test-cases.
The correct algorithm is to check for each node whether the maximum of the left subtree is lesser than the node & the minimum of the right subtree is greater than the node. This algorithm works perfect but not efficient in terms of time complexity.
Intuition says that the in-order traversal for the BST results in a sorted list of nodes and we use this in our algorithm.
1. Set prev to INT_MIN.
2. From main function call checkBST(root, prev)
//passing prev by reference to update it every time
checkBST(root, &prev)
3. if(root==NULL)
return 1; //null tree is BST
4. do in-order traversal and checking whether all tree node
data is sorted or not
if(!(checkBST(root->left,prev))) //check left subtree
return 0;
//root->data must be greater than prevsince BST results in
//sorted list after in-order traversal.
5. if(root->data<prev)
return 0;
6. prev=root->data; //update prev value
7. return checkBST(root->right,prev);//check right subtree
Example 1:
Clearly Example 1 is a binary search tree. We will check out further through our function.
Example 2:
Clearly Example 2 is not a binary tree. We will check out through our function.
C++ class implementation for tree
// tree node is defined
class tree{
public:
int data;
tree *left;
tree *right;
};
C++ function checkBST for implementation
//passing reference of prev
int checkBST(tree* root,int &prev){
//null tree is BST
if(root==NULL)
return 1;
//doing inorder traversal and checking whether
//all tree node data is sorted or not
if(!(checkBST(root->left,prev)))
return 0;
if(root->data<prev)
return 0;
prev=root->data; //update prev value
return checkBST(root->right,prev);
}
#include <bits/stdc++.h>
using namespace std;
int main()
{
//**same tree is builted as shown in example**
int c,prev=INT_MIN;//prev initialized to INT_MIN
cout<<"Tree is built like the example 1 aforesaid"<<endl;
tree *root=newnode(8);
root->left= newnode(3);
root->right= newnode(10);
root->right->right=newnode(14);
root->right->right->left=newnode(13);
root->left->left=newnode(1);
root->left->right=newnode(6);
root->left->right->left=newnode(4);
root->left->right->right=newnode(7);
cout<<"builting the binary tree like example 1......"<<endl;
c=checkBST(root,prev);
if(c)
cout<<"This binary tree is binary search tree"<<endl;
else
cout<<"This is not a binary search tree";
return 0;
}
Main driver function for example2
#include <bits/stdc++.h>
using namespace std;
int main()
{
//**same tree is builted as shown in example**
int c,prev=INT_MIN;//prev initialized to INT_MIN
cout<<"Tree is built like the example 2 aforesaid"<<endl;
tree *root=newnode(2);
root->left= newnode(7);
root->right= newnode(5);
root->right->right=newnode(9);
root->right->right->left=newnode(4);
root->left->left=newnode(2);
root->left->right=newnode(6);
root->left->right->left=newnode(5);
root->left->right->right=newnode(11);
cout<<"builting the binary tree like example 2......"<<endl;
c=checkBST(root,prev);
if(c)
cout<<"This binary tree is binary search tree"<<endl;
else
cout<<"This is not a binary search tree";
return 0;
}
Output 1
Tree is built like the example 1 aforesaid
builting the binary tree like example 1......
This binary tree is binary search tree
Output 2
Tree is built like the example 2 aforesaid
builting the binary tree like example 2......
This is not a binary search tree
Algorithm:
From the definition of BST, it may seem that for a binary tree to be BST, it’s enough to check for each node if the node on its left is smaller & node on its right is greater. But this is actually the wrong approach since it will give wrong output for many test-cases.
The correct algorithm is to check for each node whether the maximum of the left subtree is lesser than the node & the minimum of the right subtree is greater than the node. This algorithm works perfect but not efficient in terms of time complexity.
Intuition says that the in-order traversal for the BST results in a sorted list of nodes and we use this in our algorithm.
Example 1:
Clearly Example 1 is a binary search tree. We will check out further through our function.
Example 2:
Clearly Example 2 is not a binary tree. We will check out through our function.
C++ class implementation for tree
C++ function checkBST for implementation
C++ implementation for creating tree nodes
Main driver function for example1
Main driver function for example2
Output 1
Output 2
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