Question: Given a Binary Tree, Programmatically you need to Prove it is a Binary Search Tree

Solution: f the given binary tree is a Binary search tree,then the inorder traversal should output the elements in increasing order.We make use of this property of inorder traversal to check whether the given binary tree is a BST or not.We make note of the latest element that could have been printed and compare it with the current element.Given below is a C function to check it.
bool flag=true;
void inorder(tree T,int *lastprinted)
{
if(T==NULL)
{
printf("the tree is empty .Hence, it is a BST\n");
}
else
{
if(T->left!=NULL)
{
inorder(T->left,lastprinted);
}
if(T->data > *lastprinted)
{
*lastprinted=T->data;
}
else
{
printf("the given binary tree is not a BST\n");
flag=false;
exit(0);
}
inorder(T->right,lastprinted);
}
}