**1. Homework Statement**

I am working on an assignment in which I have to add a method to my BST class which checks if a binary tree object is in fact a Binary Search tree. So

(1) A left child must be smaller than the parent

(2) A right child must be larger than the parent

and:

(3) There cannot be any repeat data values

I think my code works for the first two conditions. What it does is check the root first against its maximum (right-most leaf) and minimum (left-most leaf) values. If that's true, then the method will call itself, checking that each subtree's parent is less than the right max value and and greater than the left min value.

However, this does not work correctly if a data value of the binary tree has been repeated.

I am completely stumped on how to also check for this case.

**2. Homework Equations**

bool isBST() --> sets initial min and max values to start check and calls second isBST method

bool isBST(Node<t>* r, int max, int min) --> checks to see if the < > rules have been followed

**3. The Attempt at a Solution**

Code:

```
//******************************************************************
// Function name: isBST
//*******************************************************************
template <class T>
bool BST<T> :: isBST() {
Node<T>* seekerL = root,
* seekerR = root;
T minimum,
maximum;
if(!seekerL) { // if the tree is empty return true
return true;
} else { // find the left and right min and max values of the tree
while(seekerL) {
minimum = seekerL->key;
seekerL = seekerL->left;
}
while(seekerR) {
maximum = seekerR->key;
seekerR = seekerR->right;
}
}
// check that the tree and its subtrees follow the BST rules
return isBST(root, minimum , maximum);
} // end isBST
//******************************************************************
// Function name: isBST
//*******************************************************************
template <class T>
bool BST<T> :: isBST(Node<T>* r, T min, T max) {
Node<T> *parent = r;
// if the parent has no children a leaf node has been reached
if(!parent) {
return true;
}
// if parent does not fall inbetween max or min return false
if (parent->key < min || parent->key > max) {
return false;
}
// else keep checking each subtree until rule is broken or tree is BST
return (isBST(parent->left, min, parent->key) && isBST(parent->right, parent->key+1, max));
} // end isBST
```

Edit: Oh and the test data/key I am using is a Binary Tree of integers.

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