Function doesn't return default value - c++

Question

Here is my code:
bool BinarySearchTree::CheckIfTreeIsBinary(){
bool isBinary=true;
isBinary=CheckIfTreeIsBinaryPrivate(root); // So if my tree is binary, this function does not return anything
// and isBinary should remain true, but it is false.
return isBinary;
}
bool BinarySearchTree::CheckIfTreeIsBinaryPrivate(nodePtr Ptr){
if(Ptr->left!=NULL){
CheckIfTreeIsBinaryPrivate(Ptr->left);
}
if(Ptr->left!=NULL){
if(Ptr->data<Ptr->left->data)
return false; // possibility 1 to return false
}
if(Ptr->right!=NULL){
if(Ptr->data>Ptr->right->data)
return false; // possibility 2 to return false
}
if(Ptr->right!=NULL){
CheckIfTreeIsBinaryPrivate(Ptr->right);
}
}
In my function CheckIfTreeIsBinary, I have set boolean isBinary to true for default value. After that, isBinary is assigned to function CheckIfTreeIsBinaryPrivate, which will not return anything if the tree is binary.
The problem is that function CheckIfTreeIsBinaryPrivate doesn't return anything if the tree is binary, but in the end, isBinary is false.

Answer 1

The problem is that CheckIfTreeIsBinaryPrivate does not have an explicit return value on all program control paths.
That means that the behaviour of your program is undefined.
Your compiler will warn you of this, and it's your job to heed those warnings.

Answer 2

Your recursive logic is incorrect. All paths in a function should return a value and you should always check the return value of recursive calls to CheckIfTreeIsBinaryPrivate. There's no concept of 'a value remaining the same'. Here's what I think you are trying to achieve, but it's quite complicated.
bool BinarySearchTree::CheckIfTreeIsBinaryPrivate(nodePtr Ptr) {
return
// check the left sub tree is ok
(Ptr->left == NULL || // NULL is ok OR
(Ptr->data >= Ptr->left->data && // data >= left->data && left is ok
CheckIfTreeIsBinaryPrivate(Ptr->left))) &&
// and check the right sub tree is ok
(Ptr->right == NULL || // NULL is ok OR
(Ptr->data <= Ptr->right->data && // data <= right->data && right is ok
CheckIfTreeIsBinaryPrivate(Ptr->right)));
}

Answer 3

I think I see where your misunderstanding is; you're expecting isBinary to be updated only if CheckIfTreeIsBinaryPrivate returns a value.
That's not how it works - a function that has a non-void return type must always return something.
If the function doesn't explicitly return anything - for instance, by reaching the end of the function - the program has undefined behaviour.
There is no way for you to determine whether a function returned anything or not, and you must return something on every path through the function.
You can do this with one big expression,
bool BinarySearchTree::isBST(nodePtr Ptr){
return Ptr == nullptr
|| ( (Ptr->left == nullptr || (Ptr->left->data < Ptr->data && isBST(Ptr->left)))
&& (Ptr->right == nullptr || (Ptr->right->data > Ptr->data && isBST(Ptr->right))));
}
or piece by piece:
bool BinarySearchTree::isBST(nodePtr Ptr){
// An empty tree is a BST.
if (Ptr == nullptr)
return true;
// If the left subtree is not a BST, neither is the entire tree.
else if (Ptr->left != nullptr && (Ptr->left->data > Ptr->data || !isBST(Ptr->left)))
return false;
// If the right subtree is not a BST, neither is the entire tree.
else if (Ptr->right != nullptr && (Ptr->right->data < Ptr->data || !isBST(Ptr->right)))
return false;
// All tests passed.
else
return true;
}

Answer 4

Add one more base condition in CheckIfTreeIsBinaryPrivate() to set true,
because once you assign isBinary to CheckIfTreeIsBinaryPrivate() it will set false by default, and you need a return value to get true.