Insert a node in a binary search tree The teacher gave us this code that inserts a node in a binary search tree, but I am not sure what the $z.p = y$ instruction does. wouldn't the algorithm work without it?

abr_insert(T, z) //z is the node that must be inserted
    {
            y = NULL;
            x = T.root;
            while(x != NULL)
            {
                    y  = x;
                    if(z.key &lt; x.key)
                            x = x.left;
                    else
                            x = x.right;
            }
            z.p = y; //here is the instruction that I don't understand
            if(y = NULL)
                T.root = z;
            else if(z.key &lt; y,key)
                    y.left = z;
            else
                    y.right = z;
    }
It seems like this algorithm is keeping track of parent pointers. Each node N has three fields: N.left (left child), N.right (right child), and N.p (parent). The variable y is used to keep track of the most recent parent, so when we fall off the tree (i.e. when x == NULL) we can use y as the parent of the new node z.