red black tree delete() without using successor() help...

i checked google and most of the rbt delete implementation are using successor
is there a way to do it without the successor???
he told the class to follow the book "intro to algorithms" but he wrote his version w/o even looking at the book and he wrote his answer w/o successor...
ive implemented my own with successor but my professor is forcing the class to do it w/o it

heres my codes

Code:

void deleteRb(string data)
	{
		treeNode* y;
		treeNode* z = searchDelete(data); //searchDelete finds where the node is to be deleted
		treeNode* x;

		if ( z->left == NULL || z->right == NULL )
			y=z;
		else 
			y = treeSuccessor(z);
		if (y->left != NULL)
			x= y->left;
		else
			x= y->right;
		x->parent = y->parent;
		if ( y->parent == NULL)
			root = x;
		else if (y = y->parent->left)
			y->parent->left = x;
		else
			y->parent->right = x;
		if ( y != z)
			z->data = y->data;
		if ( y->red = false)
			deleteFixUp(x);
	}

^the delete()

Code:

treeNode* treeSuccessor(treeNode* x)
	{
		if (x->right != NULL)
			return treeMinimum (x->right);

		treeNode* y;
		y = x->parent;
		while ( y != NULL)
		{
			if ( x == y->right)
			{
				x=y;
				y=y->parent;
			}

		return y;
		}
	}

^successor()

can someone help me...

>is there a way to do it without the successor???
Yes and no. If you mean without finding the successor at some point in the algorithm, no, because that's an integral part of correctly maintaining the tree's structure and invariants. If you mean without taking an extra step of finding the successor, absolutely. In fact, I have such an example in the top-down deletion function here which is described in simpler detail here.