Red Black Tree ~ 1 Child Deletes

Question

Is it ever possible for a red parent node to have just ONE black child node? I have been playing around with the Red/Black Tree simulator online and I can't manage to get a case of this to happen.

The reason behind asking this is I believe I have an unnecessary IF in my code...

if (temp_node->color == BLACK && node->color == RED)
{
    node->color = BLACK;
    global_violation = false;
}

Thanks for any Feedback!!

Answer 1

No, this isn't possible.

Remember, that in a red/black tree, all paths from the root of the tree off of the tree must pass through the same number of black nodes (that's one of the red/black tree invariants).

If you have a red node x with one black child y, it cannot have another red child (since that breaks the red/black invariant that red nodes can't have red children).

This means that a path through x to the missing child will pass through at least one fewer black node than the path through x, then to y, and then off the tree from there, breaking the red/black tree invariants.