 So what if I came in and I asked to do a lookup on a node that didn't exist? Say I did something like lookup lookup 26 now a quick note and you can tell my tree does not have a 26 I happen to kind of see that But we still have to go through and sort of confirm that so I would start in my node 50 I See that 26 is less than 50. So I would move down to 30 I see that 26 is less than 30. So I would move down to 25 and then Just to kind of show it I'd move down to see that I would get to a null node null node So in this case since we're dealing with a splay tree or our rule is oh, I access that node I have to bring it up, but since this is is null I have nothing there So what we actually do in this is instance is we find whatever the last node we were sort of accessing at that time and that's the node we would Move to the front so in our case we see that we would move 25 now if we happen to notice just like before I Identify my x I identify my y and I identify my z In this case we happen to see that we're dealing with a zig zig approach. I have a Left child from z to y I have a left child from y to x and so Just like before we would see that x we would see that y and we would see that z and As always we also have those non-existent Well, not it non-existent, but we have those sub trees that may or may not be there So that this would be I guess three instead of that being that'd be four x would have the potential for it And a t2 Now the zig zig approach that we've talked about is that x is now going to become the new Sort of root node in this situation y will stay sort of in the middle And then z will become the child of y when we talk about the inheritance there we go Of these and what sub trees go where we would see that x would still have t1 y would still have t2 and Z now this is Z would have in our case t3 and T4 So just as always we see that we have no T2 or t1 we have no that should be a one make that a little more X has no t1 or t2 y has no t3 and Z has well. Oh it happens to have a T4 So we would put this into place and my zigzag Fix to this lookup again since there is no 26. I'd use x 25 would become my new parent my new root node Y would become the child of it Z 50 would become the child of it and then since I happen to have a t4 t4 would become the right child of Z