An idea to improve Roux

[waffle=ijm]

Recently, I've been using a lot of CLS algs for my petrus solves. And I liked the idea of CLS. So I've been running through some cases during my roux solves too and I get to use CLS algs usually got to preform very nicely though not that optimized. I came to the idea of optimizing algorithms for CLS+last pair Roux to orient the LL corners while completing the last 1x2x3 block.

So the basic idea of this is to complete the last block like orienting the LL corners. The FR piece doesn't necessarily have to be in its correct position to do this. Of course the number of algorithms for all possible positions in the M slice, UL position, UR position and the FR position would be quite large. So I decided that since positions are easily manipulable through the M slice, you can get away using only the UF and FR positions for the FR piece.

The same applies with the corners. In http://cube.garron.us/MGLS/ describes CLS well if the FR piece is already in position. Though in Roux, this doesn't always apply since the FR piece can be anywhere in a different orientation. Providing that the FR piece is in UF or FR in any orientation, I decided to be more flexible and allow the last corner to be in UFL UFR and DFR positions in any orientation. These positions can be achieved using M-slice to temporary preserve a piece in the UF position and replacing to connect with the corner or attach to a corner in the B face and then bringing to the F face. Then you can use a Roux optimized CLS algorithm to properly attach the last corner and last edge while orienting the LL.

This way while completing the last block you can orient the corners and finish the corners using only 2 permutations.

I have yet to actually look into this more in depth due to the fact i'm too lazy to even go on Acube or Cube explorer to try this out.

If you have any comments, suggestions, and/or math to get an estimated amount of algorithms feel free to post.

(I'm very tired when I wrote this so if you see a typo please inform me so I can fix it.)

 

[ErikJ]

I think it would be more efficient to just do CMLL. there is no orientation step for LL with Roux so it wouldn't really skip anything like with petrus.

 

[Lofty]

I agree with Erik.
You could just use Lucas's CLS algs tho. Just make a 2x2x1 block add the final edge then do a CLS? Unless I misread what you are talking about I didn't understand most of it.
I don't think using CLS in Roux would be helpful at all. If you want to improve Roux I think you should combine the last couple steps.

 

[waffle=ijm]

I agree with Erik.
You could just use Lucas's CLS algs tho. Just make a 2x2x1 block add the final edge then do a CLS? Unless I misread what you are talking about I didn't understand most of it.
I don't think using CLS in Roux would be helpful at all. If you want to improve Roux I think you should combine the last couple steps.

It was just a thought since I got some easy CLS during my roux solves. At the rate that i'm going through right now, I focus more on block building than anything so this idea just came up to skip the LL corners.

I'm looking into Optimizing the M slice already...I'm just to lazy to pick up where I left off.

 

[cubeRemi]

If you orient corners while finishing right block you will get a CP skip quite often...

also, you can learn some CP algs that will flip edges... (maybe setup edges using M slice )

I wonder how many algs/cases the extra CP+EO algs will be.

EDIT:
no more than 1 M slice setup move: 14 algs/cases
no more than 3 U+M moves: 8 algs/cases

 

[Kenneth]

Easier must be to ignore the last edge of the block in CLS because it is really easy to put it in later using R U M/M'/M2 U' R'. If it is in place but unorieted do R U M2 U2 M U R'

For the ending I suggest orient last six edges using M' U M (as Roux) and then place FD and BD using the M' U2 M style, end in PLL.

 

[somerandomkidmike]

I think just doing CMLL is faster. If people wanted to be really fast they could use the 2.5 look last 6 edges found in Josef Jelinek's pages. If you get good at it then the last 6 edges for Roux take 2 looks instead of 3 or more.

 

[Athefre]

I think just doing CMLL is faster. If people wanted to be really fast they could use the 2.5 look last 6 edges found in Josef Jelinek's pages. If you get good at it then the last 6 edges for Roux take 2 looks instead of 3 or more.

3 looks for the usual way of solving the LSE? I almost never have to pause and remember what I have to do. The only times I ever have to are when I'm solving certain corner cases that makes it hard to see exactly what the orientation pattern will be. Seeing most of the edges orientation is easy and it doesn't matter much that you don't see the others, it's quick to recognize.