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CLL+1: An Advanced LL Method (Complete and fully generated!)

Athefre

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Jul 25, 2006
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How would one go about recognizing CLL+1 after recognizing the CLL case? Like what exactly would I look for on the scramble B2 R F2 R B2 L' B2 R D2 R B' L B2 R F2 R' B? Would the recognition be significantly harder if CLL+1 was done entirely with cycle unions and without the orientation trick? Depending on how easy the recognition is, I might start learning this set.

The idea is to recognize as ZBLL. There are a few ways of doing that. I'm not yet sure which is best for CLL+1. During development I was mentally flipping edges, but maybe there's a better way. I talked a bit about recognition before, but it's definitely something that could be developed. I'm also curious about how recognition will work once the orientation trick is removed. It may be that it is fewer cases but more difficult recognition. Or recognition may turn out to be pretty much the same. I'll have to finish it and examine the unions to really know.

For the scramble: After identifying the corner case, I would see that RU matches RFU and FU matches URF. For this case I would know that the edge at UR will be solved. That edge is oriented, so the alg is U R U2 R2 U' R U' R' U2 F R F'. This is how I was recognizing during development tests. I'm not an experienced ZBLL user, so I'm sure there are better ways.

Also a note on anyone who wants to contribute to the algs: cycle unions are not needed to generate algs if the orientation trick is used. To generate the algs for a specific CLL case, find two algs for that CLL case where applying the inverse of one algorithm then solving the corners with the other algorithm leads to an ELL case with exactly one solved or flipped edge, then find the two algs that are a 4-flip away from the original two. For example, for the Sune pure twist case, I found R U R' U R U2 R' and r' R2 U R' U r U2 r' U M'. Applying R U2 R' U' R U' R' then r' R2 U R' U r U2 r' U M' leads to an ELL case with exactly one flipped edge, so we know this pair works. Then I found F R U R' U' F' R U R' F' U2 F R U' R' and R' U2 R2 U R2 U R U' R U' R' which are a 4-flip away from the first two cases.

This is an interesting way of finding the algs. Pretty cool. In the conversations I had with TDM, he also had his own way of finding algs. His rule was that the second alg in the pair needs to be a 3-cycle difference from the first alg in the pair. I have already provided all of the possible combinations in the development files of the original post. No one has to use cycle unions anymore for CLL+1. All that is needed is to check the document, set up the corner case in CubeExplorer, and set it so that it will cycle the edges the desired way. All of the cases are in the document. So there's no need to find algs. They only need to be generated.

Well, I say that cycle unions doesn't need to be used anymore for CLL+1. However, I would like to get rid of the orientation trick and see how well it works. I have the first half of the cycle simulator built in Excel. It's just a matter of finding time to get it finished. 2,300 cycle simulations per CLL case.
 

abunickabhi

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Nice idea. I got it works practically. How do you simulate all the cycles. ZBLL conventional recognition isnt that good (just seeing block). I think recognizing COLL and the corresponding EPLL that is embedded in that LL is a better way of recognizing.
 

Athefre

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Nice idea. I got it works practically. How do you simulate all the cycles. ZBLL conventional recognition isnt that good (just seeing block). I think recognizing COLL and the corresponding EPLL that is embedded in that LL is a better way of recognizing.

I set up a cross shape of five cells. The center is labeled with the type of cycle (U-Perm, H-Perm, Infinity Cycle, etc.). The cell to the left, top, right, and bottom contain a letter code for the color of the edge on the cube. For ZBLL, I have a set of 12 of these 5-cell groups. These are all of the possible ZBLL edge positions. To the right of this group of 12 I have an identical group. Except that inside of the color code cells is instead a formula that grabs the color from a different location of the corresponding 5-cell group. It pulls from a certain location depending on the labeled cycle in the center of the 5-cell groups. This is the cycle simulator. There are 24 possible ways of cycling the edges, so I have 24 of these 12 sets of 5-cell groups. Each with a cycle simulator to the right. For the full cycle union application to remove the orientation trick, there will be 96 5-cell groups per 24 ways of cycling the edges. I provided my cycle simulator in the main post if you're interested in seeing more about how it works.

There are several ways of recognizing ZBLL, which means that there are several ways of recognizing CLL+1. I wonder which would be the best. Blocks, mentally twisting pieces to form PLL, and CLL then EP are three of the ZBLL options. Maybe one of the ZBLL methods, something unique, or a combination would be the way to go.
 
Last edited:

trangium

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Jul 24, 2019
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Another thing to note is that ELLs with no edges solved are only 3.623 STM worse than ELLs with one or more edges solved on average, using my ELLs, so any CLL+1 cases that are more than 3 moves slower than the standard CLL won't be worth it.
For reference, here is my list of ELLs: https://tinyurl.com/yyg8s9fb
 

Athefre

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That's an interesting point. It could be that for some cases, users will prefer to do CLL then ELL or OLL then PLL. Similar to how some people don't recommend S/AS for COLL and instead suggest OCLL+PLL for those cases. At least for move-count it makes sense. Overall recognition would take a hit though. Because CLL+1 guarantees a pauseless L3E, that is something that would be lost. So maybe the determination to be made for those cases is what is faster. The move difference for CLL+1 or recognition time for a different method.
 

Athefre

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Some thoughts on Union CLL+1 versus All Cases (300+ algs) CLL+1.

Recognition (after recognizing the CLL case):

Union CLL+1
- First find the edge orientation, which is 3 stickers. Then recognition is process of elimination style where cases will be either in this group or the other one. The user checks either 1 or 2 stickers on the edges currently at UF and UR to find the permutation. No need to know anything about the edges currently at UL and UB. This is 4-5 stickers total and the user is only checking whether the current case is one of 3 specific cases. If it is, use the single alg that solves an edge in all three of those cases. If it isn't one of those 3 cases, use the other alg that solves an edge in all 9 of the remaining cases. There's no reason to look any deeper into the case and recall one of several algs. There is also no need to check or worry about hidden stickers on L or B. All recognition can be done on U, F, and R if you know the edge cases.

All Cases CLL+1 - The user would have a set edge location to solve every time for every case. Say for Sune with the oriented corner placed at UFL you want to always solve the edge that goes to UF. Recognition would be: Check the FUL sticker to know what edge you are looking for then locate the edge. This edge can be in any of the four positions and possibly the identifying sticker hidden on L or B. With the edge having the possibility of being in several positions and two orientations, does this mean that many more stickers are required to be checked versus Union CLL+1? Or, how do we quantify a kind of passive scan of stickers which users would probably do? Also, how would the CLL angles be handled? For example, when the Sune case is a U or U2 away and you can't see the corner sticker to know what edge you need to look for. Maybe by adding in additional knowledge to your CLL recognition patterns? The corner sticker and or the edge you are looking for can be hidden in a large percentage of solves.

Algorithm quality:

I think the algorithm quality of Union CLL+1 is better overall than the 300 algorithm version of CLL+1. This is because the 300 alg version will include all of the possible bad cases. These bad cases can often be avoided in Union CLL+1. This is accomplished by choosing the unions which contain the best algorithms. Most bad cases can be avoided and most of the best cases will be included. There's also an addition by trangium which takes advantage of the orientation trick of the union version of CLL+1. A third algorithm can be incorporated into the union to allow for even better algorithms.

I think if the algorithms for the union version of CLL+1 were regenerated by a few people we would see some great results. I didn't incorporate S or f moves when I made the document. Additional help from the community and additional movesets will make this even better.
 

OreKehStrah

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May 24, 2019
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Some thoughts on Union CLL+1 versus All Cases (300+ algs) CLL+1.

Recognition (after recognizing the CLL case):

Union CLL+1
- First find the edge orientation, which is 3 stickers. Then recognition is process of elimination style where cases will be either in this group or the other one. The user checks either 1 or 2 stickers on the edges currently at UF and UR to find the permutation. No need to know anything about the edges currently at UL and UB. This is 4-5 stickers total and the user is only checking whether the current case is one of 3 specific cases. If it is, use the single alg that solves an edge in all three of those cases. If it isn't one of those 3 cases, use the other alg that solves an edge in all 9 of the remaining cases. There's no reason to look any deeper into the case and recall one of several algs. There is also no need to check or worry about hidden stickers on L or B. All recognition can be done on U, F, and R if you know the edge cases.

All Cases CLL+1 - The user would have a set edge location to solve every time for every case. Say for Sune with the oriented corner placed at UFL you want to always solve the edge that goes to UF. Recognition would be: Check the FUL sticker to know what edge you are looking for then locate the edge. This edge can be in any of the four positions and possibly the identifying sticker hidden on L or B. With the edge having the possibility of being in several positions and two orientations, does this mean that many more stickers are required to be checked versus Union CLL+1? Or, how do we quantify a kind of passive scan of stickers which users would probably do? Also, how would the CLL angles be handled? For example, when the Sune case is a U or U2 away and you can't see the corner sticker to know what edge you need to look for. Maybe by adding in additional knowledge to your CLL recognition patterns? The corner sticker and or the edge you are looking for can be hidden in a large percentage of solves.

Algorithm quality:

I think the algorithm quality of Union CLL+1 is better overall than the 300 algorithm version of CLL+1. This is because the 300 alg version will include all of the possible bad cases. These bad cases can often be avoided in Union CLL+1. This is accomplished by choosing the unions which contain the best algorithms. Most bad cases can be avoided and most of the best cases will be included. There's also an addition by trangium which takes advantage of the orientation trick of the union version of CLL+1. A third algorithm can be incorporated into the union to allow for even better algorithms.

I think if the algorithms for the union version of CLL+1 were regenerated by a few people we would see some great results. I didn't incorporate S or f moves when I made the document. Additional help from the community and additional movesets will make this even better.
Something I was playing around with for the full CLL+1 thing is not quite what you mentioned. Basically I would recog the OLL then CP and then use the UFR corner as the reference, then look at the UF edge and determine where it needed to move relative to the UFR reference.
 

Athefre

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Something I was playing around with for the full CLL+1 thing is not quite what you mentioned. Basically I would recog the OLL then CP and then use the UFR corner as the reference, then look at the UF edge and determine where it needed to move relative to the UFR reference.
That definitely helps with recognition. No need to worry about hidden stickers. I guess OLL first recognition would work for the union version as well.

Using that style, recognition comes down to:

Union: OLL > CP > UF edge sticker and or UR edge sticker to determine which of the two algs to use.

Full: OLL > CP > FU edge sticker and one of the UFR corner stickers.

Looks pretty equal. Possibly just a bit more calculation required for full CLL+1 for were the edge needs to go. Maybe that can helped with a good memory during CP recognition.
 

OreKehStrah

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May 24, 2019
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That definitely helps with recognition. No need to worry about hidden stickers. I guess OLL first recognition would work for the union version as well.

Using that style, recognition comes down to:

Union: OLL > CP > UF edge sticker and or UR edge sticker to determine which of the two algs to use.

Full: OLL > CP > FU edge sticker and one of the UFR corner stickers.

Looks pretty equal. Possibly just a bit more calculation required for full CLL+1 for were the edge needs to go. Maybe that can helped with a good memory during CP recognition.
Yeah I think using unions that use either the UF or UR edge would be nicer for recognition.
 
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