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Square-1 Parity Algs

blade740

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I'm really just posting this so that I can link to it instead of emailing the algs to everyone.

O: opposite
A: adjacent
N: no swap


AA: /(-3,0)/(-3,0)/(-5,0)/(-2,0)/(4,0)/(-4,0)/(-2,0)/(5,0)/(-3,0)/ (matching bars at UR and DL)
AN: /(3,3)/(-1,0)/(2,0)/(-4,0)/(4,0)/(2,0)/(1,0)/(-3,-3)/ (matching bar at UR)
AO: /(3,3)/(-1,0)/(2,0)/(-4,0)/(4,0)/(2,0)/(-5,0)/(-3,-3)/ (matching bar at UL)
NA: /(-3,-3)/(0,-5)/(-4,-2)/(-4,0)/(-4,0)/(2,-4)/(5,0)/(-3,-3)/ (matching bar at DR)
OA: /(-3,-3)/(0,-5)/(-4,-2)/(-4,0)/(-4,0)/(2,-4)/(-1,0)/(-3,-3)/ (matching bar at DL)
OO: /(3,3)/(1,0)/(4,-2)/(2,-4)/(0,-4)/(3,3)/(3,0)/(3,3)/
ON: /(3,3)/(-1,0)/(-4,2)/(-2,4)/(0,1)/(3,3)/
NO: /(3,3)/(-1,0)/-4,2)/(-2,4))/(0,-5)/(3,3)/

Basically, I recognize parity and corner permutation at the same time. If there is no parity, I do a standard corner permutation alg and continue with a normal vandenbergh solution. If there IS parity, I do the parity alg that corresponds with the corner permutation and then continue with a normal vandenbergh solution. Basically, this means that by learning a few extra CP algs, I can save myself from having to learn half of the EP algs (and the worse half, at that).

Algs generated with Jaap's wonderful sq1optim program.


Oh, bonus: the AA alg is 2gen, and was half of the secret to solving the bandaged square-1.
 
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byu

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bldmaster
#5
I'm going to have to actually use a square-1 to figure out these. I ordered mine off PuzzleProz a few days ago, and I'm still waiting for it to come. Do I need to memorize all of these to solve the Square-1?
 
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#10
I love a bit of square-1 action, and this seems really interesting although I don't quite understand the notation. When referring to Opposite, Adjacent, No Swap, what does it mean? And what does "matching bars" mean? Is a bar a solid colour of 2 corners and an edge aligned on a side? Are matching bars of the same colour?
This method has got me really interested in square-1 again, any help would be great :)
 

blade740

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Recognition for this method is essentially twofold (though you can do both together with practice) First, determine whether or not you have parity. Then, you recognize a corner permutation case (essentially an ortega/guimond PBL case) A is an adjacent swap (like a J perm) O is an opposite corner swap (like a Y perm) N is no swap (like a U perm). Matching bar refers to the 2 corners that are paired up on an adj swap.
 

blade740

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Bump. I updated a few of the algorithms in the original post (namely AO, AN, NO, ON) Thanks to dan and dene for those algs. As a byproduct of generating algs with a solver that can't ignore pieces, I have large lists of algorithms for every case (directly output from jaap's solver) hosted here: http://dl.getdropbox.com/u/1186263/cpparity.rar
They're just text files, open them with notepad or whatever. If you find any algs that are more fingertrick-friendly than the ones I have posted here, let me know. I didn't really try very hard when I picked the original algs, so not all of them are that great.
 
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#15
Sorry for this bump.

I have problems detecting whether I have parity or not. I usually try to visualize the permutations I get but it fails when it comes to O-perms (which seem to have the correct order of the edges in their respective layer but actually are parity cases). How do you go around that?
 
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fswaddle
#16
Sorry for this bump.

I have problems detecting whether I have parity or not. I usually try to visualize the permutations I get but it fails when it comes to O-perms (which seem to have the correct order of the edges in their respective layer but actually are parity cases). How do you go around that?
Do you do lots of 3x3? If you have four edges wrong and it's not a Z or H perm, then it's an O or W perm (W perm has some opposite edges)
 
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#17
I don't know if this is really effective at speed (I'm not fast at sq1 at all) but I recognise the permutation case like a 3x3 case. If the perm on top is a 3x3 perm and the one on bottom is not (or vice versa) then I know I have parity. If both top and bottom have 3x3 perms or neither top nor bottom have 3x3 perms I know I don't have parity.
 
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#18
I don't know if this is really effective at speed (I'm not fast at sq1 at all) but I recognise the permutation case like a 3x3 case. If the perm on top is a 3x3 perm and the one on bottom is not (or vice versa) then I know I have parity. If both top and bottom have 3x3 perms or neither top nor bottom have 3x3 perms I know I don't have parity.
That's like, the only way to do it :p
 

masterofthebass

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#19
I don't know if this is really effective at speed (I'm not fast at sq1 at all) but I recognise the permutation case like a 3x3 case. If the perm on top is a 3x3 perm and the one on bottom is not (or vice versa) then I know I have parity. If both top and bottom have 3x3 perms or neither top nor bottom have 3x3 perms I know I don't have parity.
That's like, the only way to do it :p
I do that in a different way than I do on 3x3 though. I usually do it by looking at blocks. For example, if there is a CEC block, I know that there cannot be another block (except for a j perm) for it not to have parity. On the same note, if there are 2 adj EC blocks, then unless there its a Jperm or Nperm (easy to detect) it has parity. Tricks like this really help me since you don't actually have to see the PLL (although I end up knowing what they are).
 

Dene

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#20
Yea I use some tricks like masterofthebass said. Basically, with time you just get the hang of recognising parity cases just like you recognise PLLs. For some of them you will have heuristics, for others you will have to figure it out with brute force. For example, I have particular trouble distinguishing E perm from what I will call "E parity"; I have to line up the edges to make sure it is one or the other.
 
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