Difference between revisions of "CPLS"

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{{Method Infobox
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{{Substep Infobox
 
|name=CPLS
 
|name=CPLS
 
|image=
 
|image=
 
|proposers=[[Baian Liu]], ?, ?
 
|proposers=[[Baian Liu]], ?, ?
 
|year=2009?
 
|year=2009?
|steps=1
+
|subgroup=
|algs=26
+
|algs=
|moves=~10
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|moves=9.1
 
|purpose=<sup></sup>
 
|purpose=<sup></sup>
 
* [[Speedsolving]]
 
* [[Speedsolving]]
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}}
 
}}
  
'''CPLS''' (short for '''Corner Permutation and Last Slot''') is a substep used to solve the final F2L corner (usually DFR) and permute the last-layer corners while preserving the corresponding F2L edge and [[EOLL]]. If used when only the last F2L corner, [[EPLL]], [[CPLL]], and [[COLL]] remain, CPLS leaves just [[EPLL]] and [[COLL]], which may be solved in [[2-gen]]erator. Although seemingly hard to recognize, CPLS can be very beneficial, especially for [[one-handed]] solvers if fast 2-generator algorithms are used.
+
'''CPLS''' (short for '''Corner Permutation and Last Slot''') is a substep used to solve the last F2L slot (usually FR) and [[CP|permute the last layer corners]] while preserving [[EO]]. [[CPLS]] leaves the solver with a [[2-gen]] last layer, which may be solved in one look using [[2GLL]] (84 algs) or in two using [[OCLL]]+[[EPLL]] (11 algs).
  
A two-step solution to [[EPLL]] and [[COLL]] requires only 11 algorithms: 7 for [[OCLL]], which leaves 4 [[EPLL]] cases. One-step solution, known as [[2GLL]], has 84 cases. Note that this is also referred to as [[ZZ-d]].
+
Although seemingly hard to recognize, CPLS can be very beneficial, especially for [[one-handed]] solvers if fast 2-generator algorithms are used.
  
 
== History ==
 
== History ==
CPLS was proposed by [[Baian Liu]] in 2009. (who else?)
+
CPLS was proposed by [[Baian Liu]] in 2009. The name initially only referred to the [[CPLC]] subset which solves the F2L corner + CP.
  
== Learning Approach ==
+
However, CPLS here refers to solving the last F2L ''pair'' + CP because the LS suffix in cubing often indicates the last pair being solved (compare [[ZBLS]],[[OLS]], [[VLS]], [[WVLS]] etc.) and thus prevents confusion for people unfamiliar with CPLS. If one wants to clearly distinguish between the "original CPLS" and the "new CPLS", they can be referred to as CPLC and Full CPLS, respectively.
CPLS is naturally divided into the subsets - +, O, I, Im, and C, the same classification used for [[CLS]]. The first three sets have 6 algorithms each, the next two have 3 each, and the final set has only 2. One recommended order, for ease of learning and recognition, is C, O, I, Im, -, +.
 
  
== Recognition ==
+
== Subsets ==
Although the seemingly difficult recognition may appear to be a possible disadvantage of CPLS, the following system due to [[Stachu Korick]] works well.
+
Full CPLS is grouped into subsets depending on the F2L case they solve and then by their corner permutation.
 +
 
 +
=== Naming by CP case ===
 +
Below, only the subsets for the individual F2L cases are listed. The naming for the different CPs of each F2L case is obtained by adding the following F2L letters to the subset, depending on the CP of the U layer corners.
 +
 
 +
{|border="0" width="100%" valign="top" cellpadding="3"
 +
|-valign="top"
 +
|
 +
 
 +
==== S ====
 +
[[File:CP_S.png]]
 +
 
 +
Solved CP
 +
|
 +
 
 +
==== D ====
 +
[[File:CP_D.png]]
 +
 
 +
Diagonal swap
 +
|
 +
 
 +
==== R ====
 +
[[File:CP_R.png]]
 +
 
 +
Adjacent swap on R
 +
|
 +
 
 +
==== B ====
 +
[[File:CP_B.png]]
 +
 
 +
Adjacent swap on B
 +
|
 +
 
 +
==== L ====
 +
[[File:CP_L.png]]
 +
 
 +
Adjacent swap on L
 +
|
 +
 
 +
==== F ====
 +
[[File:CP_F.png]]
 +
 
 +
Adjacent swap on F
 +
|}
  
# [[AUF]] the last F2L corner to URF, and note the group (O etc).
+
=== Naming by F2L case ===
# For each of the three U-layer corners, locate the sticker clockwise from its U-layer sticker. This is best done in a fixed order (say UFL, UBL, UBR).
+
==== CPLC ====
# Pretend that the face containing the each sticker is of the same color. The required corner permutation is the permutation of the corresponding faces necessary to regain the standard color scheme.
+
CPLC, the "original CPLS", stands for Corner Permutation Last Corner and solves the last LL corner and CP. It consists of 26 algorithms and is grouped into the following six subsets depending on the F2L corner, which is the same classification that is used for [[CLS]]:
  
'''Scramble:''' x R' U R U' R' U R U' R' U R U' x' (yellow on top, orange in front)
+
{|border="0" width="100%" valign="top" cellpadding="3"
 +
|-valign="top"
 +
|
  
The last F2L corner is already at URF. This is an O case. The stickers clockwise from U-layer (yellow) stickers are at FLU (red), LUB (green), BRU (orange). Pretending that F = red, L = green, and B = orange, the required permutation swaps F and B, represented by FLU and BRU corners. Thus we want O with diagonal swap (both diagonal swaps have the same effect), which is x (U R' U' R)*3 x'. We may write this case as [O BLF], meaning the true color of the B face is on F, that of L on L, and F on B.
+
===== C =====
 +
[[File:F2L37.png]]
 +
|
  
== Example Solves ==
+
===== I =====
This recognition method is best illustrated with example solves. Standard color scheme is assumed throughout. Scramble with white on top (U) and green in front (F). Notes in square brackets by [[Stachu Korick]].
+
[[File:F2L39.png]]
 +
|
  
'''Scramble 1:''' D' B' D2 F2 R F' L' R B L' F' U' R' B F2 U R2 D L2 D2 U' B R' F2 D'
+
===== Im =====
 +
[[File:F2L40.png]]
 +
|
  
A Petrus approach
+
===== - =====
2x2x2: x2 D B' R' D2 L2 (5/5)
+
[[File:F2L33.png]]
2x2x3: x' y D R D' U' L' U L (7/12) [Tthis sets up for an Im case later on]
+
|
EO: y U M' U M (4/16)
 
F2L: x y U2 R' U' R U R' U' R2 U2 R' (10/26) [ewww]
 
CPLS (Im FBL): y2 U R' F2 R D' L' U2 L' U' L2 D (11/37)
 
2GLL (Pi Ua1): y (y) R U2 R2 U2 R U R2 U R2 U' R2 U2 R' U2 R(16/53)
 
AUF: U2 (1/54)
 
  
 +
===== + =====
 +
[[File:F2L34.png]]
 +
|
  
'''Scramble 2:''' L2 F' L2 F L' D B D2 U2 L2 D L' R B' L2 U B2 R2 D2 R B2 D U2 B' F'
+
===== O =====
 +
[[File:F2L32.png]]
 +
|}
  
A RH OH ZZ approach
+
==== CPLE ====
EOCross: L B' R' U D F R D R' D R' (11/11)
+
[[File:F2L25.png]]
BL slot: U2 R U R' L U L' (7/18)
+
CPLE stands for Corner Permutation Last Edge and solves the last F2L edge and CP. It only covers F2L case 25 and consists of only 6 algorithms.
FL slot: L2 U2 L U L' U L2 (7/25)
 
BR slot: U R' U' R U' R' U R (8/33)
 
FR edge: R U R' (3/36) [It kills me not to do CLS for this case :(]
 
CPLS setup: U2 (1/37)
 
CPLS (O): y U2 z' U L' D2 L U' L' D2 z (8/45)
 
2GLL (T Ub2): z' U L2 U' L' U L' U' L U L U' L U L2 U' (15/60)
 
AUF: L2 (1/61, or 57 with cancellations)
 
  
 +
== Recognition ==
 +
The different CPLS cases can be recognized by putting the F2L corner into one position and then comparing the stickers of the corners which can be seen. This system uses the relationships same, opposite and adjacent, which is similar to standard [[CxLL]] recognition. A more in-depth guide for this recognition can be found [https://docs.google.com/spreadsheets/d/1ArN5Ya43kJH4KlQHBPye_vzyRLZh_NA8N0u5voZgAgw/ here].
  
'''Scramble 3:''' L' R' B F U B2 D2 F2 L F2 D U' B' U D2 F2 B L2 R2 B U2 B' D2 U2 R
+
== Example Solves ==
 +
The following [[ZZ-d]] solve by [[raven]] shows the method in action:
  
A CFOP approach
+
  Scramble: F' U R2 U' R2 U' B2 D2 B2 U R2 F2 L2 B L' D R2 B2 L2 U
Cross: x2 F D L2 U2 L F' (6/6)
+
 
BL slot: F' U2 F L U' L' (6/12)
+
  x2
FR slot: U R U2 R' U R' F R F' (9/21)
+
  B' F' R F D R' B2 U' L2 U2 L2 U' L // XXEOCross
BR slot: U' R' U2 R2 B R B' (7/28)
+
  U' L U L' // F2L-1
ELS setup: y U (1/29)
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  U' D R' U2 R U' R' U' R D' // CPLS
ELS: R U' R' F' U2 F (6/35)
+
  U R' U' R U R U2 R' U' R' U R U' R U' R' U2 // 2GLL
CPLS (+): U' U' y R' U L' U' R U L (9/44)
 
2GLL (Pi Ub3): y' (y) R U2 R2 U' R' U R U' R' U' R' U' R' U2 R U2 (15/59, or 56 with cancellations)
 
  
 
== See also ==
 
== See also ==
 
* [[2GLL]]
 
* [[2GLL]]
* [[CLS]]
+
* [[2-gen]]
 
* [[ZZ-d]]
 
* [[ZZ-d]]
* [[ELS]]
+
* [[One-Handed Solving]]
 
* [[Advanced F2L]]
 
* [[Advanced F2L]]
  
 
== External links ==
 
== External links ==
 +
* [https://docs.google.com/spreadsheets/d/1ArN5Ya43kJH4KlQHBPye_vzyRLZh_NA8N0u5voZgAgw Full CPLS + Recognition sheet]
 
* [https://sites.google.com/site/devastatingspeed/3x3x3/cpls Baian Liu's Original site]
 
* [https://sites.google.com/site/devastatingspeed/3x3x3/cpls Baian Liu's Original site]
 
* [http://www.speedsolving.com/forum/showthread.php?p=454801#post454801 SpeedSolving CPLS+2GLL thread]
 
* [http://www.speedsolving.com/forum/showthread.php?p=454801#post454801 SpeedSolving CPLS+2GLL thread]
 
* [http://db.tt/KIRzYvL Stachu Korick's printable OH algs]
 
* [http://db.tt/KIRzYvL Stachu Korick's printable OH algs]
  
 
[[Category:Advanced Methods]]
 
 
[[Category:Experimental methods]]
 
[[Category:Experimental methods]]
 
+
[[Category:Acronyms]]
[[Category:Abbreviations]]
+
[[Category:3x3x3 last slot substeps]]
[[Category:3x3x3 substeps]]
 

Revision as of 03:17, 13 August 2022

CPLS
[[Image:]]
Information
Proposer(s): Baian Liu, ?, ?
Proposed: 2009?
Alt Names: none
Variants: none
Subgroup:
No. Algs:
Avg Moves: 9.1
Purpose(s):


CPLS (short for Corner Permutation and Last Slot) is a substep used to solve the last F2L slot (usually FR) and permute the last layer corners while preserving EO. CPLS leaves the solver with a 2-gen last layer, which may be solved in one look using 2GLL (84 algs) or in two using OCLL+EPLL (11 algs).

Although seemingly hard to recognize, CPLS can be very beneficial, especially for one-handed solvers if fast 2-generator algorithms are used.

History

CPLS was proposed by Baian Liu in 2009. The name initially only referred to the CPLC subset which solves the F2L corner + CP.

However, CPLS here refers to solving the last F2L pair + CP because the LS suffix in cubing often indicates the last pair being solved (compare ZBLS,OLS, VLS, WVLS etc.) and thus prevents confusion for people unfamiliar with CPLS. If one wants to clearly distinguish between the "original CPLS" and the "new CPLS", they can be referred to as CPLC and Full CPLS, respectively.

Subsets

Full CPLS is grouped into subsets depending on the F2L case they solve and then by their corner permutation.

Naming by CP case

Below, only the subsets for the individual F2L cases are listed. The naming for the different CPs of each F2L case is obtained by adding the following F2L letters to the subset, depending on the CP of the U layer corners.

S

CP S.png

Solved CP

D

CP D.png

Diagonal swap

R

CP R.png

Adjacent swap on R

B

CP B.png

Adjacent swap on B

L

CP L.png

Adjacent swap on L

F

CP F.png

Adjacent swap on F

Naming by F2L case

CPLC

CPLC, the "original CPLS", stands for Corner Permutation Last Corner and solves the last LL corner and CP. It consists of 26 algorithms and is grouped into the following six subsets depending on the F2L corner, which is the same classification that is used for CLS:

C

F2L37.png

I

F2L39.png

Im

F2L40.png

-

F2L33.png

+

F2L34.png

O

F2L32.png

CPLE

F2L25.png CPLE stands for Corner Permutation Last Edge and solves the last F2L edge and CP. It only covers F2L case 25 and consists of only 6 algorithms.

Recognition

The different CPLS cases can be recognized by putting the F2L corner into one position and then comparing the stickers of the corners which can be seen. This system uses the relationships same, opposite and adjacent, which is similar to standard CxLL recognition. A more in-depth guide for this recognition can be found here.

Example Solves

The following ZZ-d solve by raven shows the method in action:

 Scramble: F' U R2 U' R2 U' B2 D2 B2 U R2 F2 L2 B L' D R2 B2 L2 U
 
 x2
 B' F' R F D R' B2 U' L2 U2 L2 U' L // XXEOCross
 U' L U L' // F2L-1
 U' D R' U2 R U' R' U' R D' // CPLS
 U R' U' R U R U2 R' U' R' U R U' R U' R' U2 // 2GLL

See also

External links