Difference between revisions of "LLEF"

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:'''Last Layer Edges First'''
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{{Substep Infobox
The '''ELL''' <small>(Edges of the Last Layer)</small> that ignores corners is easier to solve, it uses both lesser moves and has lesser cases than what is the '[[ELL|normal ELL]]'. This variation is useful for a 2-look method that solves corners last. But this corner method (sub group of [[ZBLL]]) is not in use for speed, this because of two reasons, it has twice the number of cases of [[CLL]] and the [[algorithm]]s that solves them are mostly long (the worst LL case of them all is in this group, it needs 16 [[HTM]] turns optimally). Another backdraw is that recognition for solving the edges before the corners is not so easy, you have to [[AUF]] to have a chance, sometimes even repeated AUFs.
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|name=LLEF
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|image=LLEF.png
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|variants=[[ELL]], [[EOLL]], [[EPLL]]
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|subgroup=
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|algs=15
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|moves=7.87 (Optimal [[HTM]])
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|purpose=<sup></sup>
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* [[Speedsolving]], [[FMC]]
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|previous=[[F2L cube state]]
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|next=[[LL:EO+EP cube state]]
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}}
  
It can however be useful for [[FMC]]. LLEF has a low average optimal solution length of 7.87, while for the last four corners it is 11.73 (a half move more than optimal [[PLL]]). Both of these can however be lowered. One can quite often choose a inversion/mirror version of an alg to solve the same LLEF situation thus increasing one's chances of cancelling move and/or getting a better corner case. [[Partial edge control]] can also be used to avoid the cases with four flipped edges. The corners can in turn be solved more efficiently with inserted corner 3-cycles rather than at the very end of the solution.
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'''LLEF''' (Last Layer Edges First) is a variation of [[ELL]] (Edges of the Last Layer) that ignores corners is easier to solve; it uses both fewer moves and has fewer cases than what is the '[[ELL|normal ELL]]'. This variation is useful for a 2-look method that solves corners last (see [[L4C]]). But L4C is not in use for speed solving, because of two reasons, it has twice the number of cases of [[CLL]] and the [[algorithm]]s that solve them are mostly long (the worst LL case of all is in this group, it needs 16 turns optimally ([[HTM]])). Another backdraw is that recognition for solving the edges before the corners is not so easy. If you don't have a system for colour recognition you have to [[AUF]] to have a chance, sometimes even repeated AUFs.
  
Solving ELL first is 15 cases.
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LLEF can also be useful for a [[3LLL]] method known as [[BLL]]. This method has a total of 24 algorithms and an average total of 27 moves.
  
===See also:===
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It can however be useful for [[FMC]]. LLEF has a low average optimal solution length of 7.87, while for the last four corners it is 11.73 (a half move more than optimal [[PLL]]). Both of these can however be lowered. One can quite often choose a inversion/mirror version of an alg to solve the same LLEF situation thus increasing one's chances of cancelling moves and/or getting a better corner case. [[Partial Edge Control|Partial edge control]] can also be used to avoid the cases with four flipped edges. The corners can in turn be solved more efficiently with inserted corner 3-cycles rather than at the very end of the solution.
 +
 
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Solving ELL first is 15 cases from a group of totally 48, i.e. a skip of this step occures 1:48 times, skip to [[EP]] only occures 1:8 times and skip to pure [[EO]] occures 1:6 times.
 +
 
 +
===See also===
 
* [[ELL]]
 
* [[ELL]]
 +
* [[FMC]]
  
=Algorithms=
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== External links ==
Note that all of these algorithms are written in the Western [[notation]], where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z.
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* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's LL algorithms]
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* [http://emsee.110mb.com/Speedcubing/ZZLL/No%20parity.html Michal Hordecki's algorithms for the last 4 corners]
  
<strong>Click on an algorithm (not the camera icon) to watch an animation of it.</strong>
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==Algorithms==
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{{Algnote}}
  
 
The images have corners solved in darker colours, this works as a guide for those who don't know the colour sheme or is using something diffrent from this. For all other reasons you can ignore the corners.
 
The images have corners solved in darker colours, this works as a guide for those who don't know the colour sheme or is using something diffrent from this. For all other reasons you can ignore the corners.
 +
 +
The first alg given for each case is the optimal solution in [[HTM|Half Turn Metric]].
  
 
==All edges oriented (EP) ==
 
==All edges oriented (EP) ==
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|-valign="top"
 
|-valign="top"
 
|
 
|
=== Adjacent swap ===
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=== Adjacent swap (Sune) ===
 
[[File:LLE OA.jpg]]
 
[[File:LLE OA.jpg]]
  
{{Alg|y' R'U2RUR'UR}}
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{{Alg|(y') R' U2 R U R' U R}}
  
 
|
 
|
  
=== Opposite swap===
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=== Opposite swap (T-PLL) ===
 
[[File:LLE OO.jpg]]
 
[[File:LLE OO.jpg]]
  
{{Alg|y L'BL'D2RF'R'D2L2B'}}
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{{Alg|R' F R' u2 R F' R' u2 R2 F'}}
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{{Alg|R2 u R2 u' R2 y' R2 u' R2 u R2}}
  
 
|}
 
|}
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[[File:LLE 2AP.jpg]]
 
[[File:LLE 2AP.jpg]]
  
{{Alg|R'U'R2B'R'B2U'B'}}
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{{Alg|R' U' R2 B' R' B2 U' B'}}
  
 
|
 
|
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[[File:LLE 2OP.jpg]]
 
[[File:LLE 2OP.jpg]]
  
{{Alg|y RBL'BLUB'U'R'}}
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{{Alg|(y) R B L' B L B' U B' U' R'}}
  
 
|-valign="top"
 
|-valign="top"
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[[File:LLE 4P.jpg]]
 
[[File:LLE 4P.jpg]]
  
{{Alg|R2L'BR'BLU2L'B R'L}}
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{{Alg|R2 L' B R' B L U2 L' B R' L}}
  
 
|
 
|
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[[File:LLE ASFR.jpg]]
 
[[File:LLE ASFR.jpg]]
  
{{Alg|y2 R2L'BR'BRB2R'BR'L}}
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{{Alg|(y2) R2 L' B R' B R B2 R' B R' L}}
  
 
|
 
|
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[[File:LLE ASLF.jpg]]
 
[[File:LLE ASLF.jpg]]
  
{{Alg|FURU'R'F'}}
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{{Alg|F U R U' R' F'}}
  
 
|-valign="top"
 
|-valign="top"
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[[File:LLE ASBL.jpg]]
 
[[File:LLE ASBL.jpg]]
  
{{Alg|y L'B'RB'R'B2L}}
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{{Alg|(y) L' B' R B' R' B2 L}}
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{{Alg|r U R' U R U2 r' U'}}
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{{Alg|y r U2 R' U' R U' r' U}}
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{{Alg|M U M' U2 M U M' U'}}
  
 
|
 
|
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[[File:LLE ASRB.jpg]]
 
[[File:LLE ASRB.jpg]]
  
{{Alg|y' B'U'R'URB}}
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{{Alg|(y') B' U' R' U R B}}
  
 
|-valign="top"
 
|-valign="top"
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[[File:LLE ASOF.jpg]]
 
[[File:LLE ASOF.jpg]]
  
{{Alg|y2 FRUR'U'F'}}
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{{Alg|(y2) F R U R' U' F'}}
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{{Alg|r U L' U' r' U L U' (x) U}}
  
 
|
 
|
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[[File:LLE ASOB.jpg]]
 
[[File:LLE ASOB.jpg]]
  
{{Alg|F'L'U'LUF}}
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{{Alg|F' L' U' L U F}}
  
 
|-valign="top"
 
|-valign="top"
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[[File:LLE AS4.jpg]]
 
[[File:LLE AS4.jpg]]
  
{{Alg|y' BLUL'B'U2B'RBR'}}
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{{Alg|(y) B L U L' U B' U2 B' R B R'}}
  
 
|
 
|
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[[File:LLE OSA.jpg]]
 
[[File:LLE OSA.jpg]]
  
{{Alg|y2 B'R'URBLU'L'}}
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{{Alg|(y2) B' R' U R B L U' L'}}
  
 
|
 
|
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[[File:LLE OSO.jpg]]
 
[[File:LLE OSO.jpg]]
  
{{Alg|B'R'URBL'BLB2UB}}
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{{Alg|B' R' U R B L' B L B2 U B}}
  
 
|-valign="top"
 
|-valign="top"
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[[File:LLE OS4.jpg]]
 
[[File:LLE OS4.jpg]]
  
{{Alg|RB'R'BUB2L'B'LU'B'}}
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{{Alg|R B' R' B U B2 L' B' L U' B'}}
  
 
|
 
|
 
|}
 
|}
  
 
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[[Category:Acronyms]]
[[Category:Cubing Terminology]]
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[[Category:3x3x3 last layer substeps]]
[[Category:Abbreviations and Acronyms]]
 
[[Category:Methods]]
 
[[Category:3x3x3 Methods]]
 
[[Category:Last Layer Methods]]
 
 
[[Category:Algorithms]]
 
[[Category:Algorithms]]
[[Category:Sub Steps]]
 
  
 
__NOTOC__
 
__NOTOC__

Latest revision as of 10:22, 26 February 2015

LLEF
LLEF.png
Information
Proposer(s): unknown
Proposed: unknown
Alt Names: none
Variants: ELL, EOLL, EPLL
Subgroup:
No. Algs: 15
Avg Moves: 7.87 (Optimal HTM)
Purpose(s):
Previous state: F2L cube state
Next state: LL:EO+EP cube state

F2L cube state -> LLEF step -> LL:EO+EP cube state


The LLEF step is the step between the F2L cube state and the LL:EO+EP cube state.

LLEF (Last Layer Edges First) is a variation of ELL (Edges of the Last Layer) that ignores corners is easier to solve; it uses both fewer moves and has fewer cases than what is the 'normal ELL'. This variation is useful for a 2-look method that solves corners last (see L4C). But L4C is not in use for speed solving, because of two reasons, it has twice the number of cases of CLL and the algorithms that solve them are mostly long (the worst LL case of all is in this group, it needs 16 turns optimally (HTM)). Another backdraw is that recognition for solving the edges before the corners is not so easy. If you don't have a system for colour recognition you have to AUF to have a chance, sometimes even repeated AUFs.

LLEF can also be useful for a 3LLL method known as BLL. This method has a total of 24 algorithms and an average total of 27 moves.

It can however be useful for FMC. LLEF has a low average optimal solution length of 7.87, while for the last four corners it is 11.73 (a half move more than optimal PLL). Both of these can however be lowered. One can quite often choose a inversion/mirror version of an alg to solve the same LLEF situation thus increasing one's chances of cancelling moves and/or getting a better corner case. Partial edge control can also be used to avoid the cases with four flipped edges. The corners can in turn be solved more efficiently with inserted corner 3-cycles rather than at the very end of the solution.

Solving ELL first is 15 cases from a group of totally 48, i.e. a skip of this step occures 1:48 times, skip to EP only occures 1:8 times and skip to pure EO occures 1:6 times.

See also

External links

Algorithms

Note that all of these algorithms are written in the Western notation, where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z. (how to add algorithms)

Click on an algorithm (not the camera icon) to watch an animation of it.

The images have corners solved in darker colours, this works as a guide for those who don't know the colour sheme or is using something diffrent from this. For all other reasons you can ignore the corners.

The first alg given for each case is the optimal solution in Half Turn Metric.

All edges oriented (EP)

Adjacent swap (Sune)

LLE OA.jpg

Speedsolving Logo tiny.gif Alg (y') R' U2 R U R' U R


Opposite swap (T-PLL)

LLE OO.jpg

Speedsolving Logo tiny.gif Alg R' F R' u2 R F' R' u2 R2 F'
Speedsolving Logo tiny.gif Alg R2 u R2 u' R2 y' R2 u' R2 u R2


Pure flips (EO)

2-flip (Adjacent)

LLE 2AP.jpg

Speedsolving Logo tiny.gif Alg R' U' R2 B' R' B2 U' B'


2-flip (Opposite)

LLE 2OP.jpg

Speedsolving Logo tiny.gif Alg (y) R B L' B L B' U B' U' R'


4-flip

LLE 4P.jpg

Speedsolving Logo tiny.gif Alg R2 L' B R' B L U2 L' B R' L


Adjacent swap

Adjacent RF

LLE ASFR.jpg

Speedsolving Logo tiny.gif Alg (y2) R2 L' B R' B R B2 R' B R' L


Adjacent FL

LLE ASLF.jpg

Speedsolving Logo tiny.gif Alg F U R U' R' F'


Adjacent LB

LLE ASBL.jpg

Speedsolving Logo tiny.gif Alg (y) L' B' R B' R' B2 L
Speedsolving Logo tiny.gif Alg r U R' U R U2 r' U'
Speedsolving Logo tiny.gif Alg y r U2 R' U' R U' r' U
Speedsolving Logo tiny.gif Alg M U M' U2 M U M' U'


Adjacent BR

LLE ASRB.jpg

Speedsolving Logo tiny.gif Alg (y') B' U' R' U R B


Opposite RF

LLE ASOF.jpg

Speedsolving Logo tiny.gif Alg (y2) F R U R' U' F'
Speedsolving Logo tiny.gif Alg r U L' U' r' U L U' (x) U


Opposite BR

LLE ASOB.jpg

Speedsolving Logo tiny.gif Alg F' L' U' L U F


4-flip (A4)

LLE AS4.jpg

Speedsolving Logo tiny.gif Alg (y) B L U L' U B' U2 B' R B R'


Opposite swap

Adjacent (OA)

LLE OSA.jpg

Speedsolving Logo tiny.gif Alg (y2) B' R' U R B L U' L'


Opposite (OO)

LLE OSO.jpg

Speedsolving Logo tiny.gif Alg B' R' U R B L' B L B2 U B


4-flip (O4)

LLE OS4.jpg

Speedsolving Logo tiny.gif Alg R B' R' B U B2 L' B' L U' B'