Difference between revisions of "LLEF"
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−  +  {{Substep Infobox  
+  name=LLEF  
+  image=LLEF.png  
+  variants=[[ELL]], [[EOLL]], [[EPLL]]  
+  subgroup=  
+  algs=15  
+  moves=7.87 (Optimal [[HTM]])  
+  purpose=<sup></sup>  
+  * [[Speedsolving]], [[FMC]]  
+  previous=[[F2L cube state]]  
+  next=[[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 '[[ELLnormal ELL]]'. This variation is useful for a 2look 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.  
+  
+  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 ControlPartial 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 3cycles 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===  
+  * [[ELL]]  
+  * [[FMC]]  
+  
+  == External links ==  
+  * [http://www.ai.univparis8.fr/~bh/cube/ Bernard Helmstetter's LL algorithms]  
+  * [http://emsee.110mb.com/Speedcubing/ZZLL/No%20parity.html Michal Hordecki's algorithms for the last 4 corners]  
+  
+  ==Algorithms==  
+  {{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 first alg given for each case is the optimal solution in [[HTMHalf Turn Metric]].  
+  
+  ==All edges oriented (EP) ==  
+  {border="0" width="100%" valign="top" cellpadding="3"  
+  
+  valign="top"  
+    
+  === Adjacent swap (Sune) ===  
+  [[File:LLE OA.jpg]]  
+  
+  {{Alg(y') R' U2 R U R' U R}}  
+  
+    
+  
+  === Opposite swap (TPLL) ===  
+  [[File:LLE OO.jpg]]  
+  
+  {{AlgR' F R' u2 R F' R' u2 R2 F'}}  
+  {{AlgR2 u R2 u' R2 y' R2 u' R2 u R2}}  
+  
+  }  
+  
+  ==Pure flips (EO) ==  
+  
+  {border="0" width="100%" valign="top" cellpadding="3"  
+  
+  valign="top"  
+    
+  === 2flip (Adjacent) ===  
+  [[File:LLE 2AP.jpg]]  
+  
+  {{AlgR' U' R2 B' R' B2 U' B'}}  
+  
+    
+  
+  === 2flip (Opposite) ===  
+  [[File:LLE 2OP.jpg]]  
+  
+  {{Alg(y) R B L' B L B' U B' U' R'}}  
+  
+  valign="top"  
+    
+  
+  === 4flip ===  
+  [[File:LLE 4P.jpg]]  
+  
+  {{AlgR2 L' B R' B L U2 L' B R' L}}  
+  
+    
+  }  
+  
+  ==Adjacent swap==  
+  
+  {border="0" width="100%" valign="top" cellpadding="3"  
+  
+  valign="top"  
+    
+  === Adjacent RF ===  
+  [[File:LLE ASFR.jpg]]  
+  
+  {{Alg(y2) R2 L' B R' B R B2 R' B R' L}}  
+  
+    
+  
+  === Adjacent FL ===  
+  [[File:LLE ASLF.jpg]]  
+  
+  {{AlgF U R U' R' F'}}  
+  
+  valign="top"  
+    
+  
+  === Adjacent LB ===  
+  [[File:LLE ASBL.jpg]]  
+  
+  {{Alg(y) L' B' R B' R' B2 L}}  
+  {{Algr U R' U R U2 r' U'}}  
+  {{Algy r U2 R' U' R U' r' U}}  
+  {{AlgM U M' U2 M U M' U'}}  
+  
+    
+  
+  === Adjacent BR ===  
+  [[File:LLE ASRB.jpg]]  
+  
+  {{Alg(y') B' U' R' U R B}}  
+  
+  valign="top"  
+    
+  
+  === Opposite RF ===  
+  [[File:LLE ASOF.jpg]]  
+  
+  {{Alg(y2) F R U R' U' F'}}  
+  {{Algr U L' U' r' U L U' (x) U}}  
+  
+    
+  
+  === Opposite BR ===  
+  [[File:LLE ASOB.jpg]]  
+  
+  {{AlgF' L' U' L U F}}  
+  
+  valign="top"  
+    
+  
+  === 4flip (A4) ===  
+  [[File:LLE AS4.jpg]]  
+  
+  {{Alg(y) B L U L' U B' U2 B' R B R'}}  
+  
+    
+  }  
+  
+  ==Opposite swap==  
+  
+  {border="0" width="100%" valign="top" cellpadding="3"  
+  
+  valign="top"  
+    
+  === Adjacent (OA) ===  
+  [[File:LLE OSA.jpg]]  
+  
+  {{Alg(y2) B' R' U R B L U' L'}}  
+  
+    
+  
+  === Opposite (OO) ===  
+  [[File:LLE OSO.jpg]]  
+  
+  {{AlgB' R' U R B L' B L B2 U B}}  
+  
+  valign="top"  
+    
+  
+  === 4flip (O4) ===  
+  [[File:LLE OS4.jpg]]  
+  
+  {{AlgR B' R' B U B2 L' B' L U' B'}}  
+  
+    
+  }  
+  
+  [[Category:Acronyms]]  
+  [[Category:3x3x3 last layer substeps]]  
+  [[Category:Algorithms]]  
+  
+  __NOTOC__ 
Latest revision as of 10:22, 26 February 2015


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 2look 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 3cycles 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 doublelayer 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)

Opposite swap (TPLL)

Pure flips (EO)
2flip (Adjacent)

2flip (Opposite)
 
4flip

Adjacent swap
Adjacent RF

Adjacent FL
 
Adjacent LB

Adjacent BR
 
Opposite RF

Opposite BR
 
4flip (A4)

Opposite swap
Adjacent (OA)

Opposite (OO)
 
4flip (O4)
