"Shortest" PLL Algs?

Discussion in 'General Speedcubing Discussion' started by qqwref, Oct 14, 2013.

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  1. qqwref

    qqwref Member

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    What are the shortest possible PLL algs, in terms of how long they are when written down? This should be more interesting than just finding move-optimal stuff, and I think there's a lot of room for creativity. The most common algs may not be the shortest!

    To start with, the following notations are OK:
    - [P,Q] is a commutator (that is, P Q P' Q')
    - [P:Q] is a setup move/conjugate (that is, P Q P')
    - (P)n is P repeated n times; parentheses are unnecessary if it's clear what P is
    - Any face or slice moves, rotations, or lowercase moves.
    Also, the algorithm can do the PLL on any face, and you do not have to include any adjustment at the end, or rotations at the very start/end.


    So here's a set of pretty short algs. Think you can do any better? :)
    A: R2[RFR',B2]R2, R2[B2,RFR']R2
    E: (R'UL'D2LU'RU2)2
    F: R'URU'R2F'U'FU[R,F]R2
    G: [RL:U2]yL'UR'U2LU'R, R'UL'U2RU'Ly[RL:U2], L'R'U2LRyLU'RU2L'UR', LU'RU2L'UR'yR'L'U2RL
    H: (M2U)6
    J: R'L'[d2,RUR']RL, [RL:[d2,R'U'R]]
    N: (r'DrU2)5, (rDr'U2)5
    R: R[U2R'U2,UR'F'R]R', R'[U2RU2,U'RBR']R
    T: [R2D':F2][B2D:L2]
    U: M2uMu2MuM2, B2UMU2M'UB2
    V: [F'UBU'F:U][U2,B]
    Y: F2[DR2:U][R'U'R:F2]
    Z: M2uM2D'MS2M'
     
  2. Stefan

    Stefan Member

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    How do you measure the length?
     
  3. qqwref

    qqwref Member

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    Number of characters, or equivalently string length. The length of "(M2U)6" is 6.
     
  4. Stefan

    Stefan Member

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    So my efforts of finding out that "L" is the shortest capital letter in this forum's font were in vain...

    A: L'[F,R'B2R]L (12)
    J: L'[R'd2R,U]L (12)
     
    Last edited: Oct 14, 2013
  5. Ranzha

    Ranzha Friendly, Neighbourhoodly Staff Member

    Ga: [R2F2:[B2,U][B2,D]]
    Just inverse and mirrors for the other HTM-optimal Gs.
     
  6. qqwref

    qqwref Member

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    Well this is embarrassingly obvious, but...
    [RL:U2]yL'UR'U2LU'R => [RL:U2]F'UB'U2FU'B
    R'UL'U2RU'Ly[RL:U2] => R'UL'U2RU'L[BF:U2]
    L'R'U2LRyLU'RU2L'UR' => L'R'U2LRFU'BU2F'UB'
    LU'RU2L'UR'yR'L'U2RL => LU'RU2L'UR'B'F'U2BF
     
  7. Christopher Mowla

    Christopher Mowla Premium Member

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    This is a little off topic: parity algs!

    Adjacent Double Parity
    [r2B'RwB:r(rU2)4] (17)(WCA)

    3 flip which messes one F3L slot and LL (not double parity)
    rU2[BU2B': (U2r)3]r (18)(WCA)

    Opposite Double Parity
    [r2UF2U':r][UF2U,r] (19)(WCA)

    One edge flip (not double parity)
    [F2r2:[F2,U2l]]r[U2,r'] (23)(WCA or SiGN)(Frédérick Badie modified)
    [l2B2:[B'l'B,U2][rB2:l]] (24)(WCA or SiGN)(cmowlaparity)
    [l2B2:[Bl'B',U2][rB2:l]] (24)(WCA)(cmowlaparity's cousin)
    [r2B2:[U2,lU2r'][lF2:r]] (24)(WCA or SiGN)("Standard Alg")
    [l2B2:[U2,rU2l'][rB2:l]] (24)(WCA or SiGN)
    [led:[d,b'2R'b][2Rd:2R']] (25)(SiGN)
    [U2,lU2r'][F2r:F2]r(r2F2)3 (26)(WCA or SiGN)
     
  8. cannon4747

    cannon4747 Member

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    I found this a while ago using commutators and conjugates but idk how to write it down in any other way.

    E = R'D'RLDL'R'D'RU2R'D'RLDL'R'D'R
     
  9. TDM

    TDM Member

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    Yours is (R'D'RLDL'R'D'RU2)2
    Not exactly the same, but similar:
    [R'D'RLDL'R'D'R,U2]

    EDIT:
    [noparse][[RU'L:D2],U2][/noparse]
    Shortest E perm on here.

    EDIT2:
    Similar thing for a short A perm:
    [noparse][[RU'L:D2],U][/noparse]
     
    Last edited: Oct 14, 2013
  10. Stefan

    Stefan Member

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    [noparse][[RU'L:D2],U2][/noparse]
     
  11. TDM

    TDM Member

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    I didn't know you could use those to stop smileys.
     
  12. whauk

    whauk Member

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    Z-perm: (UF2)6M'U2M
    1 charcter shorter than qq :D
     
  13. Renslay

    Renslay Member

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    Supercube centers:

    Rotate the U center with 180 degrees (like U2):
    [[RL:U2]:U]U

    Rotate the U center and L center with 90 degrees (like U and L'):
    [U,MEM']
     
  14. TDM

    TDM Member

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    (L'ULU)5
    (LUL'U)5
    (RUR'U)5
    (R'URU)5
     
  15. Renslay

    Renslay Member

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    Damn. :)

    Playing around, I found an interesting U perm (not the shortest):
    (R2d)12[D2,S]
     
  16. TDM

    TDM Member

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    I first learned the third one when someone at a comp showed it to me, but I do the first one sometimes if I have a cube in one hand. The other 2 are basically the same thing.
     
  17. qqwref

    qqwref Member

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    Haha, that's fine. Very cool stuff!

    Nice, that does save some characters on the E perm (and also: [[RU'L:d2],U] and [[R'UL':d2],U] for J). The A perm is only as good as the one I have though.

    Another short A perm: R[B,[F,R']]R' and inverse.

    And some G perms based on the same idea: [RL:U2][F'UB':d2], [R'UL',d2][BF:U2], L'R'U2LR[FU'B,d2], [LU'R,d2]B'F'U2BF

    Very cool, definitely would not have thought of that.
     
  18. TDM

    TDM Member

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    What about doing this but with fewest letters instead of fewest characters? So A perms ([R2:[B2,[R:F]]] and [R2:[[R:F],B2]]) would count as 4 etc.
     
  19. qqwref

    qqwref Member

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    Thought I'd give this a shot. Obviously in this case inverses and mirrors are the same number of letters, so I don't bother listing them separately.

    [noparse]A: [L:[[R:D2],U']] = 4
    E: [[RU'L:D2],U2] = 5
    F: [R', U][R2:[F',U'][R,F]] = 7
    G: [R2F2:[B2,U][B2,D]] = 6
    H: (M2U)6 = 2
    J: [L':[[R':d2],U]] = 4
    N: (r'DrU2)5 = 4
    R: [R:[[U2:R'],U[R':F']]] = 6
    T: [R2D':F2][B2D:L2] = 6
    U: [R2U':[S',U2]] = 4
    V: [[F'U:B]:U][U2,B] = 6
    Y: F2[DR2:U][[R':U']:F2] = 7
    Z: [M2,U](E2M')2 = 4[/noparse]
     
  20. Christopher Mowla

    Christopher Mowla Premium Member

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    With TDM's suggested metric,

    Here's an algorithm which is one move less than the other algorithms I have already listed for qqwref's metric for the visually pure single dedge flip case:
    [(rU2)2:r(r[U(RwU2)2:U2])2] = 8, where the Rw move includes the central slice on odd cubes,

    ...just in case anyone was interested.
     

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