The following provides a sequence but not necesarily
the shortest sequence. I note that some
permutations have no solution (are not in the
subgroup generated by p).
p=: 3 2 1 0 4 5, 0 4 3 2 1 5,:0 1 5 4 3 2
tab=: 3 : 0
'p q'=. y
p=. p , ,/ {"1/~ p
q=. q , , ,&.>/~ q
b=. ~: p
(b#p) ; < b#q
)
'P Q'=: tab^:_ p;<,&.>0 1 2
solve0=: Q {::~ P i. ]
solve =: solve0 @: <:
solve 1 3 2 6 5 4
1 2 1
solve 5 6 2 1 4 3
0 2
solve 6 5 4 1 2 3
0 1 2
----- Original Message -----
From: Oleg Kobchenko <[EMAIL PROTECTED]>
Date: Monday, June 11, 2007 6:55 pm
Subject: [Jprogramming] 1D Rubik's Cube
> I found an interesting game, as found on Andrew Nikitin's
> MSX-BASIC page http://nsg.upor.net/msx/basic/basic.htm ,
> and I am not sure if its solver has been given as a puzzle.
> Here it goes.
>
> 1D Rubik's Cube is a line of 6 numbers with
> original position:
>
> 1 2 3 4 5 6
>
> which can be rotated in 3 different ways
> in groups of four:
> _______ _______
> (1 2 3 4)5 6 --(0)-> (4 3 2 1)5 6
> _______ _______
> 1(2 3 4 5)6 --(1)-> 1(5 4 3 2)6
> _______ _______
> 1 2(3 4 5 6) --(2)-> 1 2(6 5 4 3)
>
> Given a scrambled line, return the shortest sequence of
> rotations to restore the original position.
>
> Examples:
>
> solve 1 3 2 6 5 4
> 1 2 1
> solve 5 6 2 1 4 3
> 0 2
> solve 6 5 4 1 2 3
> 0 1 2
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