Permutations by swapping: Difference between revisions

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Meanwhile, here's an inductive approach, using negative integers to look left and positive integers to look right:

<lang J>~~bfjt0~~=: _1 - i.

<lang J>bfsjt0=: _1 - i.

lookingat=: 0 >. <:@# <. i.@# + *

next=: | >./@:* | > | {~ lookingat

~~bfjtn~~=: (((] <@, ] + *@{~) | i. next) C. ] * _1 ^ next < |)^:(*@next)</lang>

bfsjtn=: (((] <@, ] + *@{~) | i. next) C. ] * _1 ^ next < |)^:(*@next)</lang>

Here, ~~bfjt0~~ N gives the initial permutation of order N, and ~~bfjtn~~^:M ~~bfjt0M~~ gives the Mth Steinhaus–Johnson–Trotter permutation of order N.

Here, bfsjt0 N gives the initial permutation of order N, and bfsjtn^:M bfsjt0M gives the Mth Steinhaus–Johnson–Trotter permutation of order N. (bf stands for "brute force".)

To convert from the Steinhaus–Johnson–Trotter representation of a permutation to J's representation, use <:@|, or to find J's permutation index of a Steinhaus–Johnson–Trotter representation of a permutation, use A.<:@|

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Example use:

<lang J> ~~bfjtn~~^:(i.!3) bfjt0 3

<lang J> bfsjtn^:(i.!3) bfjt0 3

_1 _2 _3

_1 _3 _2

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_2 3 _1

_2 _1 3

<:@| ~~bfjtn~~^:(i.!3) bfjt0 3

<:@| bfsjtn^:(i.!3) bfjt0 3

0 1 2

0 2 1

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1 2 0

1 0 2

A. <:@| ~~bfjtn~~^:(i.!3) bfjt0 3

A. <:@| bfsjtn^:(i.!3) bfjt0 3

0 1 4 5 3 2</lang>