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Re: Graph labeling problem

by vr (Curate)
on Feb 19, 2022 at 19:04 UTC ( #11141493=note: print w/replies, xml ) Need Help??


in reply to Graph labeling problem

If solution is thought of as symmetric matrix with all-unique elements (i.e. "edge labels") per row (and therefore, per column) and crossed-out dummy diagonal, then quite formal algorithm to build it could be as follows. Code is not pretty, at least I hope I streamlined it enough after couple of, even uglier, attempts.

use strict; use warnings; use feature 'say'; use constant LETTERS => join '', 'A'..'Z', 'a'..'z'; # template use constant N => 51; # number of "e +dges" die if not N % 2 # (1) prohibit odd nodes number or N > 51; # (2) "template" limitation say '_' . substr LETTERS, 0, N; my $last = substr LETTERS, N - 1, 1; # "collect" last line here for ( 1 .. N - 1 ) { my $s = substr LETTERS, 0, N; my $sfx = substr $s, 0, $_ - 1, ''; $s .= $sfx; # rotate left $sfx = substr $s, $_, 1, '_'; $s .= $sfx; # ...& append replaced diagona +l item say $s; $last .= substr $s, -1; } say $last . '_'; __END__

Extended 2:53 2/20/22: now here's formal generation code for both odd/even number of "edges", at expense of introducing additional "edge label" (a star) in latter case:

use strict; use warnings; use feature 'say'; use constant LETTERS => join '', 'A'..'Z', 'a'..'z'; use constant N => 12; say '_' . substr LETTERS, 0, N; my $last = substr LETTERS, N - 1, 1; for ( 1 .. N - 1 ) { my $s = substr LETTERS, 0, N; my $sfx = substr $s, 0, $_ - 1, ''; $s .= '*' unless N % 2; $s .= $sfx; $sfx = substr $s, $_, 1, '_'; $s .= $sfx if N % 2; say $s; $last .= substr $s, -1; } say $last . '_'; __END__ _ABCDEFGHIJKL A_CDEFGHIJKL* BC_EFGHIJKL*A CDE_GHIJKL*AB DEFG_IJKL*ABC EFGHI_KL*ABCD FGHIJK_*ABCDE GHIJKL*_BCDEF HIJKL*AB_DEFG IJKL*ABCD_FGH JKL*ABCDEF_HI KL*ABCDEFGH_J L*ABCDEFGHIJ_

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