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Re: Pure regex Hamiltonian Circuit solution

by blokhead (Monsignor)
on Oct 13, 2003 at 05:50 UTC ( #298775=note: print w/replies, xml ) Need Help??


in reply to Pure regex Hamiltonian Circuit solution

Here's an updated version using lookaheads to greatly shorten things. Matching time shouldn't change much.
my @E = ([1,3],[1,5],[2,3],[2,4],[2,5],[4,5]); my $V = 5; my $verbose = 1; my @all_edges = map { my $x = $_; map { [$x, $_] } $x+1 .. $V } 1 .. $ +V-1; my $string = (join(' ', 1 .. $V) . "\n") x $V . join(' ', map { join "-", @$_ } @all_edges ) . "\n" . join(' ', map { join "-", @$_ } @E ); my $regex = "^\n" . ".* \\b (\\d+) \\b .* \\n\n" x $V . join("", map { my ($x, $y) = @$_; "(?= .* \\b (?: \\$x-\\$y | \\$y-\\$x ) \\b + ) \n" } @all_edges) . ".*\\n\n" . join("", map { my ($x, $y) = ($_, $_+1); "(?= .* \\b (?: \\$x-\\$y | \\$y-\\$x ) \\b + )\n" } 1 .. ($V-1)) . "(?= .* \\b (?: \\$V-\\1 | \\1-\\$V ) \\b )\n"; print "'$string' =~ /\n$regex\n/x\n" if $verbose; if (my @c = $string =~ /$regex/x) { local $" = " -> "; print "Hamiltonian circuit: [ @c -> $1 ]\n"; } else { print "No Hamiltonian circuit\n"; } __END__ $string = q[ 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1-2 1-3 1-4 1-5 2-3 2-4 2-5 3-4 3-5 4-5 1-3 1-5 2-3 2-4 2-5 4-5 ]; $regex = q[ ^ .* \b (\d+) \b .* \n .* \b (\d+) \b .* \n .* \b (\d+) \b .* \n .* \b (\d+) \b .* \n .* \b (\d+) \b .* \n (?= .* \b (?: \1-\2 | \2-\1 ) \b ) (?= .* \b (?: \1-\3 | \3-\1 ) \b ) (?= .* \b (?: \1-\4 | \4-\1 ) \b ) (?= .* \b (?: \1-\5 | \5-\1 ) \b ) (?= .* \b (?: \2-\3 | \3-\2 ) \b ) (?= .* \b (?: \2-\4 | \4-\2 ) \b ) (?= .* \b (?: \2-\5 | \5-\2 ) \b ) (?= .* \b (?: \3-\4 | \4-\3 ) \b ) (?= .* \b (?: \3-\5 | \5-\3 ) \b ) (?= .* \b (?: \4-\5 | \5-\4 ) \b ) .*\n (?= .* \b (?: \1-\2 | \2-\1 ) \b ) (?= .* \b (?: \2-\3 | \3-\2 ) \b ) (?= .* \b (?: \3-\4 | \4-\3 ) \b ) (?= .* \b (?: \4-\5 | \5-\4 ) \b ) (?= .* \b (?: \5-\1 | \1-\5 ) \b ) ];
There's no more need for repeating the listing of @all_edges so many times. With lookaheads, it only needs to be there once. Same with the listing of @E. This reduces $string to O(V^2).

Because backtracking doesn't happen within lookaheads, I couldn't use lookaheads to select the captured vertices. So the listing of vertices 1 to $V still has to be there $V times.

blokhead

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