The stupid question is the question not asked  
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Transitive closureby larsen (Parson) 
on Sep 10, 2001 at 16:19 UTC ( #111427=snippet: print w/ replies, xml )  Need Help?? 
#!/usr/bin/perl
# Transitive closure of a directed graph
use strict;
use Math::MatrixReal;
my $n = 4; # Matrix' size
my $graph = Math::MatrixReal>new_from_string( <<'MATRIX' );
[ 0 1 0 1 ]
[ 0 0 1 0 ]
[ 0 0 0 0 ]
[ 1 1 0 0 ]
MATRIX
my $sum = $graph>shadow();
my $p = $graph>shadow();
$p>one();
# "One Ring to rule them all, One Ring to find them..."
# Sum of A^i, for i = 0..n1 (A is the adjacency matrix of our graph)
foreach (0 .. ($n  1)) {
$p = $p * $graph;
$sum = $sum + $p;
}
# Finished.
# Now we print every couple (i, j) such that
# there's a path from i to j.
foreach my $i (1..$n) {
foreach my $j (1..$n) {
print "There's a path from $i to $j.\n" if $sum>element( $i,
+$j );
}
}
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