#
# Takes a graph and a root element as arguments.
# The graph is a doubled keyed hash, with
#    $graph{a}{b} = x;
# indicating there's an edge from a to b with distance x.
#
# If the graph is supposed to be bidirectional, make sure that
# for all a, b, $graph{a}{b} = $graph{b}{a}.
#
sub dijkstra {
    my $graph = shift;
    my $root = shift;

    my %dist;   # Distance to root element.
    my @todo = [$root, 0];

    {
        my ($to, $distance) = @{shift @todo};
        unless (exists $dist{$to}) {
            #
            # Have not been here
            #
            $dist{$to} = $distance;
            @todo = sort {$$a[1] <=> $$b[1]}
                   @todo,
                    map {[$_, $distance + $$graph{$to}{$_}]} keys %{$$graph{$to}};
        }
    }

    return \%dist;
}