HI perl monks, I have undirected graph with 57 nodes and 204 linkages. I calculate the shortest path of all nodes with its sub nodes using Dijkstram algorithm, but I couldn't able to print the path of the nodes from a given root. here is how i tried.

########## the dijkstram algorithm#################
sub dijkstra {
    my ($graph, $root) = @_;
    my (%dist, %prev);

    foreach $n (keys %{$graph}) { $dist{$n} = inf; $prev{$n}=$n; }
    # .. except the source
    $dist{$root} = 0;

    # loop while we have unsolved nodes
    # sort unsolved by distance from root
    foreach my $n1 (sort keys %{$graph}) {
        foreach my $n2 (keys %{$graph->{$n1}}) {
            if (($dist{$n2} eq inf)) {
                $dist{$n2} = $dist{$n1} + $graph->{$n1}{$n2};
                $prev{$n2} = $n1;
            }
        }
    }
    return (\%prev, \%dist);
}
######## print the path and the distance for a given node#############
sub printPaths {
    my ($graph, $prev, $dist) = @_;
    my $path;

    foreach $n (keys %{$graph}) {
        my $t = $n;
        $path = $t;
        while ($t ne $root) {
            $t = $prev->{$t}; $path = "$t -> " . $path;
        }
        print "$n\t$dist->{$n}\t$path\n";
    }
}
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the problem occurs on the while loop. when it gets a node that doesn't have the same root and when the previous node always returns the same node. please help me or give me any suggestion. thanks