如何在有向图中找到从源到汇的所有路径？

Question

我想找到从源到汇的所有路径。预期：

(3 11 17 24 32 39 45)
(3 11 18 26 33 39 45)
(3 11 18 26 33 40 46)
(3 11 18 26 33 40 47)
(3 11 19 27 33 39 45)
(3 11 19 27 33 40 46)
(3 11 19 27 33 40 47)
(3 11 19 27 34 40 46)
(3 11 19 27 34 40 47)
(6 12 20 27 33 39 45)
(6 12 20 27 33 40 46)
(6 12 20 27 33 40 47)
(6 12 20 27 34 40 46)
(6 12 20 27 34 40 47)

在我的代码中，我知道如何访问每个顶点，但是如何正确记住并组合完整路径？

use 5.028;
use feature 'signatures';
use strictures;
use Graph qw();

my $g = Graph->new(directed => 1);
for my $edge_tuple (qw(
    3-11 6-12 11-17 11-18 11-19 12-20 17-24 18-26 19-27 20-27 24-32 26-33
    27-33 27-34 32-39 33-39 33-40 34-40 39-45 40-46 40-47
)) {
    my ($from, $to) = split '-', $edge_tuple;
    $g->add_edge($from, $to);
}
say join ';', $g->source_vertices;
say join ';', $g->sink_vertices;

sub visit($g, $v, $p) {
    push @$p, $v;
    if ($g->is_sink_vertex($v)) {
        return;
    } else {
        for my $s ($g->successors($v)) {
            visit($g, $s, $p)
        }
    }
}

my $p = [];
for my $v ($g->source_vertices) {
    visit($g, $v, $p);
}
use Data::Dumper; say Dumper $p;

Answer 1

我修改了代码，以将部分路径传递到visit()中，并让visit()从提供的部分路径中返回所有可能的完整路径：

sub visit($g, $path) {
    my $v = $path->[-1];
    if ($g->is_sink_vertex($v)) {
        return $path;
    } else {
        my @more;
        for my $s ($g->successors($v)) {
            push @more, visit($g, [ @$path, $s ])
        }
        return @more;
    }
}

my @p;
for my $v ($g->source_vertices) {
    push @p, visit($g, [$v]);
}
use Data::Dumper; say Dumper @p;

然后可以使用map减少循环：

sub visit($g, $path) {
    my $v = $path->[-1];
    if ($g->is_sink_vertex($v)) {
        return $path;
    } else {
        return map { visit($g, [ @$path, $_ ]) } $g->successors($v);
    }
}

my @p = map { visit($g, [$_]) } $g->source_vertices;