Perl saved a lady.
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1) A reporter hears that a lady named "Fukashigi" is in trouble, unable to solve a combinatorial problem involving counting paths on a grid. 2) The reporter implements an algorithm called Simpath in Perl to efficiently count the number of paths and solves a 9x9 grid problem in seconds, over 1 million times faster than brute force. 3) By using techniques like binary decision diagrams and sharing computation between identical subproblems, the algorithm is able to compress the exponential search space into a polynomial solution. This demonstrates the importance of algorithms for tackling combinatorial explosion.
![my %mate = %{$node->{mate}};
my $next_grid_node = $grid_edge->[1];
Binary Decision diagram
$mate{$next_grid_node} = $next_grid_node unless exists $mate{$next_grid_node};
{mate => %mate};
}
sub high_node($$) { 1
my ($node, $grid_edge) = @_;
s
２
my %mate = %{$node->{mate}};
１ 2 2
my @grid_nodes;
３ g
# loop detection
return undef if ($mate{$grid_edge->[0]} / '') eq $grid_edge->[1];
/
3 3
for my $grid_node ($grid_edge->[0], $grid_edge->[1]) {
3 3
if (! exists $mate{$grid_node}) {
push @grid_nodes, $grid_node; # That's the new grid node
} elsif (! defined $mate{$grid_node}) { # Have already connected :/
return undef;
} else {
4 4 4
push @grid_nodes, $mate{$grid_node};
4
$mate{$grid_node} = undef; # Connect to new grid node
4 4 4 4
}
}
$mate{$grid_nodes[0]} = $grid_nodes[1];
$mate{$grid_nodes[1]} = $grid_nodes[0];
・・・・・・
{mate => %mate};](https://image.slidesharecdn.com/3-120928090103-phpapp02/85/Perl-saved-a-lady-27-320.jpg)
Perl saved a lady.
- 1. Perlでおねえさんを 救った話 Perl saved a lady 2012.9.28 @hiratara
- 2. I’m a reporter of gihyo.jp
- 3. I heard a rumor that a lady is in trouble.
- 4. “フカシギ”のおねえさん She’s in trouble.
- 6. The question seems easy :)
- 8. For 10 by 10, it takes 250,000 years
- 11. I wish to help her!!!!
- 12. Look the FreakOut Sticker.
- 13. 50ms, or die
- 14. Speed up computation
- 15. Counting ways with perl ZBDD speeds up counting Knuth introduced simpath algorithm I implemented Algorithm::Simpath
- 16. Count ways in 9 by 9
- 17. 6 years
- 18. use strict; use warnings; use Algorithm::Simpath; use Algorithm::Simpath::GridMaker; my $edges = create_edges(9, 9); my $zdd = solve( start => '0,0', goal => "9,9", edges => $edges, ); print $zdd->count, "n";
- 19. % time perl -Ilib teacher99.pl 4.10442087026325e+19 perl -Ilib teacher99.pl 115.88s user 0.69s system 99% cpu 1:56.70 total
- 20. % time perl -Ilib teacher99.pl 4.10442087026325e+19 perl -Ilib teacher99.pl 115.88s user 0.69s system 99% cpu 1:56.70 total
- 21. 1,630,000 times
- 22. Algorithm
- 23. example: 1 by 2 s g
- 24. Out of 2^7 patterns, how many answers are there? s s s s g g g g s s s s g g g g s s s s g g g g
- 25. Out of 2^7 patterns, how many answers are there? s s s s g g g g s s s s g g g g s s s s g g g g
- 26. Number each edge 2 5 1 4 7 3 6
- 27. my %mate = %{$node->{mate}}; my $next_grid_node = $grid_edge->[1]; Binary Decision diagram $mate{$next_grid_node} = $next_grid_node unless exists $mate{$next_grid_node}; {mate => %mate}; } sub high_node($$) { 1 my ($node, $grid_edge) = @_; s ２ my %mate = %{$node->{mate}}; １ 2 2 my @grid_nodes; ３ g # loop detection return undef if ($mate{$grid_edge->[0]} / '') eq $grid_edge->[1]; / 3 3 for my $grid_node ($grid_edge->[0], $grid_edge->[1]) { 3 3 if (! exists $mate{$grid_node}) { push @grid_nodes, $grid_node; # That's the new grid node } elsif (! defined $mate{$grid_node}) { # Have already connected :/ return undef; } else { 4 4 4 push @grid_nodes, $mate{$grid_node}; 4 $mate{$grid_node} = undef; # Connect to new grid node 4 4 4 4 } } $mate{$grid_nodes[0]} = $grid_nodes[1]; $mate{$grid_nodes[1]} = $grid_nodes[0]; ・・・・・・ {mate => %mate};
- 28. # delete mate which isn't frontier my $child_node = sub { my $new_node = shift; Pruning trees defined $new_node or return undef; my $new_mate = $new_node->{mate}; for (@done_grid_nodes) { if ($_ eq $start || $_ eq $goal) { return undef unless defined $new_mate->{$_} && $new_mate->{$_} ne $_; } elsif (defined $new_mate->{$_} && $new_mate->{$_} ne $_ ) { Stop computing if it will be impossible return undef; # won't be connected forever } if 2 ways intersect delete $new_node->{mate}{$_}; } if a node becomes a dead end return 1 if has_one_route $new_node, $start => $goal; $next_nodes_map{node_id $new_node} / $new_node; /= }; $node->{low} = $child_node->($low_node); $node->{high} = $child_node->($high_node);
- 29. BDD 1 s ２ １ 2 2 ３ g 3 3 3 3 4 4 4 4 4 4 4 4 ・・・・・・
- 30. sub node_id($) { Sharing trees my $node = shift; my $mate = $node->{mate}; join "t", map {"$_-" . ($mate->{$_} / '')} sort keys %$mate; / } ... my @active_nodes = ($top_node); for my $grid_edge (@grid_edges) { are connected Track how nodes ... my %next_nodes_map; Share 2 trees if{ they have same status for my $node (@active_nodes) of connections $next_nodes_map{node_id $new_node} / $new_node; /= }; ... };
- 31. x is connected with y in both diagram x 2 y 5 x 2 y 5 1 4 7 1 4 7 3 6 3 6
- 32. Sharing the result of computation 1 2 2 3 3 3 3 4 4 4 4 4 4 4 4 ５ ５
- 33. Originally we must have 2^5=16 patterns. Now we have only 2 patterns.
- 35. I’m not afraid of 不可思議. ※ 1不可思議 = 1000000000000000000000 0000000000000000000000 000000000000000000000
- 36. Conclusion Perl mongers had better help ladies! Combinatorial explosion is bother. Good algorithms are very important.