--- /dev/null
+#!/usr/bin/perl -w
+
+use v5.36;
+use strict;
+
+my %flow;
+my %tun;
+
+while (<>) {
+ chomp;
+ my ($v, $f, $n) = /Valve (..) has flow rate=(\d+);.* to valves? (.*)/;
+ $flow{$v} = $f if $f;
+ $tun{$v} = [ split /, /, $n ];
+ say $n;
+}
+
+sub bfs($start) {
+ my %seen;
+ my @q = [ $start, 0 ];
+ while (@q) {
+ my $st = shift @q;
+ my ($node, $len, @path) = @$st;
+ next if $seen{$node};
+ $seen{$node} = [ $len, @path ];
+
+ for my $neigh (@{ $tun{$node} }) {
+ push @q, [ $neigh, $len+1, @path, $node ];
+ }
+ }
+ return \%seen;
+}
+
+my %paths;
+for my $node ('AA', keys %flow) {
+ $paths{$node} = bfs($node);
+}
+
+my @q = [ 'AA', 30, 0, { }, [ ] ];
+
+my $max = 0;
+while (@q) {
+ my $st = shift @q;
+ my ($node, $mins, $total, $opened, $path) = @$st;
+ say "At $node $total $mins ", join(',', @$path);
+ if ($total > $max) {
+ $max = $total;
+ }
+ for my $n1 (keys %{ $paths{$node} }) {
+ next if !$flow{$n1};
+ my $dist = $paths{$node}{$n1}[0];
+ next if $opened->{$n1};
+
+ my $m1 = $mins - $dist - 1;
+ next if $m1 < 0;
+ my %o1 = (%$opened, $n1 => 1);
+ say " opening $n1 at $m1 ", $flow{$n1}*($m1);
+ push @q, [ $n1, $m1, $total + $flow{$n1}*($m1),
+ \%o1, [ @$path, $n1 ] ];
+ }
+}
+
+say $max;
--- /dev/null
+#!/usr/bin/perl -w
+
+use v5.36;
+use strict;
+
+my %flow;
+my %tun;
+
+while (<>) {
+ chomp;
+ my ($v, $f, $n) = /Valve (..) has flow rate=(\d+);.* to valves? (.*)/;
+ $flow{$v} = $f if $f;
+ $tun{$v} = [ split /, /, $n ];
+}
+
+sub bfs($start) {
+ my %seen;
+ my @q = [ $start, 0 ];
+ while (@q) {
+ my $st = shift @q;
+ my ($node, $len, @path) = @$st;
+ next if $seen{$node};
+ $seen{$node} = [ $len, @path ];
+
+ for my $neigh (@{ $tun{$node} }) {
+ push @q, [ $neigh, $len+1, @path, $node ];
+ }
+ }
+ return \%seen;
+}
+
+my %paths;
+for my $node ('AA', keys %flow) {
+ $paths{$node} = bfs($node);
+}
+
+sub walk(@nodes) {
+ my @q = [ 'AA', 26, 0, { map { $_ => 1 } @nodes }, [ ] ];
+
+ my $max = 0;
+ while (@q) {
+ my $st = shift @q;
+ my ($node, $mins, $total, $opened, $path) = @$st;
+
+ if ($total > $max) {
+ # say "At $node $mins $total ", join(',', @$path);
+ $max = $total;
+ }
+
+ for my $n1 (keys %{ $paths{$node} }) {
+ next if !$flow{$n1};
+ my $dist = $paths{$node}{$n1}[0];
+ next if $opened->{$n1};
+
+ my $m1 = $mins - $dist - 1;
+ next if $m1 < 0;
+ my %o1 = (%$opened, $n1 => 1);
+ # say " opening $n1 at $m1 ", $flow{$n1}*($m1);
+ push @q, [ $n1, $m1, $total + $flow{$n1}*($m1),
+ \%o1, [ @$path, $n1 ] ];
+ }
+ }
+ return $max;
+}
+
+my @nodes = sort keys %flow;
+
+my $mx;
+my $walked;
+sub walk1($n1, $n2, $rest) {
+ if (!@$rest) {
+ my $sum = walk(@$n1) + walk(@$n2);
+ $walked++;
+ if (!defined $mx || $mx < $sum) {
+ say join(' ', @$n1), ' | ', join(' ', @$n2), " ($walked) = $sum";
+ $mx = $sum;
+ }
+ return;
+ }
+ my @nrest = @$rest;
+ my $node = shift @nrest;
+ walk1([ @$n1, $node ], $n2, \@nrest);
+ walk1($n1, [ @$n2, $node ], \@nrest);
+}
+
+my $first = shift @nodes;
+walk1([$first], [], \@nodes);
+say $mx;