#!/usr/bin/perl -w
#
# parses some input about ballots and computes the result according
# to Debian Constitution A.6.
#
# usage: .../compute [<input files>...]
#  (uses stdin if none supplied)
#
# input files can be in any order and should contain lines like:
#
#   <votername> :: <PREF>, (<PREF>=<PREF>), <PREF>, ....
#   V: <tallyprefs> <votername>
#   <ABBREV> = <description...>
#   <ABBREV> = <description...> [<rat>:<io>]
#   <ABBREV> = <description...> [default]
#   nodefault
#   quorum = <quorum>
#
# where
#
#   <votername> is any non-whitespace characters
#
#   <ABBREV> and <PREF> are abbreviations for choices on the ballot.
#      They must be ASCII alphanumeric.  Numeric preferences are
#      not recommended as they are confusing (particularly when
#      tally sheets are in use).
#
#      It is best to avoid FD, SQ and NOTA except for the default
#      option; if no default option is specified, it will default
#      to one of these unless a "nodefault" line is found.
#
#      In the "::" form, the commas are optional.  Either ( ) or = may
#      be used to indicate a set of equal preferences.
#
#   <tallyprefs> is a tally sheet preference order: that is,
#      a single uppercase base36 digit for each ballot choice,
#      (in the order they were specified by "=" lines), giving
#      the voter's preference rank for that option.  The numbers
#      need not be distinct or contiguous.  "-" may be used for
#      unranked preferences.
#
#   <rat>:<io> is the majority ratio for the option
#
#   <quorum> is the quorum
#
# and also allowed are
#
#   #-comments                            } all
#   blank lines                           } ignored
#   lines starting with whitespace        }

use strict;
use utf8;
use autodie;

use Graph::Directed;
use Graph::Writer::GraphViz;

binmode STDIN, 'encoding(UTF-8)';
binmode STDOUT, 'encoding(UTF-8)';
binmode STDERR, 'encoding(UTF-8)';

our @choices;
our %choices;
our @invotes_v;
our @invotes_cc;
our $defcho;
our $quorum = 0;

our $gfile;

while (@ARGV && $ARGV[0] =~ /^-/) {
    local $_ = shift @ARGV;
    if (m/^--?$/) {
	last;
    } elsif (s/^-g//) {
	$gfile = $_;
    } else {
	die "bad usage\n";
    }
}

sub addchoice {
    my $choname = shift @_;
    my $cho = $choices{$choname} = {
	@_, Index => (scalar @choices)
    };
    push @choices, $choname;
    return $cho;
}

while (<>) {
    s/\s+$//;
    next if m/^\s*\#/;
    next unless m/\S/;
    next if m/^\s/;
    if (m/^([A-Z0-9]+)\s*\=\s*(\S.*)$/) {
	my ($choname, $desc) = ($1,$2);
	my $cho = addchoice($choname, Desc => $desc);
	if ($desc =~ m/\[(\d+):(\d+)\]/) {
	    $cho->{Smaj} = [$1,$2];
	} elsif ($desc =~ m/\[default\]/) {
	    $defcho = $cho;
	}
    } elsif (m/^V:\s+(\S+)\s+(\S.*)/) {
	push @invotes_v, [ $1, $2 ];
    } elsif (m/^(\S+)\s*\:\:\s*/) {
	push @invotes_cc, [ $1, "$'" ];
    } elsif (m/^quorum = ([0-9.]+)$/) {
	$quorum = $1+0.0;
    } elsif (m/^nodefault$/) {
	$defcho = { Index => -1 }
    } else {
	die "invalid input";
    }
}

our @vab;
# $vab[$ia][$ib] = V(A,B)
# Actually, it's a list of voters who prefer A to B (A.6(3)(1))

# Go through the voters and construct V(A,B)

print "\nParsing \`simple' style ballots\n# devotee-tally-begin\n"
        if @invotes_cc;
# actually, we pre-parse them into @invotes_v
# since we want to show them as a tally sheet anyway

foreach my $iv (@invotes_cc) {
    $_ = uc $iv->[1];
    foreach my $chn (m/\b\w+\b/g) {
	next if $choices{$chn};
	addchoice($chn, Desc => "($chn from voter ballot)");
    }
}

foreach my $iv (@invotes_cc) {
    my ($voter) = $iv->[0];
    $_ = uc $iv->[1];

    s/\t/ /g;
    s/\,/ /g;
    while (s{\(([^()]+)\)}{
        my $x = $1; $x =~ s/[ =]+/=/g; $x;
    }ge) { }
    s/[ =]*=[ =*]/=/g;
    s/\s+/ /g;
    print "# normalised $_ ($voter)\n";

    my @ranks = (1000,) x @choices;
    my $rank = 1;
    foreach (split /\s+/) {
	foreach (split /=/) {
	    my $cho = $choices{$_};
	    $cho or die "unknown choice $_ ($voter)";
	    my $ix = $cho->{Index};
	    $ranks[$ix] = $rank;
	}
	$rank++;
    }
    my $vstr = join '', map {
	$_ == 1000 ? "-" :
	$_ < 10 ? (sprintf "%d", $_) :
	$_ < 36 ? (chr(ord('A') + $_ - 10)) : die
    } @ranks;
    print "V: $vstr $voter\n";
    push @invotes_v, [ $vstr, $voter ];
}

print "# devotee-tally-end\n"
        if @invotes_cc;

print "\nDetermining default option\n";

if ($defcho && $defcho->{Index} > -1) {
    print "default option was specified: $choices[$defcho->{Index}]\n";
} elsif ($defcho) {
    print "no default option\n";
} else {
    foreach my $try (qw(FD SQ NOTA)) {
	$defcho = $choices{$try};
	last if $defcho;
    }
    if ($defcho) {
	print "guessed default option: $choices[$defcho->{Index}]\n";
    } else {
	print "could not guess default option, assuming there is none\n";
    }
}

my $defi = $defcho->{Index};
die "FD has smaj?!" if $defcho->{Smaj};

print "\nParsing devotee tally sheet ballots\n" 
    if @invotes_v > @invotes_cc;

foreach my $iv (@invotes_v) {
    my ($votestr,$voter) = @$iv;
    eval {
	length $votestr eq @choices or die "wrong vote vector length";
	my @vs = split //, $votestr;
	foreach my $ix (0..$#vs) {
	    my $vchr = $vs[$ix];
	    if ($vchr eq '-') {
		$vs[$ix] = 1000;
	    } elsif ($vchr =~ m/[0-9a-z]/) {
		$vs[$ix] = ord($vchr);
	    } else {
		die "bad vote char";
	    }
	}
	foreach my $ia (0..$#vs) {
	    foreach my $ib ($ia+1..$#vs) {
		my $va = $vs[$ia];
		my $vb = $vs[$ib];
		if ($va < $vb) { push @{ $vab[$ia][$ib] }, $voter }
		elsif ($vb < $va) { push @{ $vab[$ib][$ia] }, $voter }
	    }
	}
    };
    die "voter $voter $@" if $@;
}

print "\nPreference matrix\n";

our @ch = map { $choices{$_} } @choices;

# Print the counts V(A,B)
foreach my $iy (-2..$#ch) {
    foreach my $ix (-2..$#ch) {
	if ($iy==-1) {
	    if ($ix==-1) {
		printf "+";
	    } else {
		printf "------";
	    }
	} elsif ($ix==-1) {
	    printf "|";
	} elsif ($ix==-2 && $iy==-2) {
	    printf "V(Y,X)";
	} elsif ($iy==-2) {
	    printf "%5s ", $choices[$ix];
	} elsif ($ix==-2) {
	    printf "%5s ", $choices[$iy];
	} else {
	    my $v = \( $vab[$iy][$ix] );
	    $$v ||= [ ];
	    if (@$$v) {
		printf "%5d ", (scalar @$$v);
	    } else {
		printf "%5s ", "";
	    }
	}
    }
    printf "\n";
}

sub drop ($$) {
    my ($i,$why) = @_;
    print "dropping $choices[$i]: $why\n";
    $ch[$i]{Dropped} = $why;
}

if (defined $defi) {
    print "\nQuorum A.6(2) (quorum is $quorum)\n";

    foreach my $i (0..$#choices) {
	next if $ch[$i]{Dropped};
	next if $i == $defi;
	my $v = $vab[$i][$defi];
	next if $v >= $quorum;
	drop $i, "quorum ($v < $quorum)";
    }

    print "\nMajority ratio A.6(3)\n";

    foreach my $i (0..$#choices) {
	next if $ch[$i]{Dropped};
	next if $i == $defi;
	my $majr = $ch[$i]{Smaj};
	$majr ||= [1,1]; # A.6(3)(3)
	my $vad = scalar @{ $vab[$i][$defi] };
	my $vda = scalar @{ $vab[$defi][$i] };
	next if $vad * $majr->[1] > $vda * $majr->[0];
	drop $i, "majority ratio ($vad:$vda <= $majr->[1]:$majr->[0])";
    }
}

print "\nDefeats A.6(4)\n";

my $defeats = Graph::Directed->new;

sub chremain () {
    return grep { !$ch[$_]{Dropped} } (0..$#ch);
}

foreach my $ia (0..$#ch) {
    $defeats->add_vertex($choices[$ia]);
    foreach my $ib (0..$#ch) {
	my $vab = scalar @{ $vab[$ia][$ib] };
	my $vba = scalar @{ $vab[$ib][$ia] };
	next unless $vab > $vba;
	my $diff = $vab - $vba;
	print "defeat: $choices[$ia] beats $choices[$ib]",
	    " ($vab > $vba = +$diff)\n";
	$defeats->add_edge($choices[$ia],$choices[$ib]);
	my $label = "$diff($vab:$vba)";
	if (@invotes_v < 10) {
	    $label .= "\n". join ' ', @{ $vab[$ia][$ib] };
	    $label .= "\n/". join ' ', @{ $vab[$ib][$ia] };
	}
	$defeats->set_edge_attribute($choices[$ia],$choices[$ib],
				     label => $label);
    }
}

sub chvab ($$) {
    my ($ca,$cb) = @_;
    my $v = $vab[ $choices{$ca}{Index} ][ $choices{$cb}{Index} ];
    return scalar @$v;
}

sub weaker ($$) {
    # A.6(7)(1)
    my ($def1,$def2) = @_;
    my ($ca,$cx) = @$def1;
    my ($cb,$cy) = @$def2;
    return 1 if chvab($ca, $cx) < chvab($cb, $cy);
    return 1 if chvab($ca, $cx) == chvab($cb, $cy)
              && chvab($cx, $ca) > chvab($cy, $cb);
    return 0;
}

our $showg = $defeats->deep_copy();

foreach my $ix (0..$#ch) {
    my $cho = $ch[$ix];
    next unless $cho->{Dropped};
    $defeats->delete_vertex($choices[$ix]);
}

our $schwartz;

for (my $dropiter = 1; ; $dropiter++) {
    # loop from A6(5)

    print "defeats graph: $defeats\n";

    print "\nTransitive closure A.6(5) (iteration $dropiter)\n";

    my $tdefeats = $defeats->transitive_closure();

    # this makes the debugging output prettier
    foreach my $ch (@choices) {
	$tdefeats->delete_edge($ch,$ch);
    }
    print "closure graph: $tdefeats\n";

    print "\nSchwartz set A.6(6)\n";
    
    $schwartz = $defeats->copy();

    foreach my $ia (chremain()) {
	foreach my $ib (chremain()) {
	    next if $tdefeats->has_edge($choices[$ia],$choices[$ib]);
	    next if !$tdefeats->has_edge($choices[$ib],$choices[$ia]);
	    print "not in Schwartz set: $choices[$ia] because $choices[$ib]\n";
	    $schwartz->delete_vertex($choices[$ia]);
	    last;
	}
    }

    print "set: ", (join " ", $schwartz->vertices()), "\n";

    print "\nDropping weakest defeats A.6(7)\n";

    our @weakest = ();

    foreach my $edge ($schwartz->edges()) {
#	print " considering @$edge\n";
	if (!@weakest) {
	    # no weakest edges yet
	} elsif (weaker($edge, $weakest[0])) {
	    # this edge is weaker than previous weakest, start new set
	    @weakest = ();
	} elsif (weaker($weakest[0], $edge)) {
	    # weakest edge is weaker than this one, ignore this one
	    next;
	} else {
	    # weakest edge is exactly as weak as this one, add this one
	}
	push @weakest, $edge;
    }

    last unless @weakest;

    my $w = $weakest[0];
    printf "weakest defeats are %d > %d\n", 
        chvab($w->[0], $w->[1]),
	chvab($w->[1], $w->[0]);
    foreach my $weakest (@weakest) {
	my ($ca,$cb) = @$weakest;
	print "a weakest defeat is $ca > $cb\n";
	$defeats->delete_edge($ca,$cb);
	my $label = $showg->get_edge_attribute($ca,$cb,'label');
	$label .= "\ndropped - weakest in iter.$dropiter";
	$showg->set_edge_attribute($ca,$cb,'label',$label);
	$showg->set_edge_attribute($ca,$cb,'style','dotted');
	$showg->set_edge_attribute($ca,$cb,'graphviz',{constraint=>0});
    }

    print "\nDefeats within the Schwartz set, go round again\n";
}

print "no defeats within the Schwartz set\n";
print "final schwartz set:\n\n";

my $winxlabel;
if ($schwartz->vertices() == 1) {
    print "WINNER IS:\n";
    $winxlabel = "winner";
} else {
    print "WINNER IS ONE OF (CASTING VOTE DECIDES):\n";
    $winxlabel = "potential winner";
}

printf "    %-5s %s\n", $_, $choices{$_}{Desc}
    foreach ($schwartz->vertices());

if (defined $gfile) {
    foreach my $cho (values %choices) {
	my $chn = $choices[$cho->{Index}];
	my $label = "\\$chn\n$cho->{Desc}";
	if ($cho->{Dropped}) {
	    $label .= "\nDropped: $cho->{Dropped}";
	}
	if ($schwartz->has_vertex($chn)) {
	    $label .= "\n$winxlabel";
	}
	$showg->set_vertex_attribute($chn, 'label', $label);
    }

    my $gwriter = new Graph::Writer::GraphViz -format => 'ps';
    $gwriter->write_graph($showg, $gfile);
}

print ".\n";

#p %choices;
#p @vab;