#!/usr/bin/perl

# solve.pl

use warnings;
use strict;

use YAML;
use File::Temp 'tempfile';
use List::Util 'sum';

my $points        = YAML::Load( do { local $/; <> } );

my $triangles     = compute_delaunay_triangulation( $points );
my $segs          = unique_segments( $triangles );
my @seg_endpoints = map [ @{$points}[@$_] ], @$segs;
my @seg_lengths   = map seg_length($_), @seg_endpoints;

my $count = @$segs;
my $mean  = sum(@seg_lengths) / $count;

print "edge count          = $count\n";
print "average edge length = $mean\n\n";
print "edge endpoints follow in YAML format\n\n";

print YAML::Dump( @seg_endpoints );

sub compute_delaunay_triangulation {

    # use Qhull's qdelaunay for this

    my ($points) = @_;

    my $fh = tempfile();
    die "cannot open tempfile: $!" unless $fh;

    my $pid = open my $write_to_child, "|-";
    die "cannot fork: $!" unless defined $pid;

    if ($pid) {  # parent
        print $write_to_child "2\n", scalar @$points, "\n",
            map "@$_\n", @$points;
        close $write_to_child || warn "kid exited $?";
    } else {     # child
        open STDOUT, '>&', $fh  or die "could not redirect stdout: $!";
        close $fh               or die "error on close of tempfile: $!";
        exec qw(qdelaunay Qt i) or die "could not exec qdelaunay: $!";
    }

    wait;

    seek $fh, 0, 0 or die "could not seek to start of tempfile: $!";
    my $results = do { local $/; <$fh> };
    close $fh;

    (undef, my @triangles) = split /\n/, $results;

    return [ map [split], @triangles ];
}

sub unique_segments {
    my ($triangles) = @_;
    my %segs;
    for my $tri (@$triangles) {
        for ([0,1],[1,2],[2,0]) {
            my @points = sort @{$tri}[@$_];
            $segs{"@points"} = \@points;
        }
    }
    [ values %segs ];
}

sub seg_length {
    my ($seg) = @_;
    my ($x,$y,$x1,$y1) = ( $seg->[0][0], $seg->[0][1]
                         , $seg->[1][0], $seg->[1][1] );
    sqrt( ($x - $x1) ** 2 + ($y - $y1) ** 2);
}