how to find distance between elements of two arrays?

I'm writing in perl, but it seems more like an algorithm question to me. Replies in other languages are welcome.

I have two sorted arrays of integers, short and long. For each element in short, I want to find the closest element in long, and in my particular case i want to make a histogram of the distances.

Here's the algorithm I'm using:

sub makeDistHist {
    my ($hist, $short, $long, $max) = @_; # first 3 are array references

    my $lIndex = 0;
    foreach my $s (@$short) {
        my $distance = abs( $s - $long->[$lIndex] );
        while (abs( $s - $long->[$lIndex+1] ) < $distance) {
            $distance = abs( $s - $long->[$lIndex] );
            $lIndex++;
        }
        $distance = $max if $distance>$max; # make overflow bin
        $hist->[$distance]++;
    }  
}

This relies on short and long being sorted.

Here's a subroutine i wrote to test my algorithm. The first test succeeds, but the second fails:

sub test { # test makeDistHist 

    my @long = qw(100 200 210 300 350 400 401 402 403 404 405 406);
    my @short = qw(3 6 120 190 208 210 300 350);
    my @tarHist;
    $tarHist[97]++;
    $tarHist[94]++;
    $tarHist[20]++;
    $tarHist[10]++;
    $tarHist[2]++;
    $tarHist[0]+=3;

    my $max = 3030;
    my @gotHist;
    makeDistHist(\@gotHist, \@short, \@long, $max);

    use Test::More tests => 2;
    is_deeply(\@gotHist, \@tarHist, "did i get the correct distances for two different arrays?");

    @gotHist = ();
    @tarHist = ( @long+0 );
    makeDistHist(\@gotHist, \@long, \@long, $max);
    is_deeply(\@gotHist, \@tarHist, "did i get the correct distances between an array and itself?");  # nope!
    print Dumper(\@gotHist);
}

here's the dump:

$VAR1 = [
          7,
          5
        ];

(the problem persists if I compare long to a copy of it minus one element, so it's not that the algorithm requires short to be strictly shorter than long. also, if I change 401, 402... to 402, 404... gotHist becomes (7, undef, 5).)

Here's what I'd like from y'all: first and for开发者_Go百科emost, a working algorithm for this. Either fix what I've got or devise another from whole cloth. Secondly, I could use help in my debugging skills. How would you go about identifying the problem with the existing algorithm? If I could do that I wouldn't need to ask this question :)

Thanks!

---

You should break up the subroutine: Calculating the distances and building the histogram are two different things and much clarity is lost by trying to combine the two.

Start with the simplest solution first. I understand the potential optimization by using a sorted @long, but resort to that only if List::Util::min is slow.

You can use Statistics::Descriptive to generate the frequency distribution.

#!/usr/bin/perl

use strict; use warnings;
use List::Util qw( min );
use Statistics::Descriptive;

my $stat = Statistics::Descriptive::Full->new;

my @long = (100, 200, 210, 300, 350, 400, 401, 402, 403, 404, 405, 406);
my @short = (3, 6, 120, 190, 208, 210, 300, 350);

for my $x ( @short ) {
    $stat->add_data(find_dist($x, \@long));
}

my $freq = $stat->frequency_distribution_ref([0, 2, 10, 20, 94, 97]);
for my $bin ( sort { $a <=> $b } keys %$freq ) {
    print "$bin:\t$freq->{$bin}\n";
}

sub find_dist {
    my ($x, $v) = @_;
    return min map abs($x - $_), @$v;
}

Output:

[sinan@archardy so]$ ./t.pl
0:      3
2:      1
10:     1
20:     1
94:     1
97:     1

Of course, it is possible to do this without using any modules and using your assumption of a sorted @long:

#!/usr/bin/perl

use strict; use warnings;

my @long = (100, 200, 210, 300, 350, 400, 401, 402, 403, 404, 405, 406);
my @short = (3, 6, 120, 190, 208, 210, 300, 350);

my @bins = reverse (0, 2, 10, 20, 94, 97);
my %hist;

for my $x ( @short ) {
    add_hist(\%hist, \@bins, find_dist($x, \@long));
}

for my $bucket ( sort { $a <=> $b } keys %hist ) {
    print "$bucket:\t$hist{$bucket}\n";
}

sub find_dist {
    my ($x, $v) = @_;
    my $min = abs($x - $v->[0]);
    for my $i ( 1 .. $#$v ) {
        my $dist = abs($x - $v->[$i]);
        last if $dist >= $min;
        $min = $dist;
    }
    return $min;
}

sub add_hist {
    my ($hist, $bins, $x) = @_;
    for my $u ( @$bins ) {
        if ( $x >= $u ) {
            $hist{ $u } += 1;
            last;
        }
    }
    return;
}

---

Regarding the part about debugging, use an IDE that allows breakpoints. I don't have an example for perl, but for PHP and ASP.NET, there are Eclipse and Visual Studio (or the free version, Visual Web Developer), respectively.