#!/usr/bin/env perl
#
# Create a script that prints nth order forward difference series. You should be
# a able to pass the list of numbers and order number as command line
# parameters. Let me show you with an example.
#
# Suppose we have list (X) of numbers: 5, 9, 2, 8, 1, 6 and we would like to
# create 1st order forward difference series (Y). So using the formula Y(i) =
# X(i+1) - X(i), we get the following numbers: (9-5), (2-9), (8-2), (1-8),
# (6-1). In short, the final series would be: 4, -7, 6, -7, 5. If you noticed,
# it has one less number than the original series. Similary you can carry on 2nd
# order forward difference series like: (-7-4), (6+7), (-7-6), (5+7) => -11, 13,
# -13, 12.
################################################################################

use strict;
use warnings;

@ARGV == 2 or die "Usage: $0 <order> <x1,x2,...xn>";
my $order = shift;
my @xs = split ',', shift;

foreach (1 .. $order) {
    foreach my $i (0 .. $#xs-1) {
        $xs[$i] = $xs[$i+1] - $xs[$i];
    }
    pop @xs;
}

print "@xs\n";