#!perl -w

# BinomialExpansion.pl

# usage perl BinomialExpansion.pl n, where n is an integer > 0 

# ** the memory goes crazy after the 170th power
# the expansion of (x+y)^170 peaks at 9.14484184513157e+049 * x^85 * y^85
# so you can imagine what happens if you put int n>170

my $n = ($_=shift) > 0 ? int $_ :
        die "'usage perl BinomialExpansion.pl 9, where n > 0'";

print _titled_hr(' Binomial Expansion For (x+y)^',$n,' ');

for my $j (0 .. $n)
{
    my $coefficient = nCr($n,$j);
    my $nj=$n-$j;
    print $coefficient;
    print $_ = ($nj!=0)?( ($nj>1)?(' * x^'.$nj):(' * x') ):'';
    print $_ = ($j!=0)?( ($j==1)?(' * y'):(' * y^'.$j) ):'';
    print $_ = ($j!=$n)?(" +\n"):("\n");
}

print ' 'x 25,' = (x + y)^',$n, "\n"x 3;

# returns n!/r!(n-r)!
sub nCr
{
    my $n=shift;
    my $r=shift;

    return int nFactorial($n) / int nFactorial($r) * int nFactorial($n-$r);
}

# like the name says, n!
sub nFactorial
{
    my $n=shift;
    my $product = 1;

    while($n>0)
    {
        $product *= $n--;
    }

    return  $product;
}

# neat little titled hr, that does a < 80 chars since int rounds down
# i really, really, like it
sub _titled_hr
{
    my $string = join('', @_);
    my $oy = int (80 -(length $string) )/ 2;
    return "\n","-" x $oy, $string, "-" x $oy,"\n";
}

__END__
# some random things i say
#1
"--. .-. . . - --..   -.-- .----. .- .-.. .-.."

#2
"...- .-. --- --- -- --..--   ...- .-. --- --- -- .----."

#3
--- ..-.   .- .-.. .-..   - .... .   - .... .. -. --. ...   ..   .-.. --- ... -
--..--
  ..   -- .. ... ...   -- -.--   -- .. -. -..   - .... .   -- --- ... - .-.-.-
    -....- -....-   --- --.. --.. .. .   --- ... -... --- ..- .-. -. .

# a lil sample from my machine

F:\>perl BinomialExpansion.pl 9
1 * x^9 +
9 * x^8 * y +
36 * x^7 * y^2 +
84 * x^6 * y^3 +
126 * x^5 * y^4 +
126 * x^4 * y^5 +
84 * x^3 * y^6 +
36 * x^2 * y^7 +
9 * x * y^8 +
1 *  * y^9
                 = (x + y)^9
F:\>

# Notice a pattern? Fleet attack!
# >
#   >
#     >
#     >
#       >
#       >
#     >
#     >
#   >
# >