0: #!perl -w
1: 
2: # BinomialExpansion.pl
3: 
4: # usage perl BinomialExpansion.pl n, where n is an integer > 0 
5: 
6: # ** the memory goes crazy after the 170th power
7: # the expansion of (x+y)^170 peaks at 9.14484184513157e+049 * x^85 * y^85
8: # so you can imagine what happens if you put int n>170
9: 
10: my $n = ($_=shift) > 0 ? int $_ :
11:         die "'usage perl BinomialExpansion.pl 9, where n > 0'";
12: 
13: print _titled_hr(' Binomial Expansion For (x+y)^',$n,' ');
14: 
15: for my $j (0 .. $n)
16: {
17:     my $coefficient = nCr($n,$j);
18:     my $nj=$n-$j;
19:     print $coefficient;
20:     print $_ = ($nj!=0)?( ($nj>1)?(' * x^'.$nj):(' * x') ):'';
21:     print $_ = ($j!=0)?( ($j==1)?(' * y'):(' * y^'.$j) ):'';
22:     print $_ = ($j!=$n)?(" +\n"):("\n");
23: }
24: 
25: print ' 'x 25,' = (x + y)^',$n, "\n"x 3;
26: 
27: # returns n!/r!(n-r)!
28: sub nCr
29: {
30:     my $n=shift;
31:     my $r=shift;
32: 
33:     return int nFactorial($n) / int nFactorial($r) * int nFactorial($n-$r);
34: }
35: 
36: # like the name says, n!
37: sub nFactorial
38: {
39:     my $n=shift;
40:     my $product = 1;
41: 
42:     while($n>0)
43:     {
44:         $product *= $n--;
45:     }
46: 
47:     return  $product;
48: }
49: 
50: # neat little titled hr, that does a < 80 chars since int rounds down
51: # i really, really, like it
52: sub _titled_hr
53: {
54:     my $string = join('', @_);
55:     my $oy = int (80 -(length $string) )/ 2;
56:     return "\n","-" x $oy, $string, "-" x $oy,"\n";
57: }
58: 
59: __END__
60: # some random things i say
61: #1
62: "--. .-. . . - --..   -.-- .----. .- .-.. .-.."
63: 
64: #2
65: "...- .-. --- --- -- --..--   ...- .-. --- --- -- .----."
66: 
67: #3
68: --- ..-.   .- .-.. .-..   - .... .   - .... .. -. --. ...   ..   .-.. --- ... -
69: --..--
70:   ..   -- .. ... ...   -- -.--   -- .. -. -..   - .... .   -- --- ... - .-.-.-
71:     -....- -....-   --- --.. --.. .. .   --- ... -... --- ..- .-. -. .
72: 
73: # a lil sample from my machine
74: 
75: F:\>perl BinomialExpansion.pl 9
76: 1 * x^9 +
77: 9 * x^8 * y +
78: 36 * x^7 * y^2 +
79: 84 * x^6 * y^3 +
80: 126 * x^5 * y^4 +
81: 126 * x^4 * y^5 +
82: 84 * x^3 * y^6 +
83: 36 * x^2 * y^7 +
84: 9 * x * y^8 +
85: 1 *  * y^9
86:                  = (x + y)^9
87: F:\>
88: 
89: # Notice a pattern? Fleet attack!
90: # >
91: #   >
92: #     >
93: #     >
94: #       >
95: #       >
96: #     >
97: #     >
98: #   >
99: # >