Combinations and permutations: Difference between revisions
Rename Perl 6 -> Raku, alphabetize, minor clean-up
Thundergnat (talk | contribs) (Rename Perl 6 -> Raku, alphabetize, minor clean-up) |
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1000 C 333 = 5776134553147651669777486323549601722339... (235 more digits)
</pre>
=={{header|M2000 Interpreter}}==
<lang M2000 Interpreter>
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C(600,20)=2801445153584 C(600,40)=266319106596345 C(600,60)=14409368913 C(600,80)=271441 C(600,100)=52868467287780595308
C(800,20)=1925279023672620 C(800,40)=23121069591511231041 C(800,60)=18702067923763447158 C(800,80)=1193559552292625 C(800,100)=172727802
C(1000,20)=1239329180287869852 C(1000,40)=1937726921514640866484017 C(1000,60)=149470629867337347460963500 C(1000,80)=1269150275532146867313740 C(1000,100)=10088410532027029794548
=={{header|Maple}}==
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Since the output is almost the same as perl6's, and this is only a Draft RosettaCode task, I'm not going to bother including the output of the program.
=={{header|Phix}}==
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(I'll spare this page from yet another big listing of samples...)
=={{header|Raku}}==
(formerly Perl 6)
Perl 6 can't compute arbitrary large floating point values, thus we will use logarithms, as is often needed when dealing with combinations. We'll also use a Stirling method to approximate <math>\ln(n!)</math>:
<math>\ln n! \approx
\frac{1}{2}\ln(2\pi n) + n\ln\left(\frac{n}{e} + \frac{1}{12 e n}\right)</math>
Notice that Perl6 can process arbitrary long integers, though. So it's not clear whether using floating points is useful in this case.
<lang perl6>multi P($n, $k) { [*] $n - $k + 1 .. $n }
multi C($n, $k) { P($n, $k) / [*] 1 .. $k }
sub lstirling(\n) {
n < 10 ?? lstirling(n+1) - log(n+1) !!
.5*log(2*pi*n)+ n*log(n/e+1/(12*e*n))
}
role Logarithm {
method gist {
my $e = (self/10.log).Int;
sprintf "%.8fE%+d", exp(self - $e*10.log), $e;
}
}
multi P($n, $k, :$float!) {
(lstirling($n) - lstirling($n -$k))
but Logarithm
}
multi C($n, $k, :$float!) {
(lstirling($n) - lstirling($n -$k) - lstirling($k))
but Logarithm
}
say "Exact results:";
for 1..12 -> $n {
my $p = $n div 3;
say "P($n, $p) = ", P($n, $p);
}
for 10, 20 ... 60 -> $n {
my $p = $n div 3;
say "C($n, $p) = ", C($n, $p);
}
say '';
say "Floating point approximations:";
for 5, 50, 500, 1000, 5000, 15000 -> $n {
my $p = $n div 3;
say "P($n, $p) = ", P($n, $p, :float);
}
for 100, 200 ... 1000 -> $n {
my $p = $n div 3;
say "C($n, $p) = ", C($n, $p, :float);
}</lang>
{{out}}
<pre>Exact results:
P(1, 0) = 1
P(2, 0) = 1
P(3, 1) = 3
P(4, 1) = 4
P(5, 1) = 5
P(6, 2) = 30
P(7, 2) = 42
P(8, 2) = 56
P(9, 3) = 504
P(10, 3) = 720
P(11, 3) = 990
P(12, 4) = 11880
C(10, 3) = 120
C(20, 6) = 38760
C(30, 10) = 30045015
C(40, 13) = 12033222880
C(50, 16) = 4923689695575
C(60, 20) = 4191844505805495
Floating point approximations:
P(5, 1) = 5.00000000E+0
P(50, 16) = 1.03017326E+26
P(500, 166) = 3.53487492E+434
P(1000, 333) = 5.96932629E+971
P(5000, 1666) = 6.85674576E+6025
P(15000, 5000) = 9.64985399E+20469
C(100, 33) = 2.94692433E+26
C(200, 66) = 7.26975256E+53
C(300, 100) = 4.15825147E+81
C(400, 133) = 1.25794868E+109
C(500, 166) = 3.92602839E+136
C(600, 200) = 2.50601778E+164
C(700, 233) = 8.10320356E+191
C(800, 266) = 2.64562336E+219
C(900, 300) = 1.74335637E+247
C(1000, 333) = 5.77613455E+274</pre>
=={{header|REXX}}==
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