How to resolve the algorithm Combinations and permutations step by step in the Raku programming language

Published on 12 May 2024 09:40 PM
#Raku

How to resolve the algorithm Combinations and permutations step by step in the Raku programming language

Table of Contents

Problem Statement

Implement the combination   (nCk)   and permutation   (nPk)   operators in the target language:

See the Wikipedia articles for a more detailed description. To test, generate and print examples of:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Combinations and permutations step by step in the Raku programming language

Source code in the raku programming language

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);
}

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