Combinations and permutations: Difference between revisions
m
Added the Sidef language
m (→{{header|Perl 6}}: say requires an argument) |
m (Added the Sidef language) |
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p 15000.permutation(74) #=> 896237613852967826239917238565433149353074416025197784301593335243699358040738127950872384197159884905490054194835376498534786047382445592358843238688903318467070575184552953997615178973027752714539513893159815472948987921587671399790410958903188816684444202526779550201576117111844818124800000000000000000000
</lang>
=={{header|Sidef}}==
{{trans|Perl 6}}
<lang ruby>func P(n, k) { n! / ((n-k)!) };
func C(n, k) { binomial(n, k) };
class Logarithm(value) {
method get_value { value };
method to_s {
var e = int(value/10.log);
"%.8fE%+d" % (exp(value - e*10.log), e);
}
}
func lstirling(n) {
n < 10 ? (lstirling(n+1) - log(n+1))
: (0.5*log(2*Math.pi*n) + n*log(n/Math.e + 1/(12*Math.e*n)));
}
func P_approx(n, k) {
Logarithm((lstirling(n) - lstirling(n -k)))
}
func C_approx(n, k) {
Logarithm((lstirling(n) - lstirling(n -k) - lstirling(k)))
}
say "=> Exact results:";
range(1, 12).each { |n|
var p = int(n / 3);
say "P(#{n}, #{p}) = #{P(n, p)}";
}
range(10, 60, 10).each { |n|
var p = int(n / 3);
say "C(#{n}, #{p}) = #{C(n, p)}";
}
say '';
say "=> Floating point approximations:";
[5, 50, 500, 1000, 5000, 15000].each { |n|
var p = int(n / 3);
say "P(#{n}, #{p}) = #{P_approx(n, p)}";
}
range(100, 1000, 100).each { |n|
var p = int(n / 3);
say "C(#{n}, #{p}) = #{C_approx(n, p)}";
}</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|Tcl}}==
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