Evaluate binomial coefficients: Difference between revisions

Content added Content deleted
(Rename Perl 6 -> Raku, alphabetize, minor clean-up)
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Message box shows:
Message box shows:
<pre>10</pre>
<pre>10</pre>

=={{header|AWK}}==
=={{header|AWK}}==
<lang AWK>
<lang AWK>
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131282408400
131282408400
11923179284862717872</pre>
11923179284862717872</pre>

=={{header|C++}}==
<lang cpp>double Factorial(double nValue)
{
double result = nValue;
double result_next;
double pc = nValue;
do
{
result_next = result*(pc-1);
result = result_next;
pc--;
}while(pc>2);
nValue = result;
return nValue;
}

double binomialCoefficient(double n, double k)
{
if (abs(n - k) < 1e-7 || k < 1e-7) return 1.0;
if( abs(k-1.0) < 1e-7 || abs(k - (n-1)) < 1e-7)return n;
return Factorial(n) /(Factorial(k)*Factorial((n - k)));
}
</lang>

Implementation:
<lang cpp>int main()
{
cout<<"The Binomial Coefficient of 5, and 3, is equal to: "<< binomialCoefficient(5,3);
cin.get();
}</lang>

{{Out}}
<pre>The Binomial Coefficient of 5, and 3, is equal to: 10</pre>


=={{header|C sharp|C#}}==
=={{header|C sharp|C#}}==
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}
}
}</lang>
}</lang>

=={{header|C++}}==
<lang cpp>double Factorial(double nValue)
{
double result = nValue;
double result_next;
double pc = nValue;
do
{
result_next = result*(pc-1);
result = result_next;
pc--;
}while(pc>2);
nValue = result;
return nValue;
}

double binomialCoefficient(double n, double k)
{
if (abs(n - k) < 1e-7 || k < 1e-7) return 1.0;
if( abs(k-1.0) < 1e-7 || abs(k - (n-1)) < 1e-7)return n;
return Factorial(n) /(Factorial(k)*Factorial((n - k)));
}
</lang>

Implementation:
<lang cpp>int main()
{
cout<<"The Binomial Coefficient of 5, and 3, is equal to: "<< binomialCoefficient(5,3);
cin.get();
}</lang>

{{Out}}
<pre>The Binomial Coefficient of 5, and 3, is equal to: 10</pre>


=={{header|Clojure}}==
=={{header|Clojure}}==
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Binomial (33,17) = 1166803110
Binomial (33,17) = 1166803110
</pre>
</pre>

=={{header|F Sharp|F#}}==
<lang fsharp>
let choose n k = List.fold (fun s i -> s * (n-i+1)/i ) 1 [1..k]
</lang>


=={{header|Factor}}==
=={{header|Factor}}==
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: choose-fold ( n k -- n-choose-k )
: choose-fold ( n k -- n-choose-k )
2dup 1 + [a,b] product -rot - 1 [a,b] product / ;
2dup 1 + [a,b] product -rot - 1 [a,b] product / ;
</lang>

=={{header|F Sharp|F#}}==
<lang fsharp>
let choose n k = List.fold (fun s i -> s * (n-i+1)/i ) 1 [1..k]
</lang>
</lang>


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5
5
118264581564861424</pre>
118264581564861424</pre>

=={{header|Liberty BASIC}}==
<lang lb>
' [RC] Binomial Coefficients

print "Binomial Coefficient of "; 5; " and "; 3; " is ",BinomialCoefficient( 5, 3)
n =1 +int( 10 *rnd( 1))
k =1 +int( n *rnd( 1))
print "Binomial Coefficient of "; n; " and "; k; " is ",BinomialCoefficient( n, k)

end

function BinomialCoefficient( n, k)
BinomialCoefficient =factorial( n) /factorial( n -k) /factorial( k)
end function

function factorial( n)
if n <2 then
f =1
else
f =n *factorial( n -1)
end if
factorial =f
end function
</lang>


=={{header|Logo}}==
=={{header|Logo}}==
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show choose 5 3 ; 10
show choose 5 3 ; 10
show choose 60 30 ; 1.18264581564861e+17</lang>
show choose 60 30 ; 1.18264581564861e+17</lang>

=={{header|Lua}}==
=={{header|Lua}}==
<lang lua>function Binomial( n, k )
<lang lua>function Binomial( n, k )
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print( Binomial(100,50)) -- 1.0089134454556e+029
print( Binomial(100,50)) -- 1.0089134454556e+029
</lang>
</lang>

=={{header|Liberty BASIC}}==
<lang lb>
' [RC] Binomial Coefficients

print "Binomial Coefficient of "; 5; " and "; 3; " is ",BinomialCoefficient( 5, 3)
n =1 +int( 10 *rnd( 1))
k =1 +int( n *rnd( 1))
print "Binomial Coefficient of "; n; " and "; k; " is ",BinomialCoefficient( n, k)

end

function BinomialCoefficient( n, k)
BinomialCoefficient =factorial( n) /factorial( n -k) /factorial( k)
end function

function factorial( n)
if n <2 then
f =1
else
f =n *factorial( n -1)
end if
factorial =f
end function
</lang>



=={{header|Maple}}==
=={{header|Maple}}==
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10
10
</pre>
</pre>

=={{header|МК-61/52}}==
<lang>П1 <-> П0 ПП 22 П2 ИП1 ПП 22 П3
ИП0 ИП1 - ПП 22 ИП3 * П3 ИП2 ИП3
/ С/П ВП П0 1 ИП0 * L0 25 В/О</lang>

''Input'': ''n'' ^ ''k'' В/О С/П.


=={{header|MINIL}}==
=={{header|MINIL}}==
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which results from the definition of ncr in terms of factorials.
which results from the definition of ncr in terms of factorials.

=={{header|МК-61/52}}==
<lang>П1 <-> П0 ПП 22 П2 ИП1 ПП 22 П3
ИП0 ИП1 - ПП 22 ИП3 * П3 ИП2 ИП3
/ С/П ВП П0 1 ИП0 * L0 25 В/О</lang>

''Input'': ''n'' ^ ''k'' В/О С/П.


=={{header|Nanoquery}}==
=={{header|Nanoquery}}==
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<lang OCaml>open Num;;
<lang OCaml>open Num;;
let rec binomial n k = if n = k then Int 1 else ((binomial (n-1) k) */ Int n) // Int (n-k)</lang>
let rec binomial n k = if n = k then Int 1 else ((binomial (n-1) k) */ Int n) // Int (n-k)</lang>



=={{header|Oforth}}==
=={{header|Oforth}}==
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The Math::Pari module also has binomial, but it needs large amounts of added stack space for large arguments (this is due to using a very old version of the underlying Pari library).
The Math::Pari module also has binomial, but it needs large amounts of added stack space for large arguments (this is due to using a very old version of the underlying Pari library).

=={{header|Perl 6}}==
For a start, you can get the length of the corresponding list of combinations:
<lang perl6>say combinations(5, 3).elems;</lang>
{{out}}
<pre>10</pre>

This method is efficient, as Perl 6 will not actually compute each element of the list, since it actually uses an iterator with a defined <tt>count-only</tt> method. Such method performs computations in a way similar to the following infix operator:

<lang perl6>sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. $^p }
say 5 choose 3;</lang>

A possible optimization would use a symmetry property of the binomial coefficient:

<lang perl6>sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. min($n - $^p, $p) }</lang>

One drawback of this method is that it returns a Rat, not an Int. So we actually may want to enforce the conversion:
<lang perl6>sub infix:<choose> { ([*] ($^n ... 0) Z/ 1 .. min($n - $^p, $p)).Int }</lang>

And ''this'' is exactly what the <tt>count-only</tt> method does.


=={{header|Phix}}==
=={{header|Phix}}==
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(binomial 10 5)
(binomial 10 5)
</lang>
</lang>

=={{header|Raku}}==
(formerly Perl 6)
For a start, you can get the length of the corresponding list of combinations:
<lang perl6>say combinations(5, 3).elems;</lang>
{{out}}
<pre>10</pre>

This method is efficient, as Perl 6 will not actually compute each element of the list, since it actually uses an iterator with a defined <tt>count-only</tt> method. Such method performs computations in a way similar to the following infix operator:

<lang perl6>sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. $^p }
say 5 choose 3;</lang>

A possible optimization would use a symmetry property of the binomial coefficient:

<lang perl6>sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. min($n - $^p, $p) }</lang>

One drawback of this method is that it returns a Rat, not an Int. So we actually may want to enforce the conversion:
<lang perl6>sub infix:<choose> { ([*] ($^n ... 0) Z/ 1 .. min($n - $^p, $p)).Int }</lang>

And ''this'' is exactly what the <tt>count-only</tt> method does.


=={{header|REXX}}==
=={{header|REXX}}==
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echo "Binomial Coefficient ($n,$k) = $binomial_coefficient"</lang>
echo "Binomial Coefficient ($n,$k) = $binomial_coefficient"</lang>




=={{header|Ursala}}==
=={{header|Ursala}}==
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{{Out}}
{{Out}}
<pre>the binomial coefficient of 5 and 3 = 10</pre>
<pre>the binomial coefficient of 5 and 3 = 10</pre>



=={{header|XPL0}}==
=={{header|XPL0}}==
Retrieved from "https://rosettacode.org/wiki/Evaluate_binomial_coefficients"