Evaluate binomial coefficients: Difference between revisions

=={{header|ALGOL W}}==

<lang algolw>begin

% calculates n!/k! %

integer procedure factorialOverFactorial( integer value n, k ) ;

if k > n then 0

else if k = n then 1

else % k < n % begin

integer f;

f := 1;

for i := k + 1 until n do f := f * i;

f

end factorialOverFactorial ;

% calculates n! %

integer procedure factorial( integer value n ) ;

begin

integer f;

f := 1;

for i := 2 until n do f := f * i;

f

end factorial ;

% calculates the binomial coefficient of (n k) %

% uses the factorialOverFactorial procedure for a slight optimisation %

integer procedure binomialCoefficient( integer value n, k ) ;

if ( n - k ) > k

then factorialOverFactorial( n, n - k ) div factorial( k )

else factorialOverFactorial( n, k ) div factorial( n - k );

% display the binomial coefficient of (5 3) %

write( binomialCoefficient( 5, 3 ) )

end.</lang>