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I've been looking around trying to find a simple binomial coefficient algorithm, to no avail. The problem is the language I'm using for class is a bit... odd. A lot of it is using Yacc and Lex.

Anyways we did an example in class:

n=12; p=1; i=1;
while (i <= n) {
        p = p * i;
        print p;
        i = i + 1;
};

This was an example of computing factorials, but now I need to modify it to be able to compute C(n,k) or N choose K (aka binomial coefficient), but I don't how complicated I should make it. We can choose any N and K (the user doesn't have to input them) so any random 2 numbers will work (such as the example above). I'm pretty sure this code only supports basic functions such as while loops and basic math, so I don't think using a factorial is possible... but I suppose I could use the above code as such?

Any ideas?

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    No one can answer you with 100% certainty if the language you're using is unknown. – Bart Kiers Nov 11 '10 at 19:38
  • @Niki: ["The homework tag...is now discouraged,"](http://meta.stackoverflow.com/q/10812) but, @Mercfh, please (as always) follow [general guidelines](http://tinyurl.com/so-hints): state any special restrictions, show what you've tried so far, and ask about what specifically is confusing you. –  Nov 12 '10 at 16:36

2 Answers2

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Since I'm assuming this is homework I'm not going to provide a solution. What I will say is this:

There is a formula for C(n,k) which relies on division, subtraction, multiplication and factorial:

n!/(k!(n-k)!)

You already have code that can calculate the factorial, and it looks like the language you are using supports the other math operators you need.

So all you have to do is compute three factorials: one for n, one for k and one for n-k.

Niki Yoshiuchi
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    That makes sense, and this isn't actually homework but it's an example "exercise" from class. –  Nov 11 '10 at 20:32
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You could always use the Boost library if you need a plugin lib to do the job for you: http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html

Mike Caron
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