Fastest way to generate binomial coefficients

Question

I need to calculate combinations for a number.

What is the fastest way to calculate nCp where n>>p?

I need a fast way to generate binomial coefficients for a

Answer 1

If you need to compute them for all n, Ribtoks's answer is probably the best. For a single n, you're better off doing like this:

C[0] = 1
for (int k = 0; k < n; ++ k)
    C[k+1] = (C[k] * (n-k)) / (k+1)

The division is exact, if done after the multiplication.

And beware of overflowing with C[k] * (n-k) : use large enough integers.