Algorithm for Calculating Binomial Coefficient

Question

I need a way of calculating combinations without running out of memory. Here\'s what i have so far.

public static long combination(long n, long k) // nCk
{
          


        

Answer 1

One of the best methods for calculating the binomial coefficient I have seen suggested is by Mark Dominus. It is much less likely to overflow with larger values for N and K than some other methods.

public static long GetBinCoeff(long N, long K)
{
   // This function gets the total number of unique combinations based upon N and K.
   // N is the total number of items.
   // K is the size of the group.
   // Total number of unique combinations = N! / ( K! (N - K)! ).
   // This function is less efficient, but is more likely to not overflow when N and K are large.
   // Taken from:  http://blog.plover.com/math/choose.html
   //
   long r = 1;
   long d;
   if (K > N) return 0;
   for (d = 1; d <= K; d++)
   {
      r *= N--;
      r /= d;
   }
   return r;
}