Comments and Ratings

Darren and John-

Most of what I do with Matlab is simulation. From the standpoint of a simulationist, nchoosek is probably more suitable in the development/debugging stage of a simulation, but once the development and debugging has been done, one wants the code to run as fast as possible. Below are the results of a simple timing comparison of nchoosek and choose:

>> mytime(0); for i=1:1e6; nchoosek(52,13); end; mytime;
19-May-2009 10:45:26 Timer initialized.
19-May-2009 10:46:01 Last step took 35.56 sec.; total elapsed= 35.56 sec.

>> mytime(0); for i=1:1e6; choose(52,13); end; mytime;
19-May-2009 10:46:11 Timer initialized.
19-May-2009 10:46:20 Last step took 8.70 sec.; total elapsed= 8.70 sec.

Note that my function runs over four times as fast as Matlab's builtin function. For the user who invokes nchoosek small numbers of times from the command line, the difference in speed is unimportant. But, when nchoosek or choose is being called millions or tens of milions of times from within a program, the difference becomes important. Please let me know if further explanation is required.

This code would be more efficient if all values were stored as integers, and all operations were performed on integers. There's no reason to use floating point. Also, the limitation that numbers cannot be larger than 2^32 should be removed. Otherwise, very nice.