ONECOMB

Obtain a single combination of N numbers taken K at a time.

Description

comb = ONECOMB(N,K,M) returns the M-th combination of the sorted list of all combinations from NCHOOSEK.
Makes use of a fast algorithm for the generation of a single combination.

NCHOOSEK(1:4,3) =
[ 1 2 3
  1 2 4
  1 3 4
  2 3 4 ]

onecomb(4,3,3) =
[ 1 3 4 ]

• MATLAB release: MATLAB 7 (R14)

[Darren Rowland]

@ Marco/PXlab

It is exactly correct that this function with call structure

C1 = onecomb(N,K,M)

returns the same result as

AC = nchoosek(N,K);
C2 = AC(M,:)

The advantage of this function is that the intermediate array AC is not computed by ONECOMB. The array AC can be immensely large for large N and K approx N/2, and is a waste to compute if one only requires a small number of combinations from the total.

Additionally, if one requires many combinations, my testing (not included here but simple to duplicate) showed that the time to compute all the combinations using NCHOOSEK was approximately the same as computing all the combinations one-at-a-time using ONECOMB.

[Rob Campbell]

This well coded and does what it says. Can be substantially faster than nchoosek. For example:

>> tic, for i=1:1E4;onecomb(10,5,5);end,toc/1E4
ans =
   7.3127e-05
>> tic, for i=1:1E4;NCHOOSEK(1:10,5);end,toc/1E4
ans =
   3.7945e-04

The 1 star review seems to have missed the point.

[Husam Aldahiyat]

Very useful submission, well written.