Mapping Toolbox

combntns

Determine combinations of a set of values

Syntax

combos = combntns(set,subset)

Description

The combntns command provides the combinatorial subsets of a set of numbers. It is similar to the mathematical expression a choose b, except that instead of the number of such combinations, the actual combinations are returned. In combinatorial counting, the ordering of the values is not significant.

combos = combntns(set,subset) returns a matrix whose rows are the various combinations that can be taken of the elements of the vector set of length subset. Many combinatorial applications can make use of a vector 1:n for the input set to return generalized, indexed combination subsets.

The numerical value of the mathematical statement a choose b is size(combos,1).

Examples

How can the numbers 1 to 5 be taken in sets of three (i.e., what is 5 choose 3)?

• combos = combntns(1:5,3)
  combos =
       1     2     3
       1     2     4
       1     2     5
       1     3     4
       1     3     5
       1     4     5
       2     3     4
       2     3     5
       2     4     5
       3     4     5
  size(combos,1)  % "5 choose 3"
  ans =
      10
  

Note that if a value is repeated in the input vector, each occurrence is treated as independent:

• combos = combntns([2 2 5],2)
  combos =
       2     2
       2     5
       2     5
  

Remarks

This is a recursive function.

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