nchoosecrit(S, FUN)

returns those subsets (= combinations of elements of a set) that fulfill a specific criterion


Updated 6 Feb 2018

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W = nchoosecrit(S, FUN) returns those combinations of one or more element of the set S (called a subset) that fulfill a specific criterion. This criterion is specified by the function FUN. FUN is a function handle to a function that takes one input argument and returns a logical scalar value.
W will be cell array of row vectors. Each cell of W holds one of the combinations C of S for which FH(C) is true.

[W, IX] = nchoosecrit(S, FUN) also returns the indices, such that S(IX{k}) equals W{k}.
Maximally, there are 2^N-1 possible subsets of S (N being the number of elements of S). This number therefore grows rapidly with increasing N. W is a selection of those subsets.

S can be a cell array, and each cell of W will then contain a cell array.

% find the subsets that sum op to 6
nchoosecrit([1 2 3 4 5 6], @(x) sum(x)==6)
% -> { [1 2 3], [2 4], [1 5], [6]}

% find subgroups of 4 or more people that contain either James or Bob,
% but not both!
S = {'Bob' 'Tom' 'Joe' 'Bill' 'James', 'Henry'} ; % the whole group
% criterion 1:
fh1 = @(x) numel(x) >= 4 ;
% criterion 2
fhname = @(x,y) any(strncmp(y,x,numel(y))) ;
fh2 = @(x) xor(fhname(x,'James'), fhname(x,'Bob')) ;
% the 2 criterions combined:
fhcomb = @(x) fh1(x) && fh2(x) ;
[W, IX] = nchoosecrit(S, fhcomb)
S(IX{2}), W{2} % check

- If S contain non-unique elements (e.g. S = [1 1 2]), nchoosecrit will
return non-unique cells. In other words, nchoosecrit treats all elements
of S as being unique. One could use nchoosecrit(UNIQUE(S)) to avoid that.
- The output is the same as
Wtemp = nchoose(S) ; W = Wtemp(cellfun(Wtemp, fh)) ;
but does not create the (possible very large) temporary array Wtemp.

See also nchoosek, perms
nchoose, permn, allcomb on the file Exchange

Cite As

Jos (10584) (2023). nchoosecrit(S, FUN) (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2017b
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes

included indices as second output