W = nchoose(S) returns all possible combinations of 0, 1, or more
elements of the set S, having N elements. There are 2^N combinations
in total. W is a cell array and each cell holds one of these
combination (as a row vector).
S can be a cell array, and each cell of W will then contain a cell
array. W is the powerset of S, as it includes the empty set (0
elements) as it first cell.
For a vector of integers I, W = nchoose(S, I) returns only the sets
indicated by the indices I. This might be useful for large sets.
Examples:
nchoose([2 4 6 8])
% -> { [] ;
% [2] ;
% [4] ;
% [2 4] ;
% [6] ;
% ...
% [2 6 8] ;
% [4 6 8] ;
% [2 4 6 8]} ; % in total 16 different combinations
nchoose([33 22 11], [1 8 4])
% -> { [] ; [33 22 11] ; [ 33 11]}
Notes:
- For sets containing more than 18 elements a warning is given, as this
can take some time. Hit Ctrl-C to intterupt calculations.
- If S contain non-unique elements (e.g. S = [1 1 2]), nchoose will
return non-unique cells. In other words, nchoose treats all elements
of S as being unique. One could use nchoose(UNIQUE(S)) to avoid that.
- Loosely speaking, nchoose(S) collects all output of multiple calls to
NCHOOSEK(S, K) where K is looping from 1 to the number of elements of
S. The implementation of nchoose, however, does rely of a different
method and is much faster than such a loop.
- For more information, see: http://en.wikipedia.org/wiki/Power_set
See also nchoosek, perms,
permn, nchoose2, allcomb on the file Exchange
Citation pour cette source
Jos (10584) (2024). nchoose (https://www.mathworks.com/matlabcentral/fileexchange/20011-nchoose), MATLAB Central File Exchange. Récupéré le .
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A inspiré : nchoosecrit(S, FUN)
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Version | Publié le | Notes de version | |
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3.0 | implemented powers and subset |
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2.2.0.0 | updated description
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1.1.0.0 | reference to powerset |
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1.0.0.0 | improved algorithm (thank US!) |