permn - permutations with repetition
Using two input variables V and N, M = permn(V,N) returns all
permutations of N elements taken from the vector V, with repetitions.
V can be any type of array (numbers, cells etc.) and M will be of the
same type as V. If V is empty or N is 0, M will be empty. M has the
size numel(V).^N-by-N.
When only a subset of these permutations is needed, you can call permn
with 3 input variables: M = permn(V,N,K) returns only the K-ths
permutations. The output is the same as M = permn(V,N) ; M = M(K,:),
but it avoids memory issues that may occur when there are too many
combinations. This is particulary useful when you only need a few
permutations at a given time. If V or K is empty, or N is zero, M will
be empty. M has the size numel(K)-by-N.
[M, I] = permn(...) also returns an index matrix I so that M = V(I).
Examples:
M = permn([1 2 3],2) % returns the 9-by-2 matrix:
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
M = permn([99 7],4) % returns the 16-by-4 matrix:
99 99 99 99
99 99 99 7
99 99 7 99
99 99 7 7
...
7 7 7 99
7 7 7 7
M = permn({'hello!' 1:3},2) % returns the 4-by-2 cell array
'hello!' 'hello!'
'hello!' [1x3 double]
[1x3 double] 'hello!'
[1x3 double] [1x3 double]
V = 11:15, N = 3, K = [2 124 21 99]
M = permn(V, N, K) % returns the 4-by-3 matrix:
% 11 11 12
% 15 15 14
% 11 15 11
% 14 15 14
% which are the 2nd, 124th, 21st and 99th permutations
% Check with permn using two inputs
M2 = permn(V,N) ; isequal(M2(K,:),M)
% Note that M2 is a 125-by-3 matrix
% permn can be used generate a binary table, as in
B = permn([0 1],5)
NB Matrix sizes increases exponentially at rate (n^N)*N.
See also perms, nchoosek
allcomb, permpos on the File Exchange
Zitieren als
Jos (10584) (2024). permn (https://www.mathworks.com/matlabcentral/fileexchange/7147-permn), MATLAB Central File Exchange. Abgerufen .
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Inspiriert: N_PERMUTE_K, VChooseKRO, de Bruijn sequence generator, Kautz sequence generator, permnsub(V,N, IX)
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Version | Veröffentlicht | Versionshinweise | |
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6.2.0.0 | fixed coding style warnings |
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6.1.0.0 | spelling corrections
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5.1.0.0 | Renamed file into PERMN, fixed small bug, extended help section |
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1.3.0.0 | Reference to COMBNSUB for large combinatorial problems. |
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1.2.0.0 | corrected to give column vector output for N=1. (error pointed out by Wilson via email). |
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1.1.0.0 | modified slightly based on suggestions by Jan Simon (thanks!) |
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1.0.0.0 | fast algorithm |