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All possible permutation of a given vector.

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luca
luca 2019-7-23
编辑： Stephen23 2019-7-23
Given a vector, e.g [1 2 3 4 1], I would like to obtain all the possible permutations with NO REPETITION and NO ROTATION.
With
v = [1 2 3 4 1];
P = unique(perms(v),'rows');
I can avoid repetition but no rotation.
With rotation I mean that [1 2 1 4 3] and [2 1 4 3 1] are the same vector because the sequence is the same, just view from a different initial position.
I would like to be able to obtain all the possible combinations that avoid also this fact (rotation).
Thanks
  1 个评论
Rik
Rik 2019-7-23
I suspect there are two options:
  1. looping through your array (from end to beginning) and remove all rotations (use circshift)
  2. design your own implementation of perms that avoids rotations
Neither is likely to be fast, and the first will also require the generation of a very large array for slightly larger vectors.

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Stephen23
Stephen23 2019-7-23
编辑：Stephen23 2019-7-23
V = [1,2,3,4,1];
N = numel(V);
% Permutations:
P = perms(V(2:N));
P(:,N) = V(1);
P = unique(P,'rows')
% Rotations:
R = P; % just to allow comparison.
X = hankel(2:N,[N,1:N-1]);
for k = size(R,1):-1:1
T = R(k,:);
if any(ismember(T(X),R,'rows'))
R(k,:) = [];
end
end
Giving a 12x5 matrix:
R =
1 2 3 4 1
1 2 4 3 1
1 3 2 4 1
1 3 4 2 1
1 4 2 3 1
1 4 3 2 1
2 1 3 4 1
2 1 4 3 1
2 3 1 4 1
2 4 1 3 1
3 1 4 2 1
3 2 1 4 1
See also:
https://en.wikipedia.org/wiki/Necklace_(combinatorics)

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