function [p,s]=v_permutes(n)
%V_PERMUTES All N! permutations of 1:N + signatures [P,S]=(N)
% The output P is a matrix of size (N!,N) where each row
% contains a permutation of the numbers 1:N. The rows are in 
% lexically sorted order.
%
% To permute the elements of an arbitrary vector V use
% V(PERMUTES(LENGTH(V))).

% PERMUTES(N) is the same as SORTROWS(PERMS(1:N)) but much faster.

% Thanks to Peter J Acklam for several improvements.

%      Copyright (c) 1998 Mike Brookes,  mike.brookes@ic.ac.uk
%      Version: $Id: v_permutes.m 10865 2018-09-21 17:22:45Z dmb $
%
%   VOICEBOX is a MATLAB toolbox for speech processing.
%   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   This program is free software; you can redistribute it and/or modify
%   it under the terms of the GNU Lesser General Public License as published by
%   the Free Software Foundation; either version 3 of the License, or
%   (at your option) any later version.
%
%   This program is distributed in the hope that it will be useful,
%   but WITHOUT ANY WARRANTY; without even the implied warranty of
%   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%   GNU Lesser General Public License for more details.
%
%   You can obtain a copy of the GNU Lesser General Public License from
%   https://www.gnu.org/licenses/ .
%    See files gpl-3.0.txt and lgpl-3.0.txt included in this distribution.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

p=1;
m=1;
if n>1
  for a=2:n
    q=zeros(a*m,a);
    r=2:a+1;
       ix=1:m;
    for b=1:a
       q(ix,1)=b;
      q(ix,2:a)=r(p);
      r(b)=b;
      ix=ix+m;
    end
    m=m*a;
    p=q;
  end
end
if nargout>1 s=1-2*rem(fix((1:m)'/2),2); end
