function [ npart, jarray, iarray, more ] = equiv_next ( ...
n, npart, jarray, iarray, more )
%*****************************************************************************80
%
%% equiv_next() computes the partitions of a set one at a time.
%
% Discussion:
%
% A partition of a set assigns each element to exactly one subset.
%
% The number of partitions of a set of size N is the Bell number B(N).
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 30 July 2004
%
% Author:
%
% John Burkardt.
%
% Reference:
%
% Albert Nijenhuis, Herbert Wilf,
% Combinatorial Algorithms,
% Academic Press, 1978, second edition,
% ISBN 0-12-519260-6.
%
% Input:
%
% integer N, the number of elements in the set to be partitioned.
%
% integer NPART, the number of subsets in the previous partition.
%
% integer JARRAY(N), the number of elements in each subset
% of the previous partition.
%
% integer IARRAY(N), the subset to which each element belongs
% in the previous partition.
%
% logical MORE, is set to FALSE on the first call, and the
% input values of NPART, JARRAY and IARRAY are not needed. On subsequent
% calls, MORE should be TRUE, and NPART, JARRAY, and IARRAY should have the
% values of the output quantities NPART, JARRAY and IARRAY
% from the previous call.
%
% Output:
%
% integer NPART, the number of subsets in the new partition.
%
% integer JARRAY(N), the number of elements in each subset
% of the new partition.
%
% integer IARRAY(N), the subset to which each element belongs
% in the new partition.
%
% logical MORE, is TRUE as long as the new partition returned
% is not the last one. When MORE is returned FALSE, all the partitions
% have been computed and returned.
%
if ( ~ more )
npart = 1;
iarray(1:n) = 1;
jarray(1) = n;
jarray(2:n) = 0;
else
m = n;
while ( jarray(iarray(m)) == 1 )
iarray(m) = 1;
m = m - 1;
end
l = iarray(m);
npart = npart + m - n;
jarray(1) = jarray(1) + n - m;
if ( l == npart )
npart = npart + 1;
jarray(npart) = 0;
end
iarray(m) = l + 1;
jarray(l) = jarray(l) - 1;
jarray(l+1) = jarray(l+1) + 1;
end
more = ( npart ~= n );
return
end