function [ a, done ] = ksub_next4 ( n, k, a, done )
%*****************************************************************************80
%
%% ksub_next4() generates the subsets of size K from a set of size N, one at a time.
%
% Discussion:
%
% The subsets are generated one at a time.
%
% The routine should be used by setting DONE to TRUE, and then calling
% repeatedly. Each call returns with DONE equal to FALSE, the array
% A contains information defining a new subset. When DONE returns
% equal to TRUE, there are no more subsets.
%
% There are ( N*(N-1)*...*(N+K-1)) / ( K*(K-1)*...*2*1) such subsets.
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 12 May 2018
%
% Author:
%
% John Burkardt.
%
% Input:
%
% integer N, the size of the entire set.
% K <= N.
%
% integer K, the size of the desired subset.
% 0 <= K <= N.
%
% integer A(K), is not needed on the first call, with DONE = TRUE.
% On subsequent calls, it should be the output value of A from the
% previous call.
%
% logical DONE, should be TRUE on the first call, to force
% initialization, and then FALSE on subsequent calls.
%
% Output:
%
% integer A(K), as long as DONE is returned FALSE, A
% is the next K subset.
%
% logical DONE, is TRUE if the routine is returning the
% next K subset, and FALSE if there are no more subsets to return.
%
if ( k < 0 )
fprintf ( 1, '\n' );
fprintf ( 1, 'KSUB_NEXT4 - Fatal error!\n' );
fprintf ( 1, ' K = %d\n', k );
fprintf ( 1, ' but 0 <= K is required!\n' );
error ( 'KSUB_NEXT4 - Fatal error!' );
end
if ( n < k )
fprintf ( 1, '\n' );
fprintf ( 1, 'KSUB_NEXT4 - Fatal error!\n' );
fprintf ( 1, ' N = %d\n', n );
fprintf ( 1, ' K = %d\n', k );
fprintf ( 1, ' but K <= N is required!\n' );
error ( 'KSUB_NEXT4 - Fatal error!' );
end
%
% First call:
%
if ( done )
a(1:k) = ( 1 : k )';
done = false;
%
% Empty set returned on previous call?
%
elseif ( k == 0 | n == 0 )
done = true;
%
% Next call.
%
elseif ( a(1) < n - k + 1 )
jsave = k;
for j = 1 : k - 1
if ( a(j) + 1 < a(j+1) )
jsave = j;
break
end
end
a(1:jsave-1) = ( 1 : ( jsave - 1 ) )';
a(jsave) = a(jsave) + 1;
done = false;
else
done = true;
end
return
end