function [ a, more, h, t ] = comp_next ( n, k, a, more, h, t )
%*****************************************************************************80
%
%% COMP_NEXT computes the compositions of the integer N into K parts.
%
% Discussion:
%
% A composition of the integer N into K parts is an ordered sequence
% of K nonnegative integers which sum to N. The compositions (1,2,1)
% and (1,1,2) are considered to be distinct.
%
% The routine computes one composition on each call until there are no more.
% For instance, one composition of 6 into 3 parts is
% 3+2+1, another would be 6+0+0.
%
% On the first call to this routine, set MORE = FALSE. The routine
% will compute the first element in the sequence of compositions, and
% return it, as well as setting MORE = TRUE. If more compositions
% are desired, call again, and again. Each time, the routine will
% return with a new composition.
%
% However, when the LAST composition in the sequence is computed
% and returned, the routine will reset MORE to FALSE, signaling that
% the end of the sequence has been reached.
%
% This routine originally used a SAVE statement to maintain the
% variables H and T. I have decided that it is safer
% to pass these variables as arguments, even though the user should
% never alter them. This allows this routine to safely shuffle
% between several ongoing calculations.
%
% There are 28 compositions of 6 into three parts. This routine will
% produce those compositions in the following order:
%
% I A
% - ---------
% 1 6 0 0
% 2 5 1 0
% 3 4 2 0
% 4 3 3 0
% 5 2 4 0
% 6 1 5 0
% 7 0 6 0
% 8 5 0 1
% 9 4 1 1
% 10 3 2 1
% 11 2 3 1
% 12 1 4 1
% 13 0 5 1
% 14 4 0 2
% 15 3 1 2
% 16 2 2 2
% 17 1 3 2
% 18 0 4 2
% 19 3 0 3
% 20 2 1 3
% 21 1 2 3
% 22 0 3 3
% 23 2 0 4
% 24 1 1 4
% 25 0 2 4
% 26 1 0 5
% 27 0 1 5
% 28 0 0 6
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 02 July 2008
%
% Author:
%
% Original FORTRAN77 version by Albert Nijenhuis and Herbert Wilf
% MATLAB version by John Burkardt.
%
% Reference:
%
% Albert Nijenhuis, Herbert Wilf,
% Combinatorial Algorithms for Computers and Calculators,
% Second Edition,
% Academic Press, 1978,
% ISBN: 0-12-519260-6,
% LC: QA164.N54.
%
% Input:
%
% integer N, the integer whose compositions are desired.
%
% integer K, the number of parts in the composition.
%
% integer A(K), the previous composition. On the first call,
% with MORE = FALSE, set A = []. Thereafter, A should be the
% value of A output from the previous call.
%
% logical MORE. The input value of MORE on the first
% call should be FALSE, which tells the program to initialize.
% On subsequent calls, MORE should be TRUE, or simply the
% output value of MORE from the previous call.
%
% integer H, T, two internal parameters needed for the
% computation. The user may need to initialize these before the
% very first call, but these initial values are not important.
% The user should not alter these parameters once the computation
% begins.
%
% Output:
%
% integer A(K), the next composition.
%
% logical MORE, will be TRUE unless the composition
% that is being returned is the final one in the sequence.
%
% integer H, T, the updated values of the two internal
% parameters.
%
if ( ~ more )
t = n;
h = 0;
a(1) = n;
a(2:k) = 0;
else
if ( 1 < t )
h = 0;
end
h = h + 1;
t = a(h);
a(h) = 0;
a(1) = t - 1;
a(h+1) = a(h+1) + 1;
end
more = ( a(k) ~= n );
return
end