function [ ns, ks, as ] = comp_to_ksub ( nc, kc, ac )
%*****************************************************************************80
%
%% COMP_TO_KSUB converts a composition to a K-subset.
%
% Discussion:
%
% There is a bijection between K subsets and compositions.
%
% Because we allow a composition to have entries that are 0, we need
% to implicitly add 1 to each entry before establishing the bijection.
%
% Let AC be a composition of NC into KC parts.
%
% Then let
% NS = NC + KC - 1
% KS = KC - 1
% and define
% AS(I) = sum ( AC(1:I) + 1 ), for I = 1 : KS.
%
% Then AS is a KS subset of the integers 1 through NS.
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 04 December 2013
%
% Author:
%
% John Burkardt
%
% Input:
%
% integer NC, the composition sum.
%
% integer KC, the number of parts of the composition.
%
% integer AC(KC), the parts of the composition.
%
% Output:
%
% integer NS, the size of the set.
%
% integer KS, the size of the subset.
%
% integer AS(KS), the entries of the K-subset, in increasing order.
%
ns = nc + kc - 1;
ks = kc - 1;
as = cumsum ( ac(1:kc-1) + 1 );
return
end