% MAKETERMS
% Create a list of all ways of representing a given integer n,
% as a sum of k integer terms, each having value within [minx,maxx].
%
% Simple recursive solution for illustration purposes.
% (There might be more efficient methods.)
%
% Used for computing histogram probabilities.
%
% You can also use this for the Lecture6B sum-of-three-dice example
% to list the cases: maketerms(5,3,1,6).
%
function X=maketerms(n, k, minx, maxx)
if nargin<3, minx=0; end
if nargin<4, maxx=n; end

if k==1
    if minx<=n && n<=maxx
        X = [n];
    else
        X = zeros(0,1);
    end
    return
end

firstmin = max(minx, n-(k-1)*maxx);
firstmax = min(maxx, n-(k-1)*minx);
X = zeros(0,k);
for first = firstmin:firstmax
    Y = maketerms(n-first, k-1, minx, maxx);
    Y = [repmat(first, size(Y,1), 1) Y];
    X = [X; Y];
end