% HISTPROBTOTAL
% Lecture 6B demo: Probability of obtaining
% a "nearly" uniform histogram, that is,
% all bars within given tolerance.
%
% Default parameters:
%  k=10  categories (bars)
%  n=100 points sampled
%
% Tolerance is how much the bars are allowed to differ from
% the expected height, which is n/k.
%
function p = histprobtotal(tolerance, n, k)
    if nargin<2, n=100; end
    if nargin<3, k=10; end

    % This is a laborious method, but the computer does it.
    % Consider, one by one, each possible collection of bar heights
    % such that the heights are within the tolerance.
    p = 0;
    minx = ceil(n/k - tolerance);
    maxx = floor(n/k + tolerance);
    Y = maketerms(n, k, minx, maxx);
    fprintf('we find %d different histograms within tolerance\n', size(Y,1));
    for i=1:size(Y,1)
        p = p + histprob(Y(i,:));
    end

end