function a = ksub_random4 ( n, k )
%*****************************************************************************80
%
%% ksub_random4() selects a random subset of size K from a set of size N.
%
% Discussion:
%
% This routine is somewhat impractical for the given problem, but
% it is included for comparison, because it is an interesting
% approach that is superior for certain applications.
%
% The approach is mainly interesting because it is "incremental";
% it proceeds by considering every element of the set, and does not
% need to know how many elements there are.
%
% This makes this approach ideal for certain cases, such as the
% need to pick 5 lines at random from a text file of unknown length,
% or to choose 6 people who call a certain telephone number on a
% given day. Using this technique, it is possible to make the
% selection so that, whenever the input stops, a valid uniformly
% random subset has been chosen.
%
% Obviously, if the number of items is known in advance, and
% it is easy to extract K items directly, there is no need for
% this approach, and it is less efficient since, among other costs,
% it has to generate a random number for each item, and make an
% acceptance/rejection test.
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 01 July 2021
%
% Author:
%
% John Burkardt
%
% Reference:
%
% Tom Christiansen, Nathan Torkington,
% "8.6: Picking a Random Line from a File",
% Perl Cookbook, pages 284-285,
% O'Reilly, 1999.
%
% Input:
%
% integer N, the size of the set from which subsets are drawn.
%
% integer K, number of elements in desired subsets. K must
% be between 0 and N.
%
% Output:
%
% integer A(K), contains the indices of the selected items.
%
next = 0;
%
% Here, we use a DO WHILE to suggest that the algorithm
% proceeds to the next item, without knowing how many items
% there are in total.
%
% Note that this is really the only place where N occurs,
% so other termination criteria could be used, and we really
% don't need to know the value of N!
%
while ( next < n )
next = next + 1;
if ( next <= k )
i = next;
a(i) = next;
else
r = rand ( 1, 1 );
if ( r * next <= k )
i = randi ( [ 1, k ], 1 );
%
% If we slide the current values down, and add the new item at the end,
% our subset will be ordered.
%
a(i:k-1) = a(i+1:k);
a(k) = next;
% a(i) = next;
end
end
end
return
end