A method of choosing a line randomly from a file:

 Without reading the file more than once
 When substantial parts of the file cannot be held in memory
 Without knowing how many lines are in the file
Is to:

 keep the first line of the file as a possible choice, then
 Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2.
 Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3.
 ...
 Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N
 Return the computed possible choice when no further lines exist in the file.


Task

 Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. 
The number returned can vary, randomly, in each run.
 Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times.
 Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works.


Note: You may choose a smaller number of repetitions if necessary, but mention this up-front.

Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling

 
with(RandomTools[MersenneTwister]);
one_of_n_lines_in_a_file := proc(fn)
	local fid, N, n, L, l, line;
	fid := fopen(fn,'READ');
	if fid<0 then
		return; 
	end if; 
	N := 0; 
	n := 1;
	while not feof(fid) do
		N := N+1;
		L := FileTools[Text][ReadLine](fid);
		if (N*GenerateFloat() < 1) then
			n := N;		
			line := L;
		end if;
	end do; 
	fclose(fid);
	return(n);
end proc;
 