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

 
class
	APPLICATION
 
create
	make
 
feature
 
	make
			-- Simulates one_of_n_lines a 1000000 times.
		local
			t: INTEGER
			simulator: ARRAY [INTEGER]
		do
			create simulator.make_filled (0, 1, 10)
			create one.make
			across
				1 |..| 1000000 as c
			loop
				t := one.one_of_n_lines (10)
				simulator [t] := simulator [t] + 1
			end
			across
				simulator as s
			loop
				io.put_integer (s.item)
				io.new_line
			end
		end
 
	one: ONE_OF_N_LINES
 
end
 