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

defmodule One_of_n_lines_in_file do
  def task do
    dict = Enum.reduce(1..1000000, %{}, fn _,acc ->
      Map.update( acc, one_of_n(10), 1, &(&1+1) )
    end)
    Enum.each(Enum.sort(Map.keys(dict)), fn x ->
      :io.format "Line ~2w selected: ~6w~n", [x, dict[x]]
    end)
  end
 
  def one_of_n( n ), do: loop( n, 2, :rand.uniform, 1 )
 
  def loop( max, n, _random, acc ) when n == max + 1, do: acc
  def loop( max, n, random, _acc ) when random < (1/n), do: loop( max, n + 1, :rand.uniform, n )
  def loop( max, n, _random, acc ), do: loop( max, n + 1, :rand.uniform, acc )
end
 
One_of_n_lines_in_file.task