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

BEGIN
   INT max lines = 10;		CO Should be read from a file. CO
   [max lines]INT stats;
   FOR i TO max lines DO stats[i] := 0 OD;
   first random (42);		CO Should have rather more entropy! CO
   PROC one of n = (INT n) INT :
   BEGIN
      INT result := 1;
      FOR i TO n DO (random < 1/i | result := i) OD;
      result
   END;
   TO 1000000 DO stats[one of n (max lines)] +:= 1 OD;
   print (("Line  Number times chosen", newline));
   FOR i TO max lines DO printf (($g(0)7xg(0)l$, i, stats[i])) OD
END