One of n lines in a file

One of n lines in a file is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

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

1. Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algotrithm above to return an integer - the line number of the line chosen from the file.
   The number returned can vary, randomly, in each run.
2. 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.
3. 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.

Python

<lang python>from random import random as rnd

def one_of_n(n):

   # Zero based line numbers
   choice = 0
   for i in range(1, n):
       if rnd() < 1. / (i + 1.):
           choice = i
   return choice
           

def one_of_n_test(n=10, trials=1000000):

   bins = [0] * n
   if n:
       for i in range(trials):
           bins[one_of_n(n)] += 1
   return bins

print(one_of_n_test())</lang>

Sample output

[99833, 100303, 99902, 100132, 99608, 100117, 99531, 100017, 99795, 100762]