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 Program
    {
        private static Random rnd = new Random();
        public static int one_of_n(int n)
        {
            int currentChoice = 1;
            for (int i = 2; i <= n; i++)
            {
                double outerLimit = 1D / (double)i;
                if (rnd.NextDouble() < outerLimit)
                    currentChoice = i;
            }
            return currentChoice;
        }
 
        static void Main(string[] args)
        {
            Dictionary<int, int> results = new Dictionary<int, int>();
            for (int i = 1; i < 11; i++)
                results.Add(i, 0);
 
            for (int i = 0; i < 1000000; i++)
            {
                int result = one_of_n(10);
                results[result] = results[result] + 1;
            }
 
            for (int i = 1; i < 11; i++)
                Console.WriteLine("{0}\t{1}", i, results[i]);
            Console.ReadLine();
        }
    }
 