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

Declare Function one_of_n (n As Long) As Long
 
Dim As Long L0, c, elegido(1 To 10)
 
Function one_of_n (n As Long) As Long
 
    'asume que la primera línea es 1
    Dim As Long L1, opcion
    For L1 = 1 To n
        If Int(Rnd * L1) = 0 Then opcion = L1
    Next L1
    one_of_n = opcion
End Function
 
Randomize Timer
 
For L0 = 1 To 1000000
    c = one_of_n(10)
    elegido(c) += 1
Next L0
 
For L0 = 1 To 10
    Print Using "##. #######"; L0; elegido(L0)
Next L0
 
Sleep