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

Procedure.f randomFloat()
   ProcedureReturn Random(1000000) / 1000000
EndProcedure
 
Procedure one_of_n(n)
  Protected linesRead, lineChosen
  While linesRead < n 
    linesRead + 1
    If randomFloat() <= (1.0 / (linesRead))
       lineChosen = linesRead
    EndIf
  Wend
  ProcedureReturn lineChosen
EndProcedure
 
If OpenConsole()
  #testFileLineCount = 10
  #simulationCount = 1000000
  Define i
  Dim a(#testFileLineCount) ;index 0 is not used
  For i = 1 To #simulationCount
    x = one_of_n(#testFileLineCount)
    a(x) + 1
  Next
 
  For i = 1 To #testFileLineCount
    Print(Str(a(i)) + "  ")
  Next
  PrintN("")
 
  Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
  CloseConsole()
EndIf