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

 
function Get-OneOfN ([int]$Number)
{
    $current = 1
 
    for ($i = 2; $i -le $Number; $i++)
    { 
        $limit = 1 / $i
 
        if ((Get-Random -Minimum 0.0 -Maximum 1.0) -lt $limit)
        {
            $current = $i
        }
    }
 
    $current
}
 
 
$table = [ordered]@{}
 
for ($i = 1; $i -lt 11; $i++)
{ 
    $table.Add(("Line {0,2}" -f $i), 0)
}
 
for ($i = 0; $i -lt 1000000; $i++)
{ 
    $index = (Get-OneOfN -Number 10) - 1
    $table[$index] = $table[$index] + 1
}
 
[PSCustomObject]$table
 