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

 
math.randomseed(os.time())
 
local n = 10
local trials = 1000000
 
function one(n)
    local chosen = 1
    for i = 1, n do
        if math.random() < 1/i then
            chosen = i
        end
    end
 
    return chosen
end
 
-- 0 filled table for storing results
local results = {}
for i = 1, n do results[i] = 0 end
 
-- run simulation
for i = 1, trials do
    local result = one(n)
    results[result] = results[result] + 1
end
 
print("Value","Occurrences")
print("-------------------")
for k, v in ipairs(results) do
    print(k,v)
end
 