require "table2"
local fmt = require "fmt"

local nmax <const> = 20

local function avg(n)
    local tests = 1e4
    local sum = 0
    for _ = 1, tests do
        local v = table.rep(nmax, false)
        local x = 1
        while !v[x] do
            v[x] = true
            sum += 1
            x = math.random(1, n)
        end
    end
    return sum / tests
end

local function ana(n)
    if n < 2 then return 1 end
    local term = 1
    local sum = 1
    for i = n, 2, -1 do
        term *= (i - 1) / n
        sum += term
    end
    return sum
end

print(" N    average    analytical    (error)")
print("===  =========  ============  =========")
for n = 1, nmax do
    local a = avg(n)
    local b = ana(n)
    local e = math.abs(a - b) / b * 100
    fmt.print("%3d %9.4f  %12.4f   (%6.2f%%)", n, a, b, e)
end