local fmt = require "fmt"

local d = {
    {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
    {1, 2, 3, 4, 0, 6, 7, 8, 9, 5},
    {2, 3, 4, 0, 1, 7, 8, 9, 5, 6},
    {3, 4, 0, 1, 2, 8, 9, 5, 6, 7},
    {4, 0, 1, 2, 3, 9, 5, 6, 7, 8},
    {5, 9, 8, 7, 6, 0, 4, 3, 2, 1},
    {6, 5, 9, 8, 7, 1, 0, 4, 3, 2},
    {7, 6, 5, 9, 8, 2, 1, 0, 4, 3},
    {8, 7, 6, 5, 9, 3, 2, 1, 0, 4},
    {9, 8, 7, 6, 5, 4, 3, 2, 1, 0}
}

local inv = {0, 4, 3, 2, 1, 5, 6, 7, 8, 9}

local p = {
    {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
    {1, 5, 7, 6, 2, 8, 3, 0, 9, 4},
    {5, 8, 0, 3, 7, 9, 6, 1, 4, 2},
    {8, 9, 1, 6, 0, 4, 3, 5, 2, 7},
    {9, 4, 5, 3, 1, 2, 6, 8, 7, 0},
    {4, 2, 8, 6, 5, 7, 3, 9, 0, 1},
    {2, 7, 9, 3, 8, 0, 6, 4, 1, 5},
    {7, 0, 4, 6, 9, 1, 3, 2, 5, 8}
}

local function verhoeff(s, validate, table)
    if table then
        print($"{validate ? "Validation" : "Check digit"} calculations for '{s}':\n")
        print(" i  nᵢ  p[i,nᵢ]  c")
        print("------------------")
    end
    if !validate then s ..= "0" end
    local c = 0
    local le = #s - 1
    for i = le, 0, -1 do
        local ni = s[i + 1]:byte() - 48
        local pi = p[(le - i) % 8 + 1][ni + 1]
        c = d[c + 1][pi + 1]
        if table then fmt.print("%2d  %d      %d     %d", le - i, ni, pi, c) end
    end
    if table and !validate then print($"\ninv[{c + 1}] = {inv[c + 1]}") end
    return !validate ? inv[c + 1] : c == 0
end

local sts = {{"236", true}, {"12345", true}, {"123456789012", false}}
for sts as st do
    local c = verhoeff(st[1], false, st[2])
    print($"\nThe check digit for '{st[1]}' is '{c}'\n")
    for {st[1] .. tostring(c),  st[1] .. "9"} as stc do
        local v = verhoeff(stc, true, st[2])
        print($"\nThe validation for '{stc}' is {v ? "correct" : "incorrect"}.\n")
    end
end