permutWithRepeat(string)

function permutWithRepeat(string)
    string = string:lower()
    math.randomseed(os.time())
    letters, combinations = {}, {}
    number = string:len()
    for i = 1, number do
        table.insert(letters, string.sub(string, i,i))
    end

    function getRepsTable(tab)
        local elements = {}
        for i, v in pairs(tab) do
            if not(elements[v])then
                elements[v] = 1
            else
                elements[v] = elements[v] + 1
            end
        end
        local x = 1
        for _, j in pairs(elements) do
            x = x * j
        end
        return x
    end

    function getFatorial(num)
        local x = 1
        for i = num, 1, -1 do
            x = x * i
        end
        return x
    end
    function getFatorialReps(num, letras)
        if(getRepsTable(letras) > 1)then
            return 0
        end
        return (getFatorial(num)/getFatorial(getRepsTable(letras)))
    end

    function isInTable(table, element)
        for i, v in pairs(table)do
            if(rawequal(v, element))then
                return true
            end
        end
        return false
    end

    function randomizeTable(tabela)
        local num  = #tabela
        local sequence, newTable = {}, {}
        while not rawequal(#sequence, #tabela) do
            local random = math.random(num)
            if not(isInTable(sequence, random))then
                table.insert(sequence, random)
            end
        end
        for i, v in pairs(sequence) do
            rawset (newTable, i, tabela[v])
        end
        return {concat=table.concat(newTable,""), tab = newTable}
    end

    print("O numero de anagramas é: "..getFatorialReps(number, letters)..".\n")
    if(rawequal(#combinations, getFatorialReps(number, letters)))then
        print("Não existem combinações sem repetição para essa palavra.")
    else
        print("São eles(isso pode demorar um pouco):\n")
    end
    collectgarbage ("collect")
    while true do
        local str = randomizeTable(letters)
        if not(isInTable(combinations, str.concat))then
            if(tonumber(getRepsTable(str.tab)) == 1)then
                table.insert(combinations, str.concat)
            end
        end
        if(rawequal(#combinations, getFatorialReps(number, letters)))then
           break
        end
    end
    collectgarbage ("collect")
    table.sort(combinations)
    print(table.concat(combinations, "\n"))
    print("Tempo decorrido: "..os.clock().." segundos.")
end

permutWithRepeat("abcdef")