class MathUtils

  def initialize
    @result = nil
    @necessary_primes = nil
  end

  def generate_sums(number, min_parcels = 2, max_parcels = Float::INFINITY, result_file = 'results.txt', &block)
    @result = File.open(result_file, 'w+')
    @block = block
    _partial = [number, 1]
    _generate_sums(_partial, 0, number, number, min_parcels, max_parcels)
  end

  def generate_prime_sums(number, min_parcels = 2, max_parcels = Float::INFINITY, result_file = 'results.txt')
    @necessary_primes = []

    primes_from_file = File.foreach('primes.txt').map(&:to_i)

    primes_from_file.each do |p|
      @necessary_primes << p if p <= number
    end

    primes_from_file = nil

    @necessary_primes.freeze

    generate_sums(number, min_parcels, max_parcels, result_file) do |result|
      (result - @necessary_primes).empty?
    end

  end

  private

  def _generate_sums(_partial, index, number, target, min_parcels, max_parcels)
    return if target < 0


    return if index > max_parcels

    # imprime um resultado válido
    if target == 0 && index >= min_parcels
      if @block
        if @block.call(_partial[0,index])
          @result.puts _partial[0,index].inspect
        end
      else
        @result.puts _partial[0,index].inspect
      end
    end


    index == 0 ? prev = 1 : prev = _partial[index -1]

    k = prev

    while( k <= number)
      _partial[index] = k
      _generate_sums(_partial, index+1, number, target - k, min_parcels, max_parcels)
      k+=1
    end

  end
end

# 18, 131, 138, 366


n=131
min_p = 4
max_p = 4



m = MathUtils.new

PRIMES_29 = File.foreach('primes.txt').first(29).map(&:to_i)



# m.generate_prime_sums(n, min_p, max_p, '131_sums_primes_7x7')
m.generate_sums(n, min_p, max_p, '131_sums_primes_4x4') do |result|
  (result - PRIMES_29).empty?
end