魔方陣グルグル

mahou.rb

class Mahou
  DIMENSION = 7

  def self.column_check a, b
    0.upto(DIMENSION - 1) do |i|
      sum = 0
      0.upto(DIMENSION - 1) do |j|
        sum += a[j][i]
      end
      raise "縦の行: #{j + 1} が #{sum} なので定和性を満しません" if sum != b
    end

    0.upto(DIMENSION - 1) do |i|
      sum = a[i].inject(:+)
      raise "横の行: #{i + 1} が #{sum} なので定和性を満しません" if sum != b
    end

    sum = 0
    0.upto(DIMENSION - 1) do |i|
      sum += a[i][i]
    end
    raise "左上からの対角線が #{sum} なので定和性を満しません" if sum != b

    sum = 0
    0.upto(DIMENSION - 1) do |i|
      sum += a[i][DIMENSION - 1 - i]
    end
    raise "右上からの対角線が #{sum} なので定和性を満しません" if sum != b
  end

  def self.uniq? m
    m.flatten.size == m.flatten.uniq.size
  end

  def self.format_print m
    l = "---" * DIMENSION + "-"
    puts l
    m.each do |n|
      n.each do |e|
        print "|"
        printf "%02d", e
      end
      puts "|"
      puts l
    end
  end

  def self.simple
    a = simple_a
    b = simple_b
    m = Array.new(DIMENSION) { Array.new (DIMENSION) }
    a.each_with_index do |i, j|
      i.each_with_index do |k, n|
        m[j][n] = (k - 1) * DIMENSION + b[j][n]
      end
    end
    const_sum = (DIMENSION * ((DIMENSION ** 2) +1) / 2)
    format_print m
    column_check m, const_sum
    raise "同じ要素が含まれています" if !uniq? m
  end

  def self.simple_a
    seed = [*1..DIMENSION]
    delete_elem = (DIMENSION + 1) / 2
    seed.delete(delete_elem)
    seed.shuffle!
    seed.insert(delete_elem - 1, delete_elem)
    a = Array.new(DIMENSION) { seed.clone }
    r = delete_elem
    0.upto(DIMENSION - 1) do |x|
      r -= 1
      a[x].rotate!(r)
      r = DIMENSION - 1 if r < 0
    end
    return a
  end

  def self.simple_b
    b = Array.new(DIMENSION) { Array.new(DIMENSION) }
    raw_seed = [*1..DIMENSION].shuffle
    0.upto(DIMENSION - 1) { |i| b[i][i] = raw_seed[i] }
    seed = raw_seed.reverse * DIMENSION

    0.upto(DIMENSION - 1) do |x|
      point = seed.index(raw_seed[x])
      start = x
      1.upto(DIMENSION) do |y|
        b[start][x] = seed[point]
        point += 1
        start += 1
        start = 0 if start >= b.size
      end
    end
    return b
  end
end

Mahou.simple