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Message: [QUOTE="Robert Dober, post: 4560485"] Hmm does not seem that the attachments are too readable on the Ruby Quiz site. So please forgive me for posting them here again, inline. I do not include the HTML plugin as it is not closely connected to the topic of the Quiz. Cheers Robert # cat 124-magic-square.rb # vim: sts=2 sw=2 ft=ruby expandtab nu tw=0: Usage = <<-EOS usage: ruby #{$0} [-t|--test] [-h|--html] <Square Order List> Prints Magic Squares for all indicated orders. Indicating -t also tests the results. EOS loop do case ARGV.first when "-t", "--test" require 'test-squares' ARGV.shift when "-h", "--html" require 'html-output' ARGV.shift when "-?", "--help", nil puts Usage exit when "--" ARGV.shift && break else break end end # # This is a default output module, another output # module called HTMLOutput is provided as an example # how to pull in an appropriate Output module # as plugin. # module Output def to_s decoration = false l = (@order*@order).to_s.size return @data.map{ |line| line.map{ |cell| "%#{l}d" % cell }.join(" ") }.join("\n") unless decoration sep_line = "+" << ( "-" * l.succ.succ << "+" ) * @order sep_line.dup << "\n" << @data.map{ | line | "| " << line.map{ |cell| "%#{l}d" % cell }.join(" | ") << " |" }. zip( [sep_line] * @order ).flatten.join("\n") end end # # The usage of cursors is slowing down the program a little # bit but I feel it is still fast enough. # class Cursor attr_reader :cpos, :lpos def initialize order, lpos, cpos @order = order @lpos = lpos @cpos = cpos end def move ldelta, cdelta l = @lpos + ldelta c = @cpos + cdelta l %= @order c %= @order self.class.new @order, l, c end def next! @cpos += 1 return if @cpos < @order @cpos = 0 @lpos += 1 @lpos %= @order end end # # This is where the work is done, like # testing and outputting and what was it? # Ah yes storing the data. # class SquareData include Output include HTMLOutput rescue nil include TestSquare rescue nil def initialize order @order = order @data = Array.new( @order ){ Array.new( @order ) { nil } } end def peek(i, j); @data[i][j] end def poke(i, j, v); @data[i][j] = v end def [](c); @data[c.lpos][c.cpos] end def []=(c, v); @data[c.lpos][c.cpos] = v end def each_subdiagonal (@order/4).times do | line | (@order/4).times do | col | 4.times do | l | 4.times do | c | yield [ 4*line + l, 4*col + c ] if l==c || l+c == 3 end end # 4.times do end # (@order/4).times do end # (@order/4).times do end def siamese_order model = self.class.new @order last = @order*@order @pos = Cursor.new @order, 0, @order/2 yield @pos.lpos, @pos.cpos, peek( @pos.lpos, @pos.cpos ) model[ @pos ] = true 2.upto last do npos = @pos.move -1, +1 npos = @pos.move +1, 0 if model[ npos ] model[ @pos = npos ] = true yield @pos.lpos, @pos.cpos, peek( @pos.lpos, @pos.cpos ) end # @last.times do end end # class SquareData # # The base class for Magic Squares it basically # is the result of factorizing the three classes # representing the three differnt cases, odd, even and # double even. # It's singleton class is used as a class Factory for # the three implementing classes. # class Square def to_s decoration = false @data.to_s decoration end private def initialize order @order = order.to_i @last = @order*@order @data = SquareData.new @order compute @data.test rescue nil end end # # The simplest case, the Siamese Order algorithm # is applied. # class OddSquare < Square private def compute @pos = Cursor.new @order, 0, @order/2 @data[ @pos ] = 1 2.upto @last do | n | npos = @pos.move -1, +1 npos = @pos.move +1, 0 if @data[ npos ] @data[ @pos = npos ] = n end # @last.times do end end # class OddSquare # # The Double Cross Algorithm is applied # to double even Squares. # class DoubleCross < Square def compute pos = Cursor.new @order, 0, 0 1.upto( @last ) do | n | @data[ pos ] = n pos.next! end # 1.upto( @last ) do @data.each_subdiagonal do | lidx, cidx | @data.poke lidx, cidx, @last.succ - @data.peek( lidx, cidx ) end end end # # And eventually we use the LUX algorithm of Conway for even # squares. # class FiatLux < Square L = [ [0, 1], [1, 0], [1, 1], [0, 0] ] U = [ [0, 0], [1, 0], [1, 1], [0, 1] ] X = [ [0, 0], [1, 1], [1, 0], [0, 1] ] def compute half = @order / 2 lux_data = SquareData.new half n = half/2 pos = Cursor.new half, 0, 0 n.succ.times do half.times do lux_data[ pos ] = L pos.next! end # half.times do end # n.succ.times do half.times do lux_data[ pos ] = U pos.next! end # half.times do lux_data.poke n, n, U lux_data.poke n+1, n, L 2.upto(n) do half.times do lux_data[ pos ] = X pos.next! end end # 2.upto(half) do count = 1 lux_data.siamese_order do | siam_row, siam_col, elem | elem.each do | r, c | @data.poke 2*siam_row + r, 2*siam_col + c, count count += 1 end # elem.each do end # lux_data.siamese_order do end end # class FiatLux class << Square # # trying to call the ctors with consistent values only # protected :new def Factory arg arg = arg.to_i case arg % 4 when 1, 3 OddSquare.new arg when 0 DoubleCross.new arg else FiatLux.new arg end end end ARGV.each do |arg| puts Square::Factory( arg ).to_s( true ) puts end __END__ ######################################### ######################################### #207/15 > cat test-squares.rb # vim: sts=2 sw=2 ft=ruby expandtab nu tw=0: module TestSquare def assert cdt, msg return $stderr.puts( "#{msg} . . . . . ok" ) if cdt raise Exception, msg << "\n" << to_s end def test dia1 = dia2 = 0 @order.times do | idx | dia1 += peek( idx, idx ) dia2 += peek( idx, -idx.succ ) end # @lines.each_with_index do assert dia1==dia2, "Both diagonals" @order.times do | idx1 | col_n = row_n = 0 @order.times do | idx2 | col_n += peek idx2, idx1 row_n += peek idx1, idx2 end assert dia1 == col_n, "Col #{idx1}" assert dia1 == row_n, "Row #{idx1}" end # @lines.each_with_index do end # def test def is_ok? dia1 = dia2 = 0 @order.times do | idx | dia1 += peek( idx, idx ) dia2 += peek( idx, -idx.succ ) end # @lines.each_with_index do return false unless dia1==dia2 @order.times do | idx1 | col_n = row_n = 0 @order.times do | idx2 | col_n += peek idx2, idx1 row_n += peek idx1, idx2 end return false unless dia1 == col_n return false unless dia1 == row_n end # @lines.each_with_index do true end end __END__[/i][/i] [/QUOTE]

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