From: Pedro Fortuny Ayuso <pfortuny@...>
Date: 2006-12-18T17:24:58+09:00
Subject: Re: Chess960 (#106)

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I am attaching two solutions: the first one generates all the positions
in an "unofficial" order (however, it takes advantage of symmetry and
"only" computes 480 and mirrors them) and the official one using a
"nifty" :) algorithm (basically the wikipedia one with tables but
arithmetizing
the tables). The second one is clearer *and commented*

### first one: simple
class Chess960
  @@boards = []

  def boards
    @@boards
  end

  def initialize
    board = Board.new()
    (0..2).each do |lr|
      board << lr
      (lr+1..3).each do |k|
        board << k
        (k+1..7).each do |rr|
          board << rr
          board.free_.each do |q|
            board << q
            board.free_.find_all{|x| x.odd?}.each do |bb|
              board << bb
              board.free_.find_all{|x| x.even?}.each do |wb|
                board << wb
                @@boards << b = board.to_s
                @@boards << board.to_s.reverse
                board.pop
              end # white bishop
              board.pop
            end # black bishop
            board.pop
          end # queen
          board.pop
        end # right rook
        board.pop
      end # king
      board.pop
    end # left rook
    puts @@boards.length
  end


  def to_human(i)
    lrow = @@boards[i]
    lrow.downcase + "p" * 8 + "32" + "P" * 8 + lrow
  end

  def get_one
    i = rand(960)
    to_human(i)
  end

  def [](n)
    return @@boards[n]
  end

end

class Fixnum

  def odd?
    self % 2 == 0 ? false : true
  end

  def even?
    not(self.odd?)
  end

end



class Board

  attr_reader :free_, :position

  @@pieces = %w(R K R Q B B N N)

  def initialize()
    @position = []
    @free_ = (0..7).to_a - @position
  end

  def to_s
    order = "N" * 8
    @position.each_with_index do |p,i|
      order[p] = @@pieces[i]
    end
    return order
  end

  def <<(n)
    @position << n
    @free_ = @free_ - [n]
  end

  def pop
    @free_ << @position.pop
  end


end
#######
####### second one: "official" and with standard board notation
#!/usr/bin/ruby

class Chess960

  private_class_method :new

  @@all = []

  def Chess960.setup
      (0..959).each do |i|
        @@all << Board.new(i)
      end
    true
  end

  def Chess960.[](n)
    @@all[n]
  end

  def Chess960.random()
    self.get(rand(960)).to_s
  end

  # Position p is decomposed as
  # p =     96n + 16q + b with
  # (0..15) === b, (0..5) === q, and
  # (0..9) === n. See bottom for an
  # explanation

  class Board

    attr_reader :board

    def initialize(p)
      @board = Hash.new()
      bishop = p % 16
      nights = (p - (p % 96)) / 96
      queen = ((p % 96) - bishop) / 16
      @board = iposition(bishop, nights, queen)
    end

    def to_s
      return "[FEN " + board.join("").downcase + "/" + "p" * 8 +
               "/8/8/8/8/" + "P" * 8 + "/" + board.join("") + " w KQkq - 0
1]"
    end

    private

    def bishop(i)
      white = (i - (black = i % 4)) / 4
      return ([ (white * 2), black * 2 + 1])
    end

    def nights(i)
      case i
      when 9
        n1, n2 = 3, 4
      when 7,8
        n1, n2 = 2, 3 + (i % 7)
      else
        n1 = ( i - i % 3) / 3
        n2 = i % 3 + 1
      end
      return ([n1,n2])
    end

    def queen(i) # dummy but easier to understand
      return i
    end

    # see the explanation at bottom for this method's algorithm
    def iposition(b, n, q)
      base =  %w(R R R R R R)
      @board = %w(B B B B B B B B)
      # put the queen in its place in "all-but-bishops"
      base[queen(q)] = "Q"
      # put the knights in their place in "all-but-bishops"
      nights(n).each do |x|
        (x < queen(q) && base[x] = "N") or (base[x+1] = "N")
      end
      # place the King: substitute the middle Rook by a King
      # and finish (simpler than reading the code)
      king = false
      base.each_with_index do |p,i|
        (king == true and base[i] == "R" and base[i] = "K" and break)
        (p == "R" && king = true)
      end

      # and now put the bishops in place, ie: keeping the
      # bishops in their place, put all the other pieces
      # in their order
      minus = 0
      bish = bishop(b)
      (0..7).each do |i|
        if bish.include?(i)
          minus += 1
          next
        end
        @board[i] = base[i-minus]
      end
      return @board
    end

  end


  true
end


## explanation of p = 96n + 16q + b
##
## Bishops' position. Give the bottom squares (a1..h1)
## the following values:
##    0,0,4,1,8,2,12,3
## Any number b = 0..15 can be written uniquely as
##    b = wb + bb
## with wb in a white square and bb in a black one
## This gives bishops' table.
##
##
## Consider the six remaining pieces, and number a
## six-row from 0 to 5 from left to right:
##    0,1,2,3,4,5
##
## The position of the queen inside that row is q
##
## Finally, let the remaining five squares be numbered
##    0,1,2,3,4
##
## For the right knight, the values of each square are
##    -, 0, 1, 2, 3 (the first one does not count bc is
##                     never filled by the right one)
##
## For the left knight, the corresponding values are
##    0, 3, 5, 6, - (ibid.)
##
## Now every number (0..9) can be written uniquely as
##    ln + rn (left knight + right knight) using two
##         different position on the 5-row
##
## Place the rooks and king in the remaining three squares
## following the r-k-r rule and the board is built.




Thanks for the quiz,

Pedro



-- 
Pedro Fortuny Ayuso
C/Capuchinos 14, 1. 47006 Valladolid. SPAIN
http://pfortuny.sdf-eu.org

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