From: Pedro <pedro.wotan@...>
Date: 2005-05-25T06:33:24+09:00
Subject: Re: [QUIZ] Tiling Turmoil (#33)

Here's my solution, and without googling!.

I'm new in Ruby, and I have a little doubt in my solution. The to_s 
method is too slow in the way I implemented it, Is there any better 
approach?.

class Board
    def initialize(n)
        @w = 2**n;
        @tiles = Array.new(4**n, '0')
    end
   
    # Solve a board indicating row and column of the missing tile
   
    def solve(xm, ym)
        @count = 0
        @tiles[getPos(xm, ym)] = 'X'
        solve_r(0, 0, xm, ym, @w)
    end
   
    # n: position of the tromino (upper left corner)
    # miss: tile shouldn't be marked
    # code: character writed in each position, but in miss.
   
    def setTromino(n, miss, code)
        [0, 1, @w, @w+1].each { |i|
            @tiles[n+i] = code if miss!=n+i
        }
    end

    #
    # Transform coordinates
    #
    def getPos(i, j)
        return i*@w+j
    end

    # Warning: this is too slow (Why?)
    # Avoid this method in benchmarks

    def to_s
        cad = ''
        @tiles.each_index { |i|
            cad += @tiles[i] + ' '
            cad += "\n" if i%@w==@w-1
        }
        return cad
    end
   
    private
=begin
    This is a Divide and Conquer solution.
    Base case: 2x2 board. Solution is trivial in this case
   
    0 X
    0 0
   
    General case: NxN board. We solve the 4 subboards following this scheme:
   
    p.e: 4x4
   
    0 0 0 X
    0 S 0 0
    0 S S 0
    0 0 0 0
   
    We solve 4 2x2 boards.
    If the selected tile X is in the subboard, we solve it normally.
    If not, we solve supossing selected tiles are the marked as S.
    Finally, in the place of S, we put another tromino, and the board is 
solved.
=end
    def solve_r(x0, y0, xm, ym, n)
        if(n==2)
            setTromino(getPos(x0, y0), getPos(xm, ym), @count.to_s)
            @count += 1
            return
        end
        n/=2
        s = [] # Position for missing tile in the S tromino
        [[0, 0], [0, n], [n, 0], [n, n]].each { |d|
            # (x1, y1): upper left corner of the subboard
            # (dx, dy): position of S in the subboard
            x1, y1, dx, dy = x0+d[0], y0+d[1], x0+(d[0]==0 ? n-1:n), 
y0+(d[1]==0 ? n-1:n)
            if((x1...x1+n).include?(xm) && (y1...y1+n).include?(ym))
                s = [dx, dy]
                solve_r(x1, y1, xm, ym, n)
            else
                solve_r(x1, y1, dx, dy, n)
            end
        }
       
        setTromino(getPos(x0+n-1, y0+n-1), getPos(s[0], s[1]), @count.to_s)
        @count += 1
    end

end

if ARGV.length == 2
    b = Board.new(3)
    b.solve(ARGV[0].to_i, ARGV[1].to_i)
    puts b.to_s
end