オフラインリアルタイムどう書くE32の回答

残念ながら参加できませんでしたが、解きました。
3時間以上かかっています、またかなり汚いコードになってしまいました。

xがreal、yがimagの複素数で点と、線の方向を示しています。
linesは線が重なったら1つの線としてマージした結果、
crossは線と線の交点です。
crossの組み合わせで4点とって四角か判定していますが、
ちゃんとやれば組み合わせを使う必要はないです。

実行時間はヘボノートPCで2秒程度でした。

e32.rb

def get_cross_impl( p1, d1, p2, d2 )
  x = p1.real
  y = p2.imag
  return nil unless (p2.real..(p2+d2).real).include?(x)
  return nil unless (p1.imag..(p1+d1).imag).include?(y)
  Complex(x, y)
end

def get_cross( p1, d1, p2, d2 )
  if d1.real == 0
    get_cross_impl( p1, d1, p2, d2 )
  else
    get_cross_impl( p2, d2, p1, d1 )
  end
end

def add_line( lines, cross, blp, bld )
  lines.each { |cp, cd|
    if (bld * cd).imag == 0
      next
    end
    c = get_cross( blp, bld, cp, cd )
    cross << c if c
  }
  dup_line = lines.select { |cp, cd|
    if bld.real == 0 && cd.real == 0 && blp.real == cp.real
      range = (blp.imag..(blp+bld).imag)
      range.include?(cp.imag) || range.include?((cp+cd).imag)
    elsif bld.imag == 0 && cd.imag == 0 && blp.imag == cp.imag
      range = (blp.real..(blp+bld).real)
      range.include?(cp.real) || range.include?((cp+cd).real)
    else
      false
    end
  }
  if dup_line.length != 0
    dup_line.each { |a| lines.delete(a) }
    dup_line << [ blp, bld, ]
    (aminx, aminy, amaxx, amaxy) = dup_line.map { |cp, cd|
      [ cp.real, cp.imag, (cp+cd).real, (cp+cd).imag, ]
    }.transpose
    np = Complex(aminx.min, aminy.min)
    nd = Complex(amaxx.max, amaxy.max) - np
    lines << [ np, nd, ]
  else
    lines << [ blp, bld, ]
  end
end

def include_line?( lines, start, dir )
  lines.any? { |cp, cd|
    next false if (dir * cd).imag != 0
    if dir.real == 0 && start.real == cp.real
      next cp.imag <= start.imag && (cp+cd).imag >= (start+dir).imag
    end
    if dir.imag == 0 && start.imag == cp.imag
      next cp.real <= start.real && (cp+cd).real >= (start+dir).real
    end
    false
  }
end

def is_square(lines, ul, ur, dl, dr)
  return false if ul.real != ur.real
  return false if dl.real != dr.real
  return false if (ur - ul) != (dr - dl)
  return false unless include_line?(lines, ul, (ur-ul))
  return false unless include_line?(lines, dl, (dr-dl))
  return false if ul.imag != dl.imag
  return false if ur.imag != dr.imag
  return false if (dl - ul) != (dr - ur)
  return false unless include_line?(lines, ul, (dl-ul))
  return false unless include_line?(lines, ur, (dr-ur))
  true
end

def is_dirty(sq, point, dir)
  if dir.real == 0 && (sq[0].real+1..sq[0].real+sq[1]-1).include?(point.real)
    return (point.imag..(point+dir).imag-1).include?(sq[0].imag) ||
      (point.imag+1..(point+dir).imag).include?(sq[0].imag+sq[2]) ||
      (sq[0].imag..sq[0].imag+sq[2]-1).include?(point.imag) ||
      (sq[0].imag+1..sq[0].imag+sq[2]).include?((point+dir).imag)
  end
  if dir.imag == 0 && (sq[0].imag+1..sq[0].imag+sq[2]-1).include?(point.imag)
    return (point.real..(point+dir).real-1).include?(sq[0].real) ||
      (point.real+1..(point+dir).real).include?(sq[0].real+sq[1]) ||
      (sq[0].real..sq[0].real+sq[1]-1).include?(point.real) ||
      (sq[0].real+1..sq[0].real+sq[1]).include?((point+dir).real)
  end
  false
end

def solve( input )
  lines = []
  cross = []
  input.split('/').each { |s|
    (l, u, r, d) = s.each_char.map { |c| c.to_i(36) }
    lu = Complex(l, u)
    ru = Complex(r, u)
    ld = Complex(l, d)
    rd = Complex(r, d)
    [ [lu, ru,], [lu, ld,], [ru, rd,], [ld, rd,], ].each { |p1, p2|
      add_line( lines, cross, p1, p2-p1 )
    }
  }
  cross = cross.uniq.sort { |l, r|
    (l.real <=> r.real) * 2 + (l.imag <=> r.imag)
  }
  sqs = cross.combination(4).each_with_object([]) { |(ul, ur, dl, dr), a|
    next unless is_square(lines, ul, ur, dl, dr)
    a << [ ul, (dl - ul).real, (ur - ul).imag, ]
  }
  sqs = sqs.select { |sq|
    lines.none? { |point, dir|
      is_dirty(sq, point, dir)
    }
  }
  sqs.map { |sq| sq[1] * sq[2] }.sort.join(',')
end

DATA.each { |line|
  /\/\*(?<no>\d+)\*\/ test\( "(?<input>.+)", "(?<expected>.+)" \);/ =~ line
  actual = solve( input )
  if expected != actual
    puts 'NG[%s] : input = %s, expected = %s, actual = %s' % [ no, input, expected, actual, ]
    exit 1
  else
    puts 'OK[%s]' % [ no, ]
  end
}

__END__
/*0*/ test( "43gw/d7qq/mlop", "8,57" );
/*1*/ test( "034a", "28" );
/*2*/ test( "06qr/8pnq", "15" );
/*3*/ test( "c1th/b2qy", "210" );
/*4*/ test( "c8wz/gbsg/i0xd", "20" );
/*5*/ test( "97uv/2g5x/eihv", "39,51" );
/*6*/ test( "254d/2jvu/mjvu", "16,99,220" );
/*7*/ test( "ggiu/ggzu/g5ig", "22,28,238" );
/*8*/ test( "jbnc/i7xe/i7je/icje", "2,4,5" );
/*9*/ test( "3cey/0fzo", "27,33,99,110,189" );
/*10*/ test( "00ab/p0zd/0ofz/87rs", "8,12,28" );
/*11*/ test( "1dsy/2d9s/2s9y", "21,42,105,399" );
/*12*/ test( "28db/d0lm/d1i8/l0w5", "33,35,55" );
/*13*/ test( "3aen/4fir/1lev", "2,20,40,48,60" );
/*14*/ test( "j7ou/3rms/m4vs", "3,10,16,42,60" );
/*15*/ test( "336a/3rkw/jlor/3akw", "6,21,24,85" );
/*16*/ test( "21om/87bv/67cv", "9,15,18,27,30,45" );
/*17*/ test( "4hhx/056u/4rvu", "6,20,33,39,42,110" );
/*18*/ test( "b0sh/pgxt/88lq/amux", "3,20,35,44,90" );
/*19*/ test( "c0hc/h6md/fdmk/4cfj", "2,35,49,60,77" );
/*20*/ test( "0liz/ilvz/0lvr/0rvz", "78,104,108,144" );
/*21*/ test( "81ib/q1zb/8cir/qczr", "90,100,135,150" );
/*22*/ test( "h7t8/t8ye/g8he/hetz", "6,12,30,72,252" );
/*23*/ test( "b5qy/o6qc/21tb/qoyu/b5eu", "2,10,18,48,57" );
/*24*/ test( "eajn/jkln/j8ua/nkun/u4wy", "6,21,22,60,65" );
/*25*/ test( "wwzz/nfuw/nfzz/41vw/l1r2/nfrg", "4,6,9,17" );
/*26*/ test( "46rb/t6xb/m7zk/4hrj/thxj", "4,8,10,16,20,36" );
/*27*/ test( "olwx/ogul/ogwx/ogux/agux", "10,24,30,72,238" );
/*28*/ test( "b7un/c3hv/fiyo/h6xm", "2,10,12,13,16,20,52,143" );
/*29*/ test( "d6qa/o4qr/tcur/9bto", "2,4,6,8,15,26,39,44,195" );
/*30*/ test( "2lsx/54hf/k3yi/8dhw/bhny", "3,12,18,24,33,60,66" );
/*31*/ test( "apcx/a8pv/7uwx/a2c8/c8pu", "2,4,9,10,12,13,34,286" );
/*32*/ test( "7yjz/jywz/7ejz/j5wy/bejz/jewy", "4,8,13,80,117,160,260" );
/*33*/ test( "d0wk/5dqu/6lqs/77ae/f4mq/56bm", "3,4,5,7,14,18,28,35,49,63" );
/*34*/ test( "d4gn/94in/d4rs/94xu/97xn", "6,9,12,18,27,32,48,64,70,96,144" );
/*35*/ test( "l5wh/wdxn/60xs/c5fd/jpwx/mgqx", "4,9,10,12,15,18,20,24,30,32" );
/*36*/ test( "5178/58xk/uixk/71u8/71uk/71ui/51ui", "4,6,14,20,30,46,161,230" );
/*37*/ test( "m8sp/mosp/2imp/i8sp/2isp/i8si/misp/iosp", "4,6,24,36,40,60,112" );
/*38*/ test( "34d5/253k/f4m5/m5rk/2o3u/3udy/fumy/moru", "6,7,10,15,28,30,40,75" );
/*39*/ test( "2ilw/mbnc/n9wj/9dmy/6qwy/2ekh/9dkh", "1,6,11,18,21,33,72,80,90,96" );
/*40*/ test( "j0le/10uo/q6ue/jeqt/jelf/l6xf", "2,4,5,27,28,32,35,36,40,54,63,432" );
/*41*/ test( "j4mu/31r5/qeyf/0f5h/r0v5/00qi/j5kf/jlru", "3,4,8,9,10,10,20,27,45,52" );
/*42*/ test( "g8kc/dbuv/gbkc/dbgv/evuw/dbui/d8kw", "1,4,6,9,10,12,21,24,39,52,70,130" );
/*43*/ test( "apry/a0ry/a0hx/60hp/6xhy/a0hp/a0hy/6phy/6phx", "4,7,32,56,90,100,175,250" );
/*44*/ test( "1eok/33by/d0kz/1rnw", "10,10,12,12,14,15,16,21,24,35,40,42,48,49,56,88,98" );
/*45*/ test( "0qbs/6cws/l6xj/659q/03lc/bclp/96dj/96wc", "10,12,13,14,14,21,24,42,48,66,77" );
/*46*/ test( "q8sr/98yu/clyn/s8yl/9lqr/0rsu/0l9m/0n9u", "4,8,9,12,26,27,28,36,42,57,78,221" );
/*47*/ test( "5sjy/jbsy/8dgp/gkvp/gdvh/jhvp/i2vk", "3,4,6,8,9,12,15,15,18,27,36,45,81,84,96" );
/*48*/ test( "42va/10nf/23l6/c2uw/3hpo/4ofu/m7sv", "3,5,6,8,8,15,18,20,21,24,27,32,48,50,63,70" );
/*49*/ test( "84lj/10j1/wcxd/ljnl/1njx/01xd/00x1/81wq/1c8q", "1,1,4,7,11,14,18,21,33,70,78,117,126" );
/*50*/ test( "kfvg/76vq/136d/6gvq/6g7q/137g/7dmz/63m6/m3vz", "2,3,9,10,27,45,50,81,81,90,105,135,150" );
/*51*/ test( "4eht/38jt/jeym/htjv/eeyv/eejt/3myv/h1jt/hejm", "4,6,7,12,14,14,16,21,22,24,70,80,120,135" );
/*52*/ test( "smuz/04c7/28zc/83ri/cihu/8flm/masw/8ivo", "2,4,6,8,10,10,12,16,16,20,22,24,24,30,30,36,39,48" );
/*53*/ test( "7fuu/17fd/6cpg/fghu/ahnt/adww/rhxz/4hxl/0pby", "1,2,2,2,3,3,4,4,4,5,8,8,9,10,12,12,12,12,15,15,16,16,20,24,27,30,32,48" );