MeetAndParty.scala

object MeetAndParty extends App {

  def locateParty(rectangularAreas: IndexedSeq[(Int, Int, Int, Int)]): (Int, Int, BigInt) = {

    val houses = for {
      (x1, y1, x2, y2) <- rectangularAreas
      x <- x1 to x2
      y <- y1 to y2
    } yield (x, y)

    val (xs, ys) = houses.unzip

    def median(xs: IndexedSeq[Int]): (Int, Int) = {

      val sorted = xs.sorted
      val mIndex = xs.size / 2

      if (xs.size % 2 == 0) (sorted(mIndex - 1), sorted(mIndex))
      else (sorted(mIndex), sorted(mIndex))
    }

    def medianDist(x: Int, median: (Int, Int)): Int = {
      val (a, b) = median

      if (x < a) a - x
      else if (a <= x && x < b) 0
      else x - b
    }

    val (xMed, yMed) = (median(xs), median(ys))

    val (x, y) = houses.minBy {
      case (x, y) => (medianDist(x, xMed) + medianDist(y, yMed), x, y)
    }

    def dist(xs: IndexedSeq[Int], x: Int): BigInt = xs.map(math abs _ - x).map(BigInt.apply).sum

    (x, y, dist(xs, x) + dist(ys, y))
  }

  def process(lineIn: Iterator[String])(lineOut: String => Unit) = {

    for (i <- 1 to lineIn.next().toInt) {

      val b = lineIn.next().toInt
      val rectangularAreas = Vector.fill(b) {
        val Array(x1, y1, x2, y2) = lineIn.next split ' ' map (_.toInt)
        (x1, y1, x2, y2)
      }
      val (x, y, d) = locateParty(rectangularAreas)
      lineOut(s"Case #$i: $x $y $d")

    }
  }

  val writer = new java.io.PrintWriter("b.small.out.ref")
  try {
    process(io.Source.fromFile("B-small-practice.in").getLines)(writer.println)
  } finally {
    writer.flush(); writer.close()
  }

}