case class Point(x: Int, y: Int, alive: Boolean)

case class Universe(points: Vector[Point], size: Int) {
  def apply(x: Int, y: Int) = points((x % size) * (y % size))
}

def aliveNeighbors(u: Universe)(px: Int, py: Int): Int = {
  val xs = for {
    x <- (py - 1) to (py + 1)
    y <- (px - 1) to (px + 1) if x != px && y != py
  } yield {
    if (u(x, y).alive) 1
    else 0
  }
  xs.sum
}

def life(u: Universe): Universe = {
  val aliveNeighborsU = aliveNeighbors(u)(_, _)
  val liveLimits = 2 to 3
  val updatedPoints = u.points map {
    case p @ Point(x, y, false) if aliveNeighborsU(x, y) == 3 => p.copy(alive = true)
    case p @ Point(x, y, true) if !liveLimits.contains(aliveNeighborsU(x, y)) => p.copy(alive = false)
  }
  u.copy(points = updatedPoints)
}