puzzle

solution.scala

//https://bitbucket.org/snippets/centaur/6K4kR

case class Point(x: Int, y: Int)
def isSquare(p1: Point, p2: Point, p3: Point, p4: Point): Boolean = {
  val l = List(p1, p2, p3, p4).combinations(2).map{
    case List(a, b) =>
      val delta_x = a.x - b.x
      val delta_y = a.y - b.y
      delta_x * delta_x + delta_y * delta_y
  }.toList.sorted

  val (a, b) = l.splitAt(4)
   a.forall(x => x == a.head) &&
     b.forall(x => x == b.head) &&
     (a.sum == b.sum)
}


assert(!isSquare(Point(1, 6), Point(6, 7), Point(2, 7), Point(9, 1)))
assert(!isSquare(Point(4, 1), Point(3, 4), Point(0, 5), Point(1, 2)))
assert(isSquare(Point(4, 6), Point(5, 5), Point(5, 6), Point(4, 5)))