EdgesToVerticesOfCompleteGraph.scala

// given the number of edges of a complete graph,
// determine the number of vertices. will be integer,
// if this is a complete graph.
//
// solves edges = vertices * (vertices - 1) / 2
def vertices(edges: Int): Double = {
  val q   = -2 * edges
  val ph  = -0.5
  val phs = 0.25
  val r   = math.sqrt(phs - q)
  val x1 = -ph + r  x1
}

val ex = (1 to 200).flatMap { e => val v = vertices(e); val vi = v.toInt; if (v == vi) Some(e -> vi) else None }