Infer ordering given sorted collection

OrderLearner.scala

class OrderLearner[A](root: A) {
  import scala.collection.mutable.{Map => Dict}
  private val next = Dict.empty[A, Set[A]] withDefaultValue Set.empty[A]

  def learn(words: Seq[A]*) = for {
    i <- words.indices
    _ = words(i).foreach(u => next(root) += u)
    j <- words.indices drop (i+1)
    (u, v) <- words(i) zip words(j) find {case (a, b) => a != b}
  } next(u) += v

  def inferOrdering(): Ordering[A] = {
    val depth = Dict.empty[A, Int] withDefaultValue 0
    def topologicalSort(visited: Set[A])(u: A): Unit = {
      require(!visited(u), s"Cycle detected involving $u")
      next(u).filterNot(visited).foreach(topologicalSort(visited + u))
      depth(u) = depth(u) max visited.size
    }
    topologicalSort(Set.empty)(root)
    Ordering.by(depth)
  }

  def nodes() = next.values.flatten.toSet
}

object AlphabetLearner extends OrderLearner('*') with App {
  learn("alpha", "baby", "beta", "brownies", "cat", "dad", "dog", "elephant", "ralph", "orange")
  val (alphabets, ordering) = (nodes(), inferOrdering())
  for {
    u <- alphabets
    v <- alphabets if u != v
    c = ordering.compare(u, v)
  } println(if(c < 0) s"$u < $v" else if (c > 0) s"$v < $u" else s"$u $v: ambiguous")
}