CherlysBirthday.scala

package com.github.synesso.cheryl

object Main extends App {

  val possibleAnswers = Set(
    May(15), May(16), May(19),
    Jun(17), Jun(18),
    Jul(14), Jul(16),
    Aug(14), Aug(15), Aug(17)
  )

  // the month does not include a date that would give the answer
  val monthDoesNotContainUniqueDate = {
    val datesThatGiveTheAnswer = singletonsFrom(mapByDom(possibleAnswers))
    mapByMonth(possibleAnswers).filter { case (k, v) => !v.exists(datesThatGiveTheAnswer.contains) }.values.toSet.flatten
  }

  // days-of-month that give a unique value in the remaining possible answers
  val uniqueByDom = singletonsFrom(mapByDom(monthDoesNotContainUniqueDate))
  
  // months that give a unique value in the remaining possible answers
  val uniqueByMonth = singletonsFrom(mapByMonth(uniqueByDom))

  println(s"Cheryl's birthday is ${uniqueByMonth.head}")

  def mapByMonth(days: Set[Day]) = days.foldLeft(Map.empty[String, Set[Day]].withDefaultValue(Set.empty)) { case (m, d) =>
    m.updated(d.month, m(d.month) + d)
  }

  def mapByDom(days: Set[Day]) = days.foldLeft(Map.empty[Int, Set[Day]].withDefaultValue(Set.empty)) { case (m, d) =>
    m.updated(d.dom, m(d.dom) + d)
  }

  def singletonsFrom(m: Map[_, Set[Day]]) = m.filter{case (_,v) => isSingleton(v)}.values.flatten.toSet

  def isSingleton(set: Set[_]) = set.size == 1
}

case class Day(dom: Int, month: String)
object May { def apply(d: Int) = Day(d, "May") }
object Jun { def apply(d: Int) = Day(d, "Jun") }
object Jul { def apply(d: Int) = Day(d, "Jul") }
object Aug { def apply(d: Int) = Day(d, "Aug") }