Compute max population given a list of people's birth and death year

original.scala

val persons = Seq(
  Person(2000, 2010),
  Person(2000, 2005),
  Person(1990, 2005)
)

// Create an array of population change.
val births = persons.groupBy(_.birthYear).mapValues(_.length)
val deaths = persons.groupBy(_.deathYear).mapValues(_.length)
val populationChanges = (births.keySet ++ deaths.keySet).map { year =>
  (year, births.getOrElse(year, 0) - deaths.getOrElse(year, 0))
}.toMap

println("populationChanges", populationChanges)

val sortedYears = populationChanges.keys.toSeq.sorted
println(sortedYears)

// construct an array of total populations
val populations = populationChanges.toSeq
  .sortBy(_._1)
  .scanLeft(0) { (a, b) => a + b._2 }
  .tail
  .zip(sortedYears) // this is a bit hacky
  .map{ case(count, year) => (year, count) }

println("pop", populations)
println("max pop", populations.maxBy(_._2)) // (2000, 3)