Given individual schedules and the endpoints of time, it will return all the free times.

FreeSched.scala

import scala.collection.parallel.immutable.ParRange
import scala.collection.GenSeq

object Solution extends App {
  private val NoTimes = Seq.empty[(Int, Int)]
  private val NoStart = Option.empty[Int]
  private val StdListStart = "["
  private val StdListEnd = "]"
  private val Sample = (-5, 60, Seq(Seq((0, 5), (15, 30), (45, 60)), Seq((5, 15), (30, 40))))
  private val stdin = "" // """\[(\d+), (\d+)\]""".r
  private val (start, end, schedules) = Sample

  private def markBusy(acc: Vector[Boolean], time: (Int, Int)) = {
    val (s, e) = time
    val patchSize = e - s
    val busyPatch = Vector.fill(patchSize)(false)
    val i = s - start
    acc patch (i, busyPatch, patchSize)
  }

  private def freePerSched(acc: Vector[Boolean], sched: Seq[(Int, Int)]) = sched.foldLeft(acc)(markBusy)

  // adds falsehoods on both ends to properly downstream-process potential boolean transitions
  private def bookend(xs: GenSeq[(Int, Boolean)]) = (start - 1, false) +: xs :+ (end, false)

  private def toFreeInterval(accAndLastStartOpt: (Seq[(Int, Int)], Option[Int]),
                             timeAndFree: (Int, Boolean)) = {
    val (acc, lastStartOpt) = accAndLastStartOpt
    val (time, free) = timeAndFree
    lastStartOpt match {
      case Some(lastStart) =>
        if (free) (acc, lastStartOpt)
        else (acc :+ (lastStart, time), NoStart)
      case _ =>
        if (free) (acc, Option(time))
        else (acc, NoStart)
    }
  }

  private val nTimes = end - start
  private val freeMask = Vector.fill(nTimes)(true)
  private val freeIndicator = schedules.foldLeft(freeMask)(freePerSched)
  private val timesInParallel = ParRange(0, nTimes, 1, false)
  private val freeTimeAggs = timesInParallel map { i =>
    val startTime = i + start
    (startTime, freeIndicator(i))
  }
  private val intervalReadyFreeTimes = bookend(freeTimeAggs)
  private val freeIntervals = (intervalReadyFreeTimes.foldLeft((NoTimes, NoStart))(toFreeInterval))._1
  println(StdListStart + (freeIntervals mkString " ") + StdListEnd)
}