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Scala example source code file (Stream.scala)

This example Scala source code file (Stream.scala) is included in my "Source Code Warehouse" project. The intent of this project is to help you more easily find Scala source code examples by using tags.

All credit for the original source code belongs to scala-lang.org; I'm just trying to make examples easier to find. (For my Scala work, see my Scala examples and tutorials.)

Scala tags/keywords

a, annotation, b, boolean, canbuildfrom, empty, int, stream, streamwithfilter, string, that

The Stream.scala Scala example source code

/*                     __                                               *\
**     ________ ___   / /  ___     Scala API                            **
**    / __/ __// _ | / /  / _ |    (c) 2003-2013, LAMP/EPFL             **
**  __\ \/ /__/ __ |/ /__/ __ |    http://scala-lang.org/               **
** /____/\___/_/ |_/____/_/ | |                                         **
**                          |/                                          **
\*                                                                      */

package scala
package collection
package immutable

import generic._
import mutable.{Builder, StringBuilder, LazyBuilder, ListBuffer}
import scala.annotation.tailrec
import Stream.cons
import scala.language.implicitConversions

/** The class `Stream` implements lazy lists where elements
 *  are only evaluated when they are needed. Here is an example:
 *
 *  {{{
 *  import scala.math.BigInt
 *  object Main extends App {
 *
 *    val fibs: Stream[BigInt] = BigInt(0) #:: BigInt(1) #:: fibs.zip(fibs.tail).map { n => n._1 + n._2 }
 *
 *    fibs take 5 foreach println
 *  }
 *
 *  // prints
 *  //
 *  // 0
 *  // 1
 *  // 1
 *  // 2
 *  // 3
 *  }}}
 *
 *  The `Stream` class also employs memoization such that previously computed
 *  values are converted from `Stream` elements to concrete values of type `A`.
 *  To illustrate, we will alter body of the `fibs` value above and take some
 *  more values:
 *
 *  {{{
 *  import scala.math.BigInt
 *  object Main extends App {
 *
 *    val fibs: Stream[BigInt] = BigInt(0) #:: BigInt(1) #:: fibs.zip(
 *      fibs.tail).map(n => {
 *        println("Adding %d and %d".format(n._1, n._2))
 *        n._1 + n._2
 *      })
 *
 *    fibs take 5 foreach println
 *    fibs take 6 foreach println
 *  }
 *
 *  // prints
 *  //
 *  // 0
 *  // 1
 *  // Adding 0 and 1
 *  // 1
 *  // Adding 1 and 1
 *  // 2
 *  // Adding 1 and 2
 *  // 3
 *
 *  // And then prints
 *  //
 *  // 0
 *  // 1
 *  // 1
 *  // 2
 *  // 3
 *  // Adding 2 and 3
 *  // 5
 *  }}}
 *
 *  There are a number of subtle points to the above example.
 *
 *  - The definition of `fibs` is a `val` not a method.  The memoization of the
 *  `Stream` requires us to have somewhere to store the information and a `val`
 *  allows us to do that.
 *
 *  - While the `Stream` is actually being modified during access, this does not
 *  change the notion of its immutability.  Once the values are memoized they do
 *  not change and values that have yet to be memoized still "exist", they
 *  simply haven't been realized yet.
 *
 *  - One must be cautious of memoization; you can very quickly eat up large
 *  amounts of memory if you're not careful.  The reason for this is that the
 *  memoization of the `Stream` creates a structure much like
 *  [[scala.collection.immutable.List]].  So long as something is holding on to
 *  the head, the head holds on to the tail, and so it continues recursively.
 *  If, on the other hand, there is nothing holding on to the head (e.g. we used
 *  `def` to define the `Stream`) then once it is no longer being used directly,
 *  it disappears.
 *  {{{
 *  // For example, let's build the natural numbers and do some silly iteration
 *  // over them.
 *
 *  // We'll start with a silly iteration
 *  def loop(s: String, i: Int, iter: Iterator[Int]): Unit = {
 *    // Stop after 200,000
 *    if (i < 200001) {
 *      if (i % 50000 == 0) println(s + i)
 *      loop(s, iter.next, iter)
 *    }
 *  }
 *
 *  // Our first Stream definition will be a val definition
 *  val stream1: Stream[Int] = {
 *    def loop(v: Int): Stream[Int] = v #:: loop(v + 1)
 *    loop(0)
 *  }
 *
 *  // Because stream1 is a val, everything that the iterator produces is held
 *  // by virtue of the fact that the head of the Stream is held in stream1
 *  val it1 = stream1.iterator
 *  loop("Iterator1: ", it1.next, it1)
 *
 *  // We can redefine this Stream such that all we have is the Iterator left
 *  // and allow the Stream to be garbage collected as required.  Using a def
 *  // to provide the Stream ensures that no val is holding onto the head as
 *  // is the case with stream1
 *  def stream2: Stream[Int] = {
 *    def loop(v: Int): Stream[Int] = v #:: loop(v + 1)
 *    loop(0)
 *  }
 *  val it2 = stream2.iterator
 *  loop("Iterator2: ", it2.next, it2)
 *
 *  // And, of course, we don't actually need a Stream at all for such a simple
 *  // problem.  There's no reason to use a Stream if you don't actually need
 *  // one.
 *  val it3 = new Iterator[Int] {
 *    var i = -1
 *    def hasNext = true
 *    def next(): Int = { i += 1; i }
 *  }
 *  loop("Iterator3: ", it3.next, it3)
 *  }}}
 *
 *  - The fact that `tail` works at all is of interest.  In the definition of
 *  `fibs` we have an initial `(0, 1, Stream(...))` so `tail` is deterministic.
 *  If we deinfed `fibs` such that only `0` were concretely known then the act
 *  of determining `tail` would require the evaluation of `tail` which would
 *  cause an infinite recursion and stack overflow.  If we define a definition
 *  where the tail is not initially computable then we're going to have an
 *  infinite recursion:
 *  {{{
 *  // The first time we try to access the tail we're going to need more
 *  // information which will require us to recurse, which will require us to
 *  // recurse, which...
 *  val sov: Stream[Vector[Int]] = Vector(0) #:: sov.zip(sov.tail).map { n => n._1 ++ n._2 }
 *  }}}
 *
 *  The definition of `fibs` above creates a larger number of objects than
 *  necessary depending on how you might want to implement it.  The following
 *  implementation provides a more "cost effective" implementation due to the
 *  fact that it has a more direct route to the numbers themselves:
 *
 *  {{{
 *  lazy val fib: Stream[Int] = {
 *    def loop(h: Int, n: Int): Stream[Int] = h #:: loop(n, h + n)
 *    loop(1, 1)
 *  }
 *  }}}
 *
 *  @tparam A    the type of the elements contained in this stream.
 *
 *  @author Martin Odersky, Matthias Zenger
 *  @version 1.1 08/08/03
 *  @since   2.8
 *  @see [[http://docs.scala-lang.org/overviews/collections/concrete-immutable-collection-classes.html#streams "Scala's Collection Library overview"]]
 *  section on `Streams` for more information.

 *  @define naturalsEx def naturalsFrom(i: Int): Stream[Int] = i #:: naturalsFrom(i + 1)
 *  @define Coll `Stream`
 *  @define coll stream
 *  @define orderDependent
 *  @define orderDependentFold
 *  @define willTerminateInf Note: lazily evaluated; will terminate for infinite-sized collections.
 */
@deprecatedInheritance("This class will be sealed.", "2.11.0")
abstract class Stream[+A] extends AbstractSeq[A]
                             with LinearSeq[A]
                             with GenericTraversableTemplate[A, Stream]
                             with LinearSeqOptimized[A, Stream[A]]
                             with Serializable {
self =>
  override def companion: GenericCompanion[Stream] = Stream

  import scala.collection.{Traversable, Iterable, Seq, IndexedSeq}

  /** Indicates whether or not the `Stream` is empty.
   *
   * @return `true` if the `Stream` is empty and `false` otherwise.
   */
  def isEmpty: Boolean

  /** Gives constant time access to the first element of this `Stream`.  Using
   * the `fibs` example from earlier:
   *
   * {{{
   * println(fibs head)
   * // prints
   * // 0
   * }}}
   *
   *  @return The first element of the `Stream`.
   *  @throws Predef.NoSuchElementException if the stream is empty.
   */
  def head: A

  /** A stream consisting of the remaining elements of this stream after the
   *  first one.
   *
   *  Note that this method does not force evaluation of the `Stream` but merely
   *  returns the lazy result.
   *
   *  @return The tail of the `Stream`.
   *  @throws Predef.UnsupportedOperationException if the stream is empty.
   */
  def tail: Stream[A]

  /** Is the tail of this stream defined? */
  protected def tailDefined: Boolean

  // Implementation of abstract method in Traversable

  // New methods in Stream

  /** The stream resulting from the concatenation of this stream with the argument stream.
   *  @param rest   The stream that gets appended to this stream
   *  @return       The stream containing elements of this stream and the traversable object.
   */
  def append[B >: A](rest: => TraversableOnce[B]): Stream[B] =
    if (isEmpty) rest.toStream else cons(head, tail append rest)

  /** Forces evaluation of the whole stream and returns it.
   *
   * @note Often we use `Stream`s to represent an infinite set or series.  If
   * that's the case for your particular `Stream` then this function will never
   * return and will probably crash the VM with an `OutOfMemory` exception.
   *
   *  @return The fully realized `Stream`.
   */
  def force: Stream[A] = {
    var these = this
    while (!these.isEmpty) these = these.tail
    this
  }

  /** Prints elements of this stream one by one, separated by commas. */
  def print() { print(", ") }

  /** Prints elements of this stream one by one, separated by `sep`.
   *  @param sep   The separator string printed between consecutive elements.
   */
  def print(sep: String) {
    def loop(these: Stream[A], start: String) {
      Console.print(start)
      if (these.isEmpty) Console.print("empty")
      else {
        Console.print(these.head)
        loop(these.tail, sep)
      }
    }
    loop(this, "")
  }

  /** Returns the length of this `Stream`.
   *
   * @note In order to compute the length of the `Stream`, it must first be
   * fully realized, which could cause the complete evaluation of an infinite
   * series, assuming that's what your `Stream` represents.
   *
   * @return The length of this `Stream`.
   */
  override def length: Int = {
    var len = 0
    var left = this
    while (!left.isEmpty) {
      len += 1
      left = left.tail
    }
    len
  }

  // It's an imperfect world, but at least we can bottle up the
  // imperfection in a capsule.
  @inline private def asThat[That](x: AnyRef): That     = x.asInstanceOf[That]
  @inline private def asStream[B](x: AnyRef): Stream[B] = x.asInstanceOf[Stream[B]]
  @inline private def isStreamBuilder[B, That](bf: CanBuildFrom[Stream[A], B, That]) =
    bf(repr).isInstanceOf[Stream.StreamBuilder[_]]

  // Overridden methods from Traversable

  override def toStream: Stream[A] = this

  override def hasDefiniteSize = {
    def loop(s: Stream[A]): Boolean = s.isEmpty || s.tailDefined && loop(s.tail)
    loop(this)
  }

  /** Create a new stream which contains all elements of this stream followed by
   * all elements of Traversable `that`.
   *
   * @note It's subtle why this works. We know that if the target type of the
   * [[scala.collection.mutable.Builder]] `That` is either a `Stream`, or one of
   * its supertypes, or undefined, then `StreamBuilder` will be chosen for the
   * implicit.  We recognize that fact and optimize to get more laziness.
   *
   * @note This method doesn't cause the `Stream` to be fully realized but it
   * should be noted that using the `++` operator from another collection type
   * could cause infinite realization of a `Stream`.  For example, referring to
   * the definition of `fibs` in the preamble, the following would never return:
   * `List(BigInt(12)) ++ fibs`.
   *
   * @tparam B The element type of the returned collection.'''That'''
   * @param that The [[scala.collection.GenTraversableOnce]] the be contatenated
   * to this `Stream`.
   * @return A new collection containing the result of concatenating `this` with
   * `that`.
   */
  override def ++[B >: A, That](that: GenTraversableOnce[B])(implicit bf: CanBuildFrom[Stream[A], B, That]): That =
    // we assume there is no other builder factory on streams and therefore know that That = Stream[A]
    if (isStreamBuilder(bf)) asThat(
      if (isEmpty) that.toStream
      else cons(head, asStream[A](tail ++ that))
    )
    else super.++(that)(bf)

  override def +:[B >: A, That](elem: B)(implicit bf: CanBuildFrom[Stream[A], B, That]): That =
    if (isStreamBuilder(bf)) asThat(cons(elem, this))
    else super.+:(elem)(bf)

  /**
   * Create a new stream which contains all intermediate results of applying the
   * operator to subsequent elements left to right.  `scanLeft` is analogous to
   * `foldLeft`.
   *
   * @note This works because the target type of the
   * [[scala.collection.mutable.Builder]] `That` is a `Stream`.
   *
   * @param z The initial value for the scan.
   * @param op A function that will apply operations to successive values in the
   * `Stream` against previous accumulated results.
   * @return A new collection containing the modifications from the application
   * of `op`.
   */
  override final def scanLeft[B, That](z: B)(op: (B, A) => B)(implicit bf: CanBuildFrom[Stream[A], B, That]): That =
    if (isStreamBuilder(bf)) asThat(
      if (isEmpty) Stream(z)
      else cons(z, asStream[B](tail.scanLeft(op(z, head))(op)))
    )
    else super.scanLeft(z)(op)(bf)

  /** Returns the stream resulting from applying the given function `f` to each
   * element of this stream.  This returns a lazy `Stream` such that it does not
   * need to be fully realized.
   *
   * @example {{{
   * $naturalsEx
   * naturalsFrom(1).map(_ + 10) take 5 mkString(", ")
   * // produces: "11, 12, 13, 14, 15"
   * }}}
   *
   * @tparam B The element type of the returned collection '''That'''.
   * @param f function to apply to each element.
   * @return  `f(a,,0,,), ..., f(a,,n,,)` if this sequence is `a,,0,,, ..., a,,n,,`.
   */
  override final def map[B, That](f: A => B)(implicit bf: CanBuildFrom[Stream[A], B, That]): That = {
    if (isStreamBuilder(bf)) asThat(
      if (isEmpty) Stream.Empty
      else cons(f(head), asStream[B](tail map f))
    )
    else super.map(f)(bf)
  }

  override final def collect[B, That](pf: PartialFunction[A, B])(implicit bf: CanBuildFrom[Stream[A], B, That]): That = {
    if (!isStreamBuilder(bf)) super.collect(pf)(bf)
    else {
      // this implementation avoids:
      // 1) stackoverflows (could be achieved with tailrec, too)
      // 2) out of memory errors for big streams (`this` reference can be eliminated from the stack)
      var rest: Stream[A] = this

      // Avoids calling both `pf.isDefined` and `pf.apply`.
      var newHead: B = null.asInstanceOf[B]
      val runWith = pf.runWith((b: B) => newHead = b)

      while (rest.nonEmpty && !runWith(rest.head)) rest = rest.tail

      //  without the call to the companion object, a thunk is created for the tail of the new stream,
      //  and the closure of the thunk will reference `this`
      if (rest.isEmpty) Stream.Empty.asInstanceOf[That]
      else Stream.collectedTail(newHead, rest, pf, bf).asInstanceOf[That]
    }
  }

  /** Applies the given function `f` to each element of this stream, then
   * concatenates the results.  As with `map` this function does not need to
   * realize the entire `Stream` but continues to keep it as a lazy `Stream`.
   *
   * @example {{{
   * // Let's create a Stream of Vectors, each of which contains the
   * // collection of Fibonacci numbers up to the current value.  We
   * // can then 'flatMap' that Stream.
   *
   * val fibVec: Stream[Vector[Int]] = Vector(0) #:: Vector(0, 1) #:: fibVec.zip(fibVec.tail).map(n => {
   *   n._2 ++ Vector(n._1.last + n._2.last)
   * })
   *
   * fibVec take 5 foreach println
   * // prints
   * // Vector(0)
   * // Vector(0, 1)
   * // Vector(0, 1, 1)
   * // Vector(0, 1, 1, 2)
   * // Vector(0, 1, 1, 2, 3)
   *
   * // If we now want to `flatMap` across that stream by adding 10
   * // we can see what the series turns into:
   *
   * fibVec.flatMap(_.map(_ + 10)) take 15 mkString(", ")
   * // produces: 10, 10, 11, 10, 11, 11, 10, 11, 11, 12, 10, 11, 11, 12, 13
   * }}}
   *
   * ''Note:''  Currently `flatMap` will evaluate as much of the Stream as needed
   * until it finds a non-empty element for the head, which is non-lazy.
   *
   * @tparam B The element type of the returned collection '''That'''.
   * @param f  the function to apply on each element.
   * @return  `f(a,,0,,) ::: ... ::: f(a,,n,,)` if
   *           this stream is `[a,,0,,, ..., a,,n,,]`.
   */
  override final def flatMap[B, That](f: A => GenTraversableOnce[B])(implicit bf: CanBuildFrom[Stream[A], B, That]): That =
    // we assume there is no other builder factory on streams and therefore know that That = Stream[B]
    // optimisations are not for speed, but for functionality
    // see tickets #153, #498, #2147, and corresponding tests in run/ (as well as run/stream_flatmap_odds.scala)
    if (isStreamBuilder(bf)) asThat(
      if (isEmpty) Stream.Empty
      else {
        // establish !prefix.isEmpty || nonEmptyPrefix.isEmpty
        var nonEmptyPrefix = this
        var prefix = f(nonEmptyPrefix.head).toStream
        while (!nonEmptyPrefix.isEmpty && prefix.isEmpty) {
          nonEmptyPrefix = nonEmptyPrefix.tail
          if(!nonEmptyPrefix.isEmpty)
            prefix = f(nonEmptyPrefix.head).toStream
        }

        if (nonEmptyPrefix.isEmpty) Stream.empty
        else prefix append asStream[B](nonEmptyPrefix.tail flatMap f)
      }
    )
    else super.flatMap(f)(bf)

  /** Returns all the elements of this `Stream` that satisfy the predicate `p`
   * in a new `Stream` - i.e. it is still a lazy data structure. The order of
   * the elements is preserved
   *
   *  @param p the predicate used to filter the stream.
   *  @return the elements of this stream satisfying `p`.
   *
   * @example {{{
   * $naturalsEx
   * naturalsFrom(1)  10 } filter { _ % 5 == 0 } take 10 mkString(", ")
   * // produces
   * }}}
   */
  override def filter(p: A => Boolean): Stream[A] = {
    // optimization: drop leading prefix of elems for which f returns false
    // var rest = this dropWhile (!p(_)) - forget DRY principle - GC can't collect otherwise
    var rest = this
    while (!rest.isEmpty && !p(rest.head)) rest = rest.tail
    // private utility func to avoid `this` on stack (would be needed for the lazy arg)
    if (rest.nonEmpty) Stream.filteredTail(rest, p)
    else Stream.Empty
  }

  override final def withFilter(p: A => Boolean): StreamWithFilter = new StreamWithFilter(p)

  /** A lazier implementation of WithFilter than TraversableLike's.
   */
  final class StreamWithFilter(p: A => Boolean) extends WithFilter(p) {

    override def map[B, That](f: A => B)(implicit bf: CanBuildFrom[Stream[A], B, That]): That = {
      def tailMap(coll: Stream[A]): Stream[B] = {
        var head: A = null.asInstanceOf[A]
        var tail: Stream[A] = coll
        while (true) {
          if (tail.isEmpty)
            return Stream.Empty
          head = tail.head
          tail = tail.tail
          if (p(head))
            return cons(f(head), tailMap(tail))
        }
        throw new RuntimeException()
      }

      if (isStreamBuilder(bf)) asThat(tailMap(Stream.this))
      else super.map(f)(bf)
    }

    override def flatMap[B, That](f: A => GenTraversableOnce[B])(implicit bf: CanBuildFrom[Stream[A], B, That]): That = {
      def tailFlatMap(coll: Stream[A]): Stream[B] = {
        var head: A = null.asInstanceOf[A]
        var tail: Stream[A] = coll
        while (true) {
          if (tail.isEmpty)
            return Stream.Empty
          head = tail.head
          tail = tail.tail
          if (p(head))
            return f(head).toStream append tailFlatMap(tail)
        }
        throw new RuntimeException()
      }

      if (isStreamBuilder(bf)) asThat(tailFlatMap(Stream.this))
      else super.flatMap(f)(bf)
    }

    override def foreach[B](f: A => B) =
      for (x <- self)
        if (p(x)) f(x)

    override def withFilter(q: A => Boolean): StreamWithFilter =
      new StreamWithFilter(x => p(x) && q(x))
  }

  /** A lazier Iterator than LinearSeqLike's. */
  override def iterator: Iterator[A] = new StreamIterator(self)

  /** Apply the given function `f` to each element of this linear sequence
   * (while respecting the order of the elements).
   *
   *  @param f The treatment to apply to each element.
   *  @note  Overridden here as final to trigger tail-call optimization, which
   *  replaces 'this' with 'tail' at each iteration. This is absolutely
   *  necessary for allowing the GC to collect the underlying stream as elements
   *  are consumed.
   *  @note  This function will force the realization of the entire stream
   *  unless the `f` throws an exception.
   */
  @tailrec
  override final def foreach[B](f: A => B) {
    if (!this.isEmpty) {
      f(head)
      tail.foreach(f)
    }
  }

  /** Stream specialization of foldLeft which allows GC to collect along the
   * way.
   *
   * @tparam B The type of value being accumulated.
   * @param z The initial value seeded into the function `op`.
   * @param op The operation to perform on successive elements of the `Stream`.
   * @return The accumulated value from successive applications of `op`.
   */
  @tailrec
  override final def foldLeft[B](z: B)(op: (B, A) => B): B = {
    if (this.isEmpty) z
    else tail.foldLeft(op(z, head))(op)
  }

  /** Stream specialization of reduceLeft which allows GC to collect
   *  along the way.
   *
   * @tparam B The type of value being accumulated.
   * @param f The operation to perform on successive elements of the `Stream`.
   * @return The accumulated value from successive applications of `f`.
   */
  override final def reduceLeft[B >: A](f: (B, A) => B): B = {
    if (this.isEmpty) throw new UnsupportedOperationException("empty.reduceLeft")
    else {
      var reducedRes: B = this.head
      var left = this.tail
      while (!left.isEmpty) {
        reducedRes = f(reducedRes, left.head)
        left = left.tail
      }
      reducedRes
    }
  }

  /** Returns all the elements of this stream that satisfy the predicate `p`
   * returning of [[scala.Tuple2]] of `Stream`s obeying the partition predicate
   * `p`. The order of the elements is preserved.
   *
   * @param p the predicate used to filter the stream.
   * @return the elements of this stream satisfying `p`.
   *
   * @example {{{
   * $naturalsEx
   * val parts = naturalsFrom(1) partition { _ % 2 == 0 }
   * parts._1 take 10 mkString ", "
   * // produces: "2, 4, 6, 8, 10, 12, 14, 16, 18, 20"
   * parts._2 take 10 mkString ", "
   * // produces: "1, 3, 5, 7, 9, 11, 13, 15, 17, 19"
   * }}}
   *
   */
  override def partition(p: A => Boolean): (Stream[A], Stream[A]) = (filter(p(_)), filterNot(p(_)))

  /** Returns a stream formed from this stream and the specified stream `that`
   * by associating each element of the former with the element at the same
   * position in the latter.
   *
   * If one of the two streams is longer than the other, its remaining elements
   * are ignored.
   *
   * The return type of this function may not be obvious.  The lazy aspect of
   * the returned value is different than that of `partition`.  In `partition`
   * we get back a [[scala.Tuple2]] of two lazy `Stream`s whereas here we get
   * back a single lazy `Stream` of [[scala.Tuple2]]s where the
   * [[scala.Tuple2]]'s type signature is `(A1, B)`.
   *
   * @tparam A1 The type of the first parameter of the zipped tuple
   * @tparam B The type of the second parameter of the zipped tuple
   * @tparam That The type of the returned `Stream`.
   * @return `Stream({a,,0,,,b,,0,,}, ...,
   *         {a,,min(m,n),,,b,,min(m,n),,)}` when
   *         `Stream(a,,0,,, ..., a,,m,,)
   *         zip Stream(b,,0,,, ..., b,,n,,)` is invoked.
   *
   * @example {{{
   * $naturalsEx
   * naturalsFrom(1) zip naturalsFrom(2) take 5 foreach println
   * // prints
   * // (1,2)
   * // (2,3)
   * // (3,4)
   * // (4,5)
   * // (5,6)
   * }}}
   */
  override final def zip[A1 >: A, B, That](that: scala.collection.GenIterable[B])(implicit bf: CanBuildFrom[Stream[A], (A1, B), That]): That =
    // we assume there is no other builder factory on streams and therefore know that That = Stream[(A1, B)]
    if (isStreamBuilder(bf)) asThat(
      if (this.isEmpty || that.isEmpty) Stream.Empty
      else cons((this.head, that.head), asStream[(A1, B)](this.tail zip that.tail))
    )
    else super.zip(that)(bf)

  /** Zips this iterable with its indices. `s.zipWithIndex` is equivalent to `s
   * zip s.indices`.
   *
   * This method is much like `zip` in that it returns a single lazy `Stream` of
   * [[scala.Tuple2]].
   *
   * @tparam A1 The type of the first element of the [[scala.Tuple2]] in the
   * resulting stream.
   * @tparam That The type of the resulting `Stream`.
   * @return `Stream({a,,0,,,0}, ..., {a,,n,,,n)}`
   *
   * @example {{{
   * $naturalsEx
   * (naturalsFrom(1) zipWithIndex) take 5 foreach println
   * // prints
   * // (1,0)
   * // (2,1)
   * // (3,2)
   * // (4,3)
   * // (5,4)
   * }}}
   */
  override def zipWithIndex[A1 >: A, That](implicit bf: CanBuildFrom[Stream[A], (A1, Int), That]): That =
    this.zip[A1, Int, That](Stream.from(0))

  /** Write all defined elements of this iterable into given string builder.
   *  The written text begins with the string `start` and is finished by the string
   *  `end`. Inside, the string representations of defined elements (w.r.t.
   *  the method `toString()`) are separated by the string `sep`. The method will
   *  not force evaluation of undefined elements. A tail of such elements will be
   * represented by a `"?"` instead.
   *
   * @param b The [[collection.mutable.StringBuilder]] factory to which we need
   * to add the string elements.
   * @param start The prefix of the resulting string (e.g. "Stream(")
   * @param sep The separator between elements of the resulting string (e.g. ",")
   * @param end The end of the resulting string (e.g. ")")
   * @return The original [[collection.mutable.StringBuilder]] containing the
   * resulting string.
   */
  override def addString(b: StringBuilder, start: String, sep: String, end: String): StringBuilder = {
    def loop(pre: String, these: Stream[A]) {
      if (these.isEmpty) b append end
      else {
        b append pre append these.head
        if (these.tailDefined) loop(sep, these.tail)
        else b append sep append "?" append end
      }
    }
    b append start
    loop("", this)
    b
  }

  override def mkString(sep: String): String = mkString("", sep, "")
  override def mkString: String = mkString("")
  override def mkString(start: String, sep: String, end: String): String = {
    this.force
    super.mkString(start, sep, end)
  }
  override def toString = super.mkString(stringPrefix + "(", ", ", ")")

  override def splitAt(n: Int): (Stream[A], Stream[A]) = (take(n), drop(n))

  /** Returns the `n` first elements of this `Stream` as another `Stream`, or
   * else the whole `Stream`, if it has less than `n` elements.
   *
   * The result of `take` is, again, a `Stream` meaning that it also does not
   * make any needless evaluations of the `Stream` itself, delaying that until
   * the usage of the resulting `Stream`.
   *
   * @param n the number of elements to take.
   * @return the `n` first elements of this stream.
   *
   * @example {{{
   * $naturalsEx
   * scala> naturalsFrom(5) take 5
   * res1: scala.collection.immutable.Stream[Int] = Stream(5, ?)
   *
   * scala> naturalsFrom(5) take 5 mkString ", "
   * // produces: "5, 6, 7, 8, 9"
   * }}}
   */
  override def take(n: Int): Stream[A] = (
    // Note that the n == 1 condition appears redundant but is not.
    // It prevents "tail" from being referenced (and its head being evaluated)
    // when obtaining the last element of the result. Such are the challenges
    // of working with a lazy-but-not-really sequence.
    if (n <= 0 || isEmpty) Stream.empty
    else if (n == 1) cons(head, Stream.empty)
    else cons(head, tail take n-1)
  )

  @tailrec final override def drop(n: Int): Stream[A] =
    if (n <= 0 || isEmpty) this
    else tail drop n-1

  /** A substream starting at index `from` and extending up to (but not including)
   *  index `until`.  This returns a `Stream` that is lazily evaluated.
   *
   * @param from    The index of the first element of the returned subsequence
   * @param until   The index of the element following the returned subsequence
   * @return A new string containing the elements requested from `start` until
   * `end`.
   *
   * @example {{{
   * naturalsFrom(0) slice(50, 60) mkString ", "
   * // produces: "50, 51, 52, 53, 54, 55, 56, 57, 58, 59"
   * }}}
   */
  override def slice(from: Int, until: Int): Stream[A] = {
    val lo = from max 0
    if (until <= lo || isEmpty) Stream.empty
    else this drop lo take (until - lo)
  }

  /** The stream without its last element.
   *
   * @return A new `Stream` containing everything but the last element.  If your
   * `Stream` represents an infinite series, this method will not return.
   *
   *  @throws `Predef.UnsupportedOperationException` if the stream is empty.
   */
  override def init: Stream[A] =
    if (isEmpty) super.init
    else if (tail.isEmpty) Stream.Empty
    else cons(head, tail.init)

  /** Returns the rightmost `n` elements from this iterable.
   *
   * @note Take serious caution here.  If the `Stream` represents an infinite
   * series then this function ''will not return''.  The right most elements of
   * an infinite series takes an infinite amount of time to produce.
   *
   *  @param n the number of elements to take
   *  @return The last `n` elements from this `Stream`.
   */
  override def takeRight(n: Int): Stream[A] = {
    var these: Stream[A] = this
    var lead = this drop n
    while (!lead.isEmpty) {
      these = these.tail
      lead = lead.tail
    }
    these
  }

  /**
   * @inheritdoc
   * $willTerminateInf
   */
  override def dropRight(n: Int): Stream[A] = {
    // We make dropRight work for possibly infinite streams by carrying
    // a buffer of the dropped size. As long as the buffer is full and the
    // rest is non-empty, we can feed elements off the buffer head.  When
    // the rest becomes empty, the full buffer is the dropped elements.
    def advance(stub0: List[A], stub1: List[A], rest: Stream[A]): Stream[A] = {
      if (rest.isEmpty) Stream.empty
      else if (stub0.isEmpty) advance(stub1.reverse, Nil, rest)
      else cons(stub0.head, advance(stub0.tail, rest.head :: stub1, rest.tail))
    }
    if (n <= 0) this
    else advance((this take n).toList, Nil, this drop n)
  }

  /** Returns the longest prefix of this `Stream` whose elements satisfy the
   * predicate `p`.
   *
   * @param p the test predicate.
   * @return A new `Stream` representing the values that satisfy the predicate
   * `p`.
   *
   * @example {{{
   + naturalsFrom(0) takeWhile { _ < 5 } mkString ", "
   * produces: "0, 1, 2, 3, 4"
   * }}}
   */
  override def takeWhile(p: A => Boolean): Stream[A] =
    if (!isEmpty && p(head)) cons(head, tail takeWhile p)
    else Stream.Empty

  /** Returns the a `Stream` representing the longest suffix of this iterable
   * whose first element does not satisfy the predicate `p`.
   *
   * @note This method realizes the entire `Stream` beyond the truth value of
   * the predicate `p`.
   *
   * @param p the test predicate.
   * @return A new `Stream` representing the results of applying `p` to the
   * oringal `Stream`.
   *
   * @example {{{
   * // Assume we have a Stream that takes the first 20 natural numbers
   * def naturalsLt50(i: Int): Stream[Int] = i #:: { if (i < 20) naturalsLt50(i * + 1) else Stream.Empty }
   * naturalsLt50(0) dropWhile { _ < 10 }
   * // produces: "10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20"
   * }}}
   */
  override def dropWhile(p: A => Boolean): Stream[A] = {
    var these: Stream[A] = this
    while (!these.isEmpty && p(these.head)) these = these.tail
    these
  }

  /** Builds a new stream from this stream in which any duplicates (as
   * determined by `==`) have been removed. Among duplicate elements, only the
   * first one is retained in the resulting `Stream`.
   *
   * @return A new `Stream` representing the result of applying distinctness to
   * the original `Stream`.
   * @example {{{
   * // Creates a Stream where every element is duplicated
   * def naturalsFrom(i: Int): Stream[Int] = i #:: { i #:: naturalsFrom(i + 1) }
   * naturalsFrom(1) take 6 mkString ", "
   * // produces: "1, 1, 2, 2, 3, 3"
   * (naturalsFrom(1) distinct) take 6 mkString ", "
   * // produces: "1, 2, 3, 4, 5, 6"
   * }}}
   */
  override def distinct: Stream[A] = {
    // This should use max memory proportional to N, whereas
    // recursively calling distinct on the tail is N^2.
    def loop(seen: Set[A], rest: Stream[A]): Stream[A] = {
      if (rest.isEmpty) rest
      else if (seen(rest.head)) loop(seen, rest.tail)
      else cons(rest.head, loop(seen + rest.head, rest.tail))
    }
    loop(Set(), this)
  }

  /** Returns a new sequence of given length containing the elements of this
   * sequence followed by zero or more occurrences of given elements.
   *
   * @tparam B The type of the value to pad with.
   * @tparam That The type contained within the resulting `Stream`.
   * @param len The number of elements to pad into the `Stream`.
   * @param elem The value of the type `B` to use for padding.
   * @return A new `Stream` representing the collection with values padding off
   * to the end. If your `Stream` represents an infinite series, this method will
   * not return.
   * @example {{{
   * def naturalsFrom(i: Int): Stream[Int] = i #:: { if (i < 5) naturalsFrom(i + 1) else Stream.Empty }
   * naturalsFrom(1) padTo(10, 0) foreach println
   * // prints
   * // 1
   * // 2
   * // 3
   * // 4
   * // 5
   * // 0
   * // 0
   * // 0
   * // 0
   * // 0
   * }}}
   */
  override def padTo[B >: A, That](len: Int, elem: B)(implicit bf: CanBuildFrom[Stream[A], B, That]): That = {
    def loop(len: Int, these: Stream[A]): Stream[B] =
      if (these.isEmpty) Stream.fill(len)(elem)
      else cons(these.head, loop(len - 1, these.tail))

    if (isStreamBuilder(bf)) asThat(loop(len, this))
    else super.padTo(len, elem)(bf)
  }

  /** A list consisting of all elements of this list in reverse order.
   *
   * @note This function must realize the entire `Stream` in order to perform
   * this operation so if your `Stream` represents an infinite sequence then
   * this function will never return.
   *
   * @return A new `Stream` containing the representing of the original `Stream`
   * in reverse order.
   *
   * @example {{{
   * def naturalsFrom(i: Int): Stream[Int] = i #:: { if (i < 5) naturalsFrom(i + 1) else Stream.Empty }
   * (naturalsFrom(1) reverse) foreach println
   * // prints
   * // 5
   * // 4
   * // 3
   * // 2
   * // 1
   * }}}
   */
  override def reverse: Stream[A] = {
    var result: Stream[A] = Stream.Empty
    var these = this
    while (!these.isEmpty) {
      val r = Stream.consWrapper(result).#::(these.head)
      r.tail // force it!
      result = r
      these = these.tail
    }
    result
  }

  /** Evaluates and concatenates all elements within the `Stream` into a new
   * flattened `Stream`.
   *
   * @tparam B The type of the elements of the resulting `Stream`.
   * @return A new `Stream` of type `B` of the flattened elements of `this`
   * `Stream`.
   * @example {{{
   * val sov: Stream[Vector[Int]] = Vector(0) #:: Vector(0, 0) #:: sov.zip(sov.tail).map { n => n._1 ++ n._2 }
   * sov.flatten take 10 mkString ", "
   * // produces: "0, 0, 0, 0, 0, 0, 0, 0, 0, 0"
   * }}}
   */
  override def flatten[B](implicit asTraversable: A => /*<:<!!!*/ GenTraversableOnce[B]): Stream[B] = {
    var st: Stream[A] = this
    while (st.nonEmpty) {
      val h = asTraversable(st.head)
      if (h.isEmpty) {
        st = st.tail
      } else {
        return h.toStream #::: st.tail.flatten
      }
    }
    Stream.empty
  }

  override def view = new StreamView[A, Stream[A]] {
    protected lazy val underlying = self.repr
    override def iterator = self.iterator
    override def length = self.length
    override def apply(idx: Int) = self.apply(idx)
  }

  /** Defines the prefix of this object's `toString` representation as `Stream`.
   */
  override def stringPrefix = "Stream"

}

/** A specialized, extra-lazy implementation of a stream iterator, so it can
 *  iterate as lazily as it traverses the tail.
 */
final class StreamIterator[+A] private() extends AbstractIterator[A] with Iterator[A] {
  def this(self: Stream[A]) {
    this()
    these = new LazyCell(self)
  }

  // A call-by-need cell.
  class LazyCell(st: => Stream[A]) {
    lazy val v = st
  }

  private var these: LazyCell = _

  def hasNext: Boolean = these.v.nonEmpty
  def next(): A =
    if (isEmpty) Iterator.empty.next()
    else {
      val cur    = these.v
      val result = cur.head
      these = new LazyCell(cur.tail)
      result
    }
  override def toStream = {
    val result = these.v
    these = new LazyCell(Stream.empty)
    result
  }
  override def toList   = toStream.toList
}

/**
 * The object `Stream` provides helper functions to manipulate streams.
 *
 * @author Martin Odersky, Matthias Zenger
 * @version 1.1 08/08/03
 * @since   2.8
 */
object Stream extends SeqFactory[Stream] {

  /** The factory for streams.
   *  @note Methods such as map/flatMap will not invoke the `Builder` factory,
   *        but will return a new stream directly, to preserve laziness.
   *        The new stream is then cast to the factory's result type.
   *        This means that every CanBuildFrom that takes a
   *        Stream as its From type parameter must yield a stream as its result parameter.
   *        If that assumption is broken, cast errors might result.
   */
  class StreamCanBuildFrom[A] extends GenericCanBuildFrom[A]

  implicit def canBuildFrom[A]: CanBuildFrom[Coll, A, Stream[A]] = new StreamCanBuildFrom[A]

  /** Creates a new builder for a stream */
  def newBuilder[A]: Builder[A, Stream[A]] = new StreamBuilder[A]

  import scala.collection.{Iterable, Seq, IndexedSeq}

  /** A builder for streams
   *  @note This builder is lazy only in the sense that it does not go downs the spine
   *        of traversables that are added as a whole. If more laziness can be achieved,
   *        this builder should be bypassed.
   */
  class StreamBuilder[A] extends scala.collection.mutable.LazyBuilder[A, Stream[A]] {
    def result: Stream[A] = parts.toStream flatMap (_.toStream)
  }

  object Empty extends Stream[Nothing] {
    override def isEmpty = true
    override def head = throw new NoSuchElementException("head of empty stream")
    override def tail = throw new UnsupportedOperationException("tail of empty stream")
    def tailDefined = false
  }

  /** The empty stream */
  override def empty[A]: Stream[A] = Empty

  /** A stream consisting of given elements */
  override def apply[A](xs: A*): Stream[A] = xs.toStream

  /** A wrapper class that adds `#::` for cons and `#:::` for concat as operations
   *  to streams.
   */
  class ConsWrapper[A](tl: => Stream[A]) {
    def #::(hd: A): Stream[A] = cons(hd, tl)
    def #:::(prefix: Stream[A]): Stream[A] = prefix append tl
  }

  /** A wrapper method that adds `#::` for cons and `#::: for concat as operations
   *  to streams.
   */
  implicit def consWrapper[A](stream: => Stream[A]): ConsWrapper[A] =
    new ConsWrapper[A](stream)

  /** An extractor that allows to pattern match streams with `#::`.
   */
  object #:: {
    def unapply[A](xs: Stream[A]): Option[(A, Stream[A])] =
      if (xs.isEmpty) None
      else Some((xs.head, xs.tail))
  }

  /** An alternative way of building and matching Streams using Stream.cons(hd, tl).
   */
  object cons {

    /** A stream consisting of a given first element and remaining elements
     *  @param hd   The first element of the result stream
     *  @param tl   The remaining elements of the result stream
     */
    def apply[A](hd: A, tl: => Stream[A]) = new Cons(hd, tl)

    /** Maps a stream to its head and tail */
    def unapply[A](xs: Stream[A]): Option[(A, Stream[A])] = #::.unapply(xs)
  }

  /** A lazy cons cell, from which streams are built. */
  @SerialVersionUID(-602202424901551803L)
  final class Cons[+A](hd: A, tl: => Stream[A]) extends Stream[A] {
    override def isEmpty = false
    override def head = hd
    @volatile private[this] var tlVal: Stream[A] = _
    @volatile private[this] var tlGen = tl _
    def tailDefined: Boolean = tlGen eq null
    override def tail: Stream[A] = {
      if (!tailDefined)
        synchronized {
          if (!tailDefined) {
            tlVal = tlGen()
            tlGen = null
          }
        }

      tlVal
    }
  }

  /** An infinite stream that repeatedly applies a given function to a start value.
   *
   *  @param start the start value of the stream
   *  @param f     the function that's repeatedly applied
   *  @return      the stream returning the infinite sequence of values `start, f(start), f(f(start)), ...`
   */
  def iterate[A](start: A)(f: A => A): Stream[A] = cons(start, iterate(f(start))(f))

  override def iterate[A](start: A, len: Int)(f: A => A): Stream[A] =
    iterate(start)(f) take len

  /**
   * Create an infinite stream starting at `start` and incrementing by
   * step `step`.
   *
   * @param start the start value of the stream
   * @param step the increment value of the stream
   * @return the stream starting at value `start`.
   */
  def from(start: Int, step: Int): Stream[Int] =
    cons(start, from(start+step, step))

  /**
   * Create an infinite stream starting at `start` and incrementing by `1`.
   *
   * @param start the start value of the stream
   * @return the stream starting at value `start`.
   */
  def from(start: Int): Stream[Int] = from(start, 1)

  /**
   * Create an infinite stream containing the given element expression (which
   * is computed for each occurrence).
   *
   * @param elem the element composing the resulting stream
   * @return the stream containing an infinite number of elem
   */
  def continually[A](elem: => A): Stream[A] = cons(elem, continually(elem))

  override def fill[A](n: Int)(elem: => A): Stream[A] =
    if (n <= 0) Empty else cons(elem, fill(n-1)(elem))

  override def tabulate[A](n: Int)(f: Int => A): Stream[A] = {
    def loop(i: Int): Stream[A] =
      if (i >= n) Empty else cons(f(i), loop(i+1))
    loop(0)
  }

  override def range[T: Integral](start: T, end: T, step: T): Stream[T] = {
    val num = implicitly[Integral[T]]
    import num._

    if (if (step < zero) start <= end else end <= start) Empty
    else cons(start, range(start + step, end, step))
  }

  private[immutable] def filteredTail[A](stream: Stream[A], p: A => Boolean) = {
    cons(stream.head, stream.tail filter p)
  }

  private[immutable] def collectedTail[A, B, That](head: B, stream: Stream[A], pf: PartialFunction[A, B], bf: CanBuildFrom[Stream[A], B, That]) = {
    cons(head, stream.tail.collect(pf)(bf).asInstanceOf[Stream[B]])
  }
}


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