理解流中的递归

Question

我试图理解流中的递归，这令人困惑。我的代码是这样的

  val bigIntFromStream : Stream[BigInt] = BigInt(0) #:: BigInt(1) #:: bigIntFromStream.zip(bigIntFromStream.tail).map{x =>
    println(s"stream = ${bigIntFromStream} + stream.tail = ${bigIntFromStream.tail} + zipped value = ${bigIntFromStream.zip(bigIntFromStream.tail)}")
    println(s"Calculating value for ${x}, {x._1} = ${x._1}, {x._2} = ${x._2}")
    x._1 + x._2}

代码的输出是这样的

0 1 stream = Stream(0, 1, ?) + stream.tail = Stream(1, ?) + zipped value = Stream((0,1), ?)

Calculating value for (0,1), {x._1} = 0, {x._2} = 1
1 stream = Stream(0, 1, 1, ?) + stream.tail = Stream(1, 1, ?) + zipped value = Stream((0,1), ?)

Calculating value for (1,1), {x._1} = 1, {x._2} = 1
2 stream = Stream(0, 1, 1, 2, ?) + stream.tail = Stream(1, 1, 2, ?) + zipped value = Stream((0,1), ?)

Calculating value for (1,2), {x._1} = 1, {x._2} = 2
3 stream = Stream(0, 1, 1, 2, 3, ?) + stream.tail = Stream(1, 1, 2, 3, ?) + zipped value = Stream((0,1), ?)

Calculating value for (2,3), {x._1} = 2, {x._2} = 3
5 stream = Stream(0, 1, 1, 2, 3, 5, ?) + stream.tail = Stream(1, 1, 2, 3, 5, ?) + zipped value = Stream((0,1), ?)

Calculating value for (3,5), {x._1} = 3, {x._2} = 5

我的问题是 x 如何获得 zip 在实际值和它的尾部之间的最后一个值？如果我遗漏了什么，请告诉我

Answer 1

回想一下，Stream 最初是一个单一元素，并承诺在需要时获得更多。即使所有元素都已完全定义，情况也是如此。

val ns = Stream(1,2,3,4,5)
//ns: scala.collection.immutable.Stream[Int] = Stream(1, ?)

一个带有自己尾巴的集合有效地将每个元素与其邻居配对。

val paired = ns zip ns.tail
//paired: scala.collection.immutable.Stream[(Int, Int)] = Stream((1,2), ?)
// The rest are (2,3), (3,4) and (4,5), but they haven't been realized yet.

此外，当您索引 Stream 时，它是一个线性运算。换句话说，如果你想要paired(3)，代码将逐步遍历（“实现”）paired(0)，然后是paired(1)，然后是paired(2)，最后是paired(3)。

所以你发布的Stream本质上是：

// This is concept, not code.
Stream(a=0, b=1, c=a+b, d=b+c, e=c+d, ...)

请注意，在每个索引处，在前两个之后，新元素是前两个元素的总和，但在我们到达这里之前，必须先实现这些前一个元素，所以没关系。这可能是一个无限的进程，但 Stream 仅根据请求计算（实现）一个元素，因此未被请求的元素尚不存在，因此它们不会占用任何内存。

Answer 2

object Test extends App {
  var bigIntFromStream : Stream[BigInt] = Stream(0,1)

  def addItems(n: Int)(x: Stream[BigInt]): Unit = {
    if(n > 0){
      val lastIndex: Int = bigIntFromStream.indices.last
      bigIntFromStream ++= Stream(bigIntFromStream(lastIndex - 1) + bigIntFromStream(lastIndex))
      addItems(n-1)(bigIntFromStream)
    }
  }

  addItems(10)(bigIntFromStream)

  println(bigIntFromStream.mkString(","))
}