在 Scala 中使用 Streams 进行迭代 [英] Using Streams for iteration in Scala

问题描述

SICP 说迭代过程(例如平方根计算的牛顿方法、pi"计算等)可以用Streams来表述.

SICP says that iterative processes (e.g. Newton method of square root calculation, "pi" calculation, etc.) can be formulated in terms of Streams.

有人在 Scala 中使用 streams 来模拟迭代吗?

Does anybody use streams in Scala to model iterations?

推荐答案

这是产生 pi 近似值流的一种方法:

Here is one way to produce the stream of approximations of pi:

val naturals = Stream.from(0) // 0, 1, 2, ...
val odds = naturals.map(_ * 2 + 1) // 1, 3, 5, ...
val oddInverses = odds.map(1.0d / _) // 1/1, 1/3, 1/5, ...
val alternations = Stream.iterate(1)(-_) // 1, -1, 1, ...
val products = (oddInverses zip alternations)
      .map(ia => ia._1 * ia._2) // 1/1, -1/3, 1/5, ...

// Computes a stream representing the cumulative sum of another one
def sumUp(s : Stream[Double], acc : Double = 0.0d) : Stream[Double] =
  Stream.cons(s.head + acc, sumUp(s.tail, s.head + acc))

val pi = sumUp(products).map(_ * 4.0) // Approximations of pi.

现在，假设您想要第 200 次迭代:

Now, say you want the 200th iteration:

scala> pi(200)
resN: Double = 3.1465677471829556

...或第 300000 个:

...or the 300000th:

scala> pi(300000)
resN : Double = 3.14159598691202

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