Coursera Scala Functional Programming 3rd Week factorial generalization

mapReduce.scala

/**
 * 1. Write a product function that calculates the product of the values of a function for the points on a given interval
 */ 

  def product(f: Double => Double)(a: Double, b: Double): Double = {
    def loop(a: Double, acc: Double): Double =
      if(a > b) acc else loop(a+1, f(a) * acc)
    loop(a, 1)
  }

/**
 * 2. Write factorial in terms of product
 */ 
 def factorial(a: Int) = product((a: Double) => a)(1, a)
 
 /**
  * Write a more general function, which generalizes both sum and product
  */ 
  def mapReduce(map: Double => Double, reduce: (Double, Double) => Double)(a: Int, b: Int) = {
    scala.collection.immutable.Range.inclusive(a, b)
      .map(elem => map(elem))
      .reduce((elem, acc) => reduce(elem, acc))
  }
  
  def factorialAsAMapReduce = mapReduce(a => a, (a, acc) => a * acc)(1, a)
  
  def sumAsMapReduce(a: Int, b: Int) = mapReduce(a => a, (a, acc) => a + acc)(a, b)

@deigote Pretty cool how you can think of the factorial function as a simple mapReduce sequence, and the calculation using the mapReduce above is using tail recursion automatically because of reduce.