ProgFun.sc

def factorial(n: Int): Int = {
  def loop(acc: Int, n: Int): Int =
    if (n == 0) acc
    else loop(acc * n, n-1)
  loop(1, n)
}

factorial(5)

def sum(f: Int => Int, a: Int, b: Int): Int = {
  def loop(a: Int, acc: Int): Int = {
    if (a > b) acc
    else loop(a + 1, f(a) + acc)
  }
  loop(a, 0)
}

sum(x => x*x, 3,5)

def product(f: Int => Int) (a: Int, b: Int): Int =
  if (a > b) 1
  else f(a) * product(f)(a + 1, b)

product(x => x * x)(3, 4)

def fact(n: Int) = product(x => x)(1, n)

fact(5)

def mapReduce(f: Int => Int, combine: (Int, Int) => Int, zero: Int) (a: Int, b: Int) : Int=
  if (a > b) zero
  else combine(f(a), mapReduce(f, combine, zero)(a+1, b))

def productMapReduce(f: Int => Int)(a: Int, b: Int): Int = mapReduce(f, (x, y) => x * y, 1)(a, b)

productMapReduce(x => x * x)(3, 4)