worksheet of week1 for course <Functional Programming Principles in Scala>

scala.sc

import scala.annotation.tailrec

println("Welcome to the Scala worksheet")       //> Welcome to the Scala worksheet

def loop: Boolean = loop
def abs(x: Double) = if (x < 0) -x else x
def and(x: Boolean, y:Boolean) = if (x) y else false
//> and: (x: Boolean, y: Boolean)Boolean
and(true, true)                                 //> res0: Boolean = true
and(true, false)                                //> res1: Boolean = false
and(false, true)                                //> res2: Boolean = false
and(false, false)                               //> res3: Boolean = false

def sqrt(x: Double) = {
  def sqrtIter(guess: Double, x: Double): Double =
    if (isGoodEnough(guess, x)) guess
    else sqrtIter(improve(guess, x), x)

  //proportionally small error
  def isGoodEnough(guess: Double, x: Double): Boolean =
    abs(guess * guess - x) / x < 0.001

  def improve(guess: Double, x: Double) =
    (guess + x / guess) / 2

  sqrtIter(1.0, x)
}

def sqrtSimplify(x: Double) = {

  def sqrtIter(guess: Double): Double =
    if (isGoodEnough(guess)) guess
    else sqrtIter(improve(guess))

  //proportionally small error
  def isGoodEnough(guess: Double): Boolean =
    abs(guess * guess - x) / x < 0.001

  def improve(guess: Double) =
    (guess + x / guess) / 2

  sqrtIter(1.0)
}

sqrt(2)
sqrt(3)
sqrt(1e-6) //expect: 1e-3
sqrt(1e60) //expect: 1e30

//@tailrec
def gcd(a: Int, b: Int): Int =
  if(b == 0) a else gcd(b, a % b)
//non-tail recursion
def factorialNT(n: Int): Int =
  if (n == 0) 1 else n * factorial(n - 1)

def factorial(n: Int): Int = {
  //loop call itself is ===>> tail recursion function
  def loop(acc: Int, n: Int): Int =
      if(n == 0) acc
      else loop(acc * n ,(n - 1))

  loop(1, n);
}

factorial(3)
factorial(5)