package greeter

object Chapter5 {

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

  /////////////////////////////////////////////////////////////////////////////

  //   CHAPTER 5: FIRST-CLASS FUNCTIONS

  /*

  // Write a function to sumall integers between two given numbers a and b

  def sumInts(a: Int, b: Int): Int =

    if (a > b) 0 else a + sumInts(a + 1, b)

  sumInts(1, 5)

  //Write a function to sum the squares of all integers between two given numbers a and b

  def square(x: Int): Int = x * x

  def sumSquares(a: Int, b: Int): Int =

    if (a > b) 0 else square(a) + sumSquares(a + 1, b)

  square(5)

  //Write a function to sum the powers 2n of all integers n between two given numbers a and b:

  def powerOfTwo(x: Int): Int = if (x == 0) 1 else 2 * powerOfTwo(x - 1)

  def sumPowersOfTwo(a: Int, b: Int): Int =

    if (a > b) 0 else powerOfTwo(a) + sumPowersOfTwo(a + 1, b)

  sumPowersOfTwo(2, 4)

  */

  /*

  def sum(f: Int => Int, a: Int, b: Int): Int =

    if (a > b) 0 else f(a) + sum(f, a + 1, b)

  //def sumInts(a: Int, b: Int): Int = sum(id, a, b)

  //def sumInts(a: Int, b: Int): Int = sum((x: Int) => x, a, b)

  def sumInts(a: Int, b: Int): Int = sum(x => x, a, b)

  //def sumSquares(a: Int, b: Int): Int = sum(square, a, b)

  //def sumSquares(a: Int, b: Int): Int = sum((x: Int) => x * x, a, b)

  def sumSquares(a: Int, b: Int): Int = sum(x => x * x, a, b)

  def sumPowersOfTwo(a: Int, b: Int): Int = sum(powerOfTwo, a, b)

  def id(x: Int): Int = x

	def square(x: Int): Int = x * x

	*/

	def powerOfTwo(x: Int): Int = if (x == 0) 1 else 2 * powerOfTwo(x - 1)

                                                  //> powerOfTwo: (x: Int)Int

  // 5.2: Currying

  def sum(f: Int => Int): (Int, Int) => Int = {

    def sumF(a: Int, b: Int): Int =

      if (a > b) 0 else f(a) + sumF(a + 1, b)

    sumF

  }                                               //> sum: (f: Int => Int)(Int, Int) => Int

  def sumInts = sum(x => x)                       //> sumInts: => (Int, Int) => Int

  def sumSquares = sum(x => x * x)                //> sumSquares: => (Int, Int) => Int

  def sumPowersOfTwo = sum(powerOfTwo)            //> sumPowersOfTwo: => (Int, Int) => Int

  sumSquares(1,10) + sumPowersOfTwo(10,20)        //> res0: Int = 2096513

  sum(x => x * x)(2,4)                            //> res1: Int = 29

	// 5.3: Finding Fixed Points of Functions

	val tolerance = 0.001                     //> tolerance  : Double = 0.001

	def isCloseEnough(x: Double, y: Double) = Math.abs((x-y) / x) < tolerance

                                                  //> isCloseEnough: (x: Double, y: Double)Boolean

	def fixedPoint(f: Double => Double)(firstGuess: Double) = {

		def iterate(guess: Double): Double = {

			val next = f(guess)

			if (isCloseEnough(guess, next)) next

			else iterate(next)

		}

		iterate(firstGuess)

	}                                         //> fixedPoint: (f: Double => Double)(firstGuess: Double)Double

}