package ex1

object Main {
  def main(args: Array[String]) {

    val num: Double = 18.7 * 18.7

    println("Exercice 1")
    println(java.lang.Math.sqrt(num))
    println(sqrt2(num))


    println("Exercice 2")
    println(java.lang.Math.cbrt(num))
    println(cbrt(num))


    println("Exercice 3")
    for (lin <- 1 to 10) {
      for (col <- 1 to lin)
        print(pascal(col, lin) + " ")
      println()
    }


    println("Exercice 4")
    println(balance("(if (zero? x) max (/ 1 x))".toList))
    println(balance("Je lui ai dit (que ce n'est pas (encore) fini).\n(Mais il faisait la sourde oreille)".toList))
    println(balance(":-)".toList))
    println(balance("())(".toList))

  }

  /* Fonctions du cours */

  def abs(x: Double): Double =
    if (x >= 0) x else -x

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

  def isGoodEnough(guess: Double, x: Double): Boolean =
    abs(square(guess) - x) < 0.001

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

  def sqrt1(x: Double): Double = {
    def sqrtIter(guess: Double, x: Double): Double =
      if (isGoodEnough(guess, x))
        guess
      else
        sqrtIter(improve(guess, x), x)
    sqrtIter(1.0, x)
  }

  /* Exercice 1 */
  def sqrt2(x: Double): Double = {
    0.0 // TODO
  }

  /* Exercice 2 */
  def cbrt(x: Double): Double = {
    0.0 // TODO
  }

  /* Exercice 3 */
  def pascal(col: Int, lin: Int): Int = {
    0 // TODO
  }

  /**
   * Exercice 4
   *
   * Il y a trois methodes sur List[Char] qui sont utiles pour cet exercise
   *   - chars.isEmpty: Boolean  // true si la liste est vide
   *   - chars.head: Char        // le premier élément
   *   - chars.tail: List[Char]  // la liste sans le premier élément
   */
  def balance(chars: List[Char]): Boolean = {
    false // TODO
  }

}