✎ fp:lab01 [books]

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====== Introduction to Scala ======

===== Scala setup =====

==== Installation ====

**Scala** can be downloaded and installed on either a Windows or NIX platform (e.g. Linux, OS-X) [[https://www.scala-lang.org/download/|here]]. For this lecture you must install **Scala 3**, and we recommend installing it using //Coursier// (see the previous link)

==== IDE ====

One of the most widely used IDE (Integrated Development Environment) for Scala is:
  * [[https://www.jetbrains.com/idea/download/ | IntellIJ]]
  * alternatively, you can use [[https://www.sublimetext.com/download | Sublime]], which is a simpler (faster) editor. You can add syntax highlighting plugins for Scala (see: [[https://scalameta.org/metals/docs/editors/sublime/ | scalameta ]]), as well as worksheet/REPL support (see: [[https://packagecontrol.io/packages/SublimeREPL | SublimeREPL]]).

===== Online exercises =====

Consider the following code:
<code scala>
def fact(n: Integer): Integer =
  if (n == 1) 1
  else n*fact(n-1)
</code>

The function ''fact'' is not tail recursive and will quickly fill the call stack. Starting from the code stub below, implement a tail-recursive factorial:
<code scala>
def fact (n: Integer): Integer = {
   def aux_fact(n: Integer, acc: Integer): Integer = 
       if (???) acc
       else ???
   aux_fact(n,1)
}
</code>





===== Homework - Newton's Square Root method =====

  * Video (Newton's Square Root solution)

A very fast way to numerically compute $math[\sqrt{a}], is using Newton's Square Root approximation:
  * Start with $math[x_0 = 1].
  * Compute $math[x_{n+1} = \displaystyle\frac{1}{2}(x_n+\frac{a}{x_n})]

Implement the following function:
<code scala>
  //given a guess x_n, it computes x_{n+1}
  def improve(xn: Double, a: Double): Double = ???

  // computes the nth estimation of sqrt(a)
  def nth_guess(n: Double, a: Double): Double = 
     if (n == 0) ???
     else ???
</code>

Note that ''nth_guess'' will return a more accurate estimation for smaller a, than for larger a's. We may waste a lot of iterations on small numbers, and spend insufficient ones on large numbers. Thus, instead of ''nth_guess'', implement ''acceptable(xn,a)'' which returns ''true'' iff $math[\mid x_n^2 - a \mid \leq 0.001]. (Hint, google the ''abs'' function in Scala. Don't forget to import ''scala.math._'').
<code scala>
  def acceptable(xn: Double, a: Double): Boolean = ???
</code>