===== Lecture 2: Recursive functions ======

<code Scala>
"Hello world"

// in Scala (FP in general)
// fiecare bucata de cod este
// O EXPRESIE si ea se evalueaza
// la ceva TOT TIMPUL.

var x = 0
if (x > 0) 1 else 0

// efecte laterale (side effects)
// calculam suma tuturor numerelor de la 0 la 10
var sum = 0
for (i <- 0 to 10)
  sum += i
sum
// functie recursiva
def sumTo(start: Int, stop: Int): Int =
  if (start > stop) 0
  else start + sumTo(start+1,stop)
sumTo(0,10)

def tail_sumTo(start: Int, stop: Int): Int = {
  def loop (i: Int, sum: Int): Int =
    if (i > stop) sum
    else loop(i+1, sum+ i)
  loop(start,0)
}


//factorial

var fact = 1
for (i <- 1 to 5)
  fact *= i
fact

def fact(n: Int): Int =
  if (n == 1) 1
  else n*fact(n-1)

def tail_fact(n: Int): Int = {
  def loop(i: Int, crt_fact: Int): Int =
    if (i > n) crt_fact
    else loop(i+1,i*crt_fact)
  loop(1,1)
}
tail_fact(10)

// nrele lui Fibonacci
// f0 = 0, f1 = 1
// fn = f{n-1} + f{n-2}

var bf_last = 0
var last = 1
var n = 5
for (i <- 0 to n-2){
  var aux = last + bf_last
  bf_last = last
  last = aux
}
last

def fibo(n: Int): Int =
  if (n == 0) 0
  else if (n == 1) 1
  else fibo(n-1)+fibo(n-2)

def tail_fibo(n: Int): Int = {
  def loop(i: Int,
           before_last: Int,
           last: Int): Int = {
    if (i > n-2) last
    else loop(i+1,last,before_last+last)
  }
  loop(0,0,1)
}
tail_fibo(500)


</code>