// Function that finds the n number in the fibonacci sequence
// Takes 1 parameter (desired element's order number in the sequence)
// Returns 1 value (desired element's value)
// Bonus: works with negative numbers

/*
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610
0 1 2 3 4 5 6 7  8  9  10 11 12  13  14  15
 */

/*
def recursiveFib(n: Long): Long ={
  if (n <= 1)
    n
  else
    recursiveFib(n-1) + recursiveFib(n-2)
}
*/

def recursiveFib(n: Long): Long ={
  if (n == 0 || n == 1)
    n
  else if (n < 0)
    recursiveFib(n+2) - recursiveFib(n+1)
  else
    recursiveFib(n-1) + recursiveFib(n-2)
}



println("Recursive function with 0, 1, 10, 7, 13, -6")
  recursiveFib(0)
  recursiveFib(1)
  recursiveFib(7)
  recursiveFib(10)
  recursiveFib(13)
  recursiveFib(-6)


def tailRecursiveFib(n: Long): Long ={
  def rec(counter:Long, resultOne:Long, resultTwo:Long):Long={
    //println(s"$counter | $resultOne $resultTwo\n")
    if (counter <= 1)
      resultTwo
    else
      rec(counter-1, resultTwo, resultOne+resultTwo)
  }
  rec(n, 0, 1)
}

println("Tail recursive function with 0, 1, 10, 7, 13")
  tailRecursiveFib(0)
  tailRecursiveFib(1)
  tailRecursiveFib(7)
  tailRecursiveFib(10)
  tailRecursiveFib(13)



def imperativeFib(n: Long): Long ={
  if (n == 0) n
  else{
    var counter = n
    var first = 0L
    var second = 1L
    var result = 1L
    while (counter >= 2){
      //println(s"$counter | $first $second | $result\n")
      result = first + second
      first = second
      second = result
      counter -= 1
    }
    result
  }
}

println("Imperative function with 0, 1, 10, 7, 13")
  imperativeFib(0)
  imperativeFib(1)
  imperativeFib(7)
  imperativeFib(10)
  imperativeFib(13)

def fib(n: Long): Long={
  ((scala.math.pow(1.618034, n) - scala.math.pow(-0.618034, n))/scala.math.sqrt(5)).toLong
}

println("Mathematical function using the Golden Ratio with 0, 1, 10, 7, 13")
  fib(0)
  fib(1)
  fib(7)
  fib(10)
  fib(13)