Fibonacci numbers (Scala)

From LiteratePrograms

The Fibonacci numbers are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined recursively by

$F(n) = \begin{cases} 0 & n = 0 \\ 1 & n = 1 \\ F(n-1)+F(n-2) & n > 1 \\ \end{cases} .$

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist.

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Recursion

The recursive definition can be translated directly into Scala as follows:

<<fibonacci_recursive.scala>>=

  def fib( n: Int): Int = n match {

    case 0 => 0
    case 1 => 1
    case _ => fib( n -1) + fib( n-2)
  }

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Iteration

<<fibonacci_iterative.scala>>=

  def fib( n: Int) = {
    // initial values
    var a = 0    // inferred type: Int
    var b = 1    // inferred type: Int
    
    // function next
    // inferred result type: Pair[Int, Int]
    
    def next( a: Int, b: Int) = Pair( b, a + b) ;    
  
    var i = 0
    while( i < n) {
      
      // get result pair members by pattern matching
      val Pair( c, d) = next( a, b) ;
      
      // assign result
      a = c
      b = d
      
      //iterate
      i = i +1
    }
    // return 'a'
    a
  }

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Tail Recursive

<<fibonacci_tail_recursive.scala>>=

  def fib( n:Int) = fib_tr( n, 1, 0) 

  def fib_tr( n: Int, b: Int, a: Int): Int = n match {

    case 0 => a 
    case _ => fib_tr( n -1, a + b, b)
  }