SICP exercise 1.11 in Swift

SICP_ex_1-11.swift

//: SICP Exercise 1.11
//: Xcode 7.0, Swift 2.0
//: A function f is defined by the rule that f(n)=n if n<3 and f(n)=f(n−1)+2f(n−2)+3f(n−3) if n≥3. Write a procedure that computes f by means of a recursive process. Write a procedure that computes f by means of an iterative process.

func recursive(n: Int) -> Int {
    if n < 3 { return n }
    else { return recursive(n-1) + 2 * recursive(n-2) + 3 * recursive(n-3) }
}

for n in (0...10) {
    print("f(\(n)) = \(recursive(n))")
}

//    f(0) = 0
//    f(1) = 1
//    f(2) = 2
//    f(3) = 4
//    f(4) = 11
//    f(5) = 25
//    f(6) = 59
//    f(7) = 142
//    f(8) = 335
//    f(9) = 796
//    f(10) = 1892


func iterative(n: Int) -> Int {
    
    if n < 3 { return n }
    
    // This iteration's `a` value will be the next iteration's `b` value, 
    // this iterations's `b` will be the next iteration's `c`, and so on
    // until at last it exits `while` and returns f(n+1)'s `a` value, which equals f(n).
    func iter(a: Int, _ b: Int, _ c: Int, counter: Int) -> Int {
        while counter <= n {
            return iter(fn(a, b, c), a, b, counter: counter+1)
        }
        return a
    }
    
    func fn(a: Int, _ b: Int, _ c: Int) -> Int {
        return (1 * a) + (2 * b) + (3 * c)
    }
    
    // 2 = f(n-1), 1 = f(n-2), 0 = f(n-3), when n = 3
    return iter(2, 1, 0, counter: 3)
}

for n in (0...10) {
    print("f(\(n)) = \(iterative(n))")
}

//    f(0) = 0
//    f(1) = 1
//    f(2) = 2
//    f(3) = 4
//    f(4) = 11
//    f(5) = 25
//    f(6) = 59
//    f(7) = 142
//    f(8) = 335
//    f(9) = 796
//    f(10) = 1892

/*

Iterative version in Scheme...

(define (iteritive n)

    (define (iter a b c counter)
    (if (> counter n)
        a
        (iter (fn a b c) a b (+ counter 1))
    )
)

    (define (fn a b c)
        (+ a (* 2 b) (* 3 c))
    )

    (if (< n 3)
        n
        (iter 2 1 0 3)
    )
)

*/