SICP exercise 1.12 in Swift

SICP_ex_1-11.swift

//: SICP Exercise 1.12
//: //: Xcode 7.0, Swift 2.0
/* The following pattern of numbers is called Pascal’s triangle.

                     1
                   1   1
                 1   2   1
               1   3   3   1
             1   4   6   4   1
                   . . .

The numbers at the edge of the triangle are all 1, and each number inside the triangle is the sum of the two numbers above it.(1) Write a procedure that computes elements of Pascal’s triangle by means of a recursive process.

(1) The elements of Pascal’s triangle are called the binomial coefficients, because the nth row consists of the coefficients of the terms in the expansion of (x+y)^n.

I take this assignment to be asking for a function that takes a row number and returns the elements for that row.

*/

func elementsAtRow(row: Int) -> [Int] {

    var elements = [Int]()
    
    func element(row: Int, _ index: Int) -> Int {
        guard index != 0 else { return 1 }
        guard row != index else { return 1 }
        return element(row - 1, index - 1) + element(row - 1, index)
    }

    for i in (0...row) {
        elements.append(element(row, i))
    }
    
    return elements
}

assert(elementsAtRow(0) ==        [1])
assert(elementsAtRow(1) ==       [1,1])
assert(elementsAtRow(2) ==      [1,2,1])
assert(elementsAtRow(3) ==     [1,3,3,1])
assert(elementsAtRow(4) ==    [1,4,6,4,1])
assert(elementsAtRow(5) ==  [1,5,10,10,5,1])