//: ## version that only accepts positive values
//:
//: This version follows the instructions of only working for positive values of sum and product

func sumAndProduct(sum: Int, product: Int) -> [Int] {
    for x in 1...sum/2 {
        let y = sum - x
        if x * y == product {
            return [x, y]
        }
    }
    return []
}

sumAndProduct(sum: 6, product: 9)       // [3, 3]
sumAndProduct(sum: 21, product: 108)    // [9, 12]
sumAndProduct(sum: 10, product: 25)     // [5, 5]
sumAndProduct(sum: 20, product: 100)    // [10, 10]
sumAndProduct(sum: 101, product: 100)   // [1, 100]
sumAndProduct(sum: 67, product: 3)      // []

//:-------------------------------------------------------
//:
//: Everything below was added after the deadline passed
//:
//: ## version for any int values (not just positive)

func sumAndProductAny(sum: Int, product: Int) -> [Int] {
    var x = sum / 2
    var y = sum - x

    while x * y >= product {
        if x * y == product {
            if x > y {
                return [y, x]
            }
            return [x, y]
        }
        x -= 1
        y += 1
    }
    return []
}

sumAndProductAny(sum: 8, product: -20)    // -2, 10
sumAndProductAny(sum: -6, product: 9)     // -3, -3
sumAndProductAny(sum: -8, product: -20)   // -10, 2
sumAndProductAny(sum: 5, product: 0)      // 0, 5
sumAndProductAny(sum: 2, product: 1)      // 1, 1
sumAndProductAny(sum: -2, product: 1)     // -1, -1
sumAndProductAny(sum: 0, product: 25)     // []
sumAndProductAny(sum: 0, product: -25)    // -5, 5
sumAndProductAny(sum: 6, product: 9)      // 3, 3
sumAndProductAny(sum: 21, product: 108)   // 9, 12
sumAndProductAny(sum: 10, product: 25)    // 5, 5
sumAndProductAny(sum: 20, product: 100)   // 10, 10
sumAndProductAny(sum: 101, product: 100)  // 1, 100
sumAndProductAny(sum: 23, product: 60)    // 3, 20
sumAndProductAny(sum: 67, product: 3)     // []
sumAndProductAny(sum: 1, product: 2)      // []
sumAndProductAny(sum: -2, product: 20)    // []
sumAndProductAny(sum: 2, product: -20)    // []
sumAndProductAny(sum: -32, product: -42)  // []

//: ## Messy version I made along the way
//:
//: The following version of `sumAndProductAny()` was made before I made the much cleaner version above.

func sumAndProductAnyMessy(sum: Int, product: Int) -> [Int] {
    if abs(sum) == 1 && product != 0 { return [] }
    if sum > 0 {
        if product > 0 {            // sum pos, prod pos
            for x in 1 ... (sum / 2) {
                let y = sum - x
                if x * y == product {
                    return [x, y]
                }
            }
        } else if product == 0 {    // sum pos, prod 0
            return [0, sum]
        } else if product < 0 {                    // sum pos, prod neg
            for x in ((-sum / 2) ... -1) {
                let y = sum - x
                if x * y == product {
                    return [x, y]
                }
            }
        }
    } else if sum == 0 {
        //                          // sum 0, prod pos -> []
        if product == 0 {           // sum 0, prod 0
            return [0,0]
        } else if product < 0 {     // sum 0, prod neg
            var x = -1, y = 1
            while x * y >= product {
                if x * y == product {
                    return [x,y]
                }
                x -= 1
                y += 1
            }
        }
    } else if sum < 0 {
        if product > 0 {            // sum neg, prod pos
            let absSum = -sum
            for x in 1 ... (absSum / 2) {
                let y = absSum - x
                if x * y == product {
                    return [-x, -y]
                }
            }
        } else if product == 0 {    // sum neg, prod 0
            return [sum, 0]
        } else {                    // sum neg, prod neg
            let absSum = -sum
            for x in 1 ... (absSum / 2) {
                let y = -1 * (sum - x)
                if -x * y == product {
                    return [-y, x]
                }
            }
        }
    }
    return []
}

sumAndProductAnyMessy(sum: 8, product: -20)    // -2, 10
sumAndProductAnyMessy(sum: -6, product: 9)     // -3, -3
sumAndProductAnyMessy(sum: -8, product: -20)   // -10, 2
sumAndProductAnyMessy(sum: 5, product: 0)      // 0, 5
sumAndProductAnyMessy(sum: 2, product: 1)      // 1, 1
sumAndProductAnyMessy(sum: -2, product: 1)     // -1, -1
sumAndProductAnyMessy(sum: 0, product: 25)     // []
sumAndProductAnyMessy(sum: 0, product: -25)    // -5, 5
sumAndProductAnyMessy(sum: 6, product: 9)      // 3, 3
sumAndProductAnyMessy(sum: 21, product: 108)   // 9, 12
sumAndProductAnyMessy(sum: 10, product: 25)    // 5, 5
sumAndProductAnyMessy(sum: 20, product: 100)   // 10, 10
sumAndProductAnyMessy(sum: 101, product: 100)  // 1, 100
sumAndProductAnyMessy(sum: 67, product: 3)     // []
sumAndProductAnyMessy(sum: 1, product: 2)      // []
sumAndProductAnyMessy(sum: -2, product: 20)    // []
sumAndProductAnyMessy(sum: 2, product: -20)    // []
sumAndProductAnyMessy(sum: -32, product: -42)  // []