Learning Exercises from Scala For The Impatient

Chapter 12: Higher-Order Functions

1. Write a function values(fun: (Int) => Int, low: Int, high: Int) that yields a collection of function inputs and outputs in a given range. For example, values(x => x * x, -5, 5) should produce a collection of pairs (-5, 25), (-4, 16), (-3, 9) ...., (5, 25).

2. How do you get the largest element of an array with reduceLeft?

3. Implement the factorial function using to and reduceLeft, without a loop or recursion.

4. The previous implementation needed a special case when n < 1. Show how you can avoid this using foldLeft.

5. Write a function called largest(fun: (Int) => Int, inputs: Seq[Int]) that yields the largest value of a function within a given sequence of inputs. For example, largest(x => 10 * x - x * 10, 1 to 10) should return 25. Don't use a loop recursion.

6. Modify the previous function to return the input at which the output is largest. For example, largestAt(fun: (Int) => Int, inputs: Seq[Int]) should return 5. Don't use a loop or recursion.

7. It's easy to get a sequence of pairs, for example val pairs = (1 to 10) zip (11 to 20) Now suppose you want to do something with such a sequence - say, add up the values. But you can't do pairs.map(_ + _ ) The function _ + _ takes two Int parameters, not an (Int, Int) pair. Write a function adjustToPair that receives a function of type (Int, Int) => Int, and returns the equivalent function that operates on a pair. For example, adjustToPair(_ * _)((6, 7)) is 42. Then use this function in conjunction with map to compute the sums of the elements in pair.