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3. this are different exercise you must not use while...

# Question: this are different exercise you must not use while...

###### Question details

this are different EXERCISE

* You MUST NOT use while loops or (re)assignment to variables (you can use "val" declarations,
* but not "var" declarations). You must use recursion instead.
*
* You may declare auxiliary functions if you like.
*
* SUBMISSION
*/

object fp1 {

// EXAMPLE: here is the definition of the factorial function.
def fact (n : Int) : Int = {
if (n <= 1)
1
else
n * fact (n - 1)
}

// EXERCISE 8: complete the following definition of the function "max" that finds the maximum
// integer in a list of integers. Note that no value can be returned when the list is empty,
// hence the "NoSuchElementException". Your function MUST be recursive and MUST NOT use a while
// loop. You MUST NOT use the "max" method on lists, but can use the "max" method on integers.
def max (xs : List[Int]) : Int = {
// TODO: Provide definition here.
-1
}

// EXERCISE 9: given the definition of the function "maxTailRecursive" below, complete the
// definition of the function "maxTailRecursiveAux" so that "maxTailRecursive" also finds the
// maximum of a list of integers. You must not alter the definition of "maxTailRecursive". Your
// definition for "maxTailRecursiveAux" must be recursive and not use while loops.
def maxTailRecursiveAux (accumulator : Int, xs : List[Int]) : Int = {
// TODO: Provide definition here.
-1
}

def maxTailRecursive (xs : List[Int]) : Int = {
xs match {
case Nil => throw new RuntimeException ()
case y::ys => maxTailRecursiveAux (y, ys)
}
}

// EXERCISE 10: Write a recursive function "otpu" ("upto" backwards) that takes two Int parameters
// "start" and "end" and produces a "List[Int]" that counts DOWN from "start" to "end" (inclusive
// at both ends) one at a time. If "start < end", the empty list must be returned.
def otpu (start : Int, end : Int) : List[Int] = {
// TODO: Provide definition here.
null
}
}

###### Solution by an expert tutor 