Problems Solve each of the following problems using only the features of F# that

Question

Problems

Solve each of the following problems using only the features of F# that we have discussed in class. In particular, you will not receive credit for solutions that use imperative programming constructs, or predefined (built-in) functions that make the solutions completely trivial. If you have doubts about what is allowed, check with me.

For each problem, write a single function definition without any nested functions. Your solutions do not need to be tail recursive.

Define a function called max that takes a list and returns the largest value in the list. You may assume that the list is not empty. Do not use the built-in List.max function.

Define a function called nth that takes an integer, n, and a list as arguments. The nth element of the list, indexed from 0, should be returned. You may assume that the list has at least one element.

Define a function called zip that takes a pair (tuple) of equal length lists as a single parameter and returns a list of pairs. The first pair should contain the first element of each list, the second pair contains the second element of each list, and so on.

Define a function called search that takes a boolean function, f, and a list as arguments and returns the zero-based index of the first element of the list, e, such that (f e) is true. If no such element exists, search should return -1.

Explanation / Answer

1) Max function to get max element of the list

let maxElement = 0
let elementList= [|1; 2; 3; 4; 11; 12; 13; 14|]

for j in 0 .. elementList.Length - 1 do

if maxElement < (elementList.[i]) then

       maxElement <- elementList.[i]
     
       printfn "%j" maxElement
     
2) Return nth element of the list

let rec nthElement list i =

    match list with
  
    | hd::x1 ->
  
        if i = 0 then hd
      
        else nthElement xl (i - 1)
      
    | [] -> failWith "Index not found"

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