How do I find largest number in List in SML

Question

We want to find the largest value in a given nonempty list of integers. Then we have to compare elements in the list. Since data values are given as a sequence, we can do comparisons from the beginning or from the end of the list. Define in both ways. a) comparison from the beginning b) comparison from the end (How can we do this when data values are in a list?)

What I have done is find the largest number by comparison from the beginning.

How can I do it from the end? What logic should I apply?

Here is my code for comparing from the beginning.

- fun largest[x] = x
= | largest(x::y::xs) =
= if x>y then largest(x::xs) else largest(y::xs)
= | largest[] = 0;
val largest = fn : int list -> int


output

- largest [1,4,2,3,6,5,4,6,7];
val it = 7 : int

Answer 1

In your function, first two elements of the list are compared and the bigger value is compared to the remaining elements. I think comparison from the end means that you try to find the largest number of the tail of the list first and compare it with the head element later.

fun largest [] = raise Empty 
 | largest [x] = x
 | largest (x::xs) =
      let 
        val y = largest xs
      in
        if x > y then x else y
      end

Although it is not required, you should handle the case of empty list for completeness. And you can shorten the function if using max function.

fun largest [] = raise Empty 
 | largest [x] = x
 | largest (x::xs) = max(x, largest xs)

To be honest, I would prefer your version which is tail-recursive (it doesn't blow the stack on big lists). My function could be rewritten to be tail-recursive as other answers demonstrated, but certainly it is more sophisticated than your function.