Question

Please answer this and leave copyable code and output for this question along with the question it is asking, thank you

(30 points) Here is an SML mergesort program: fun merge ([], ys) -ys I merge (xs, [)xs merge (x: xs, y: ys) if x< y then x: :merge (xs, y::ys) else y: :merge (x: :xs, ys) fun split [] I split [a] I split (a::b::cs) let val (M, N)split cs in end fun mergesort [[ merge sort [a] [a] I mergesort [a,bif a <b then [a,b] else [b, a] I mergesort L - let val (M, N) = split L ln merge (mergesort M, mergesort N) end

Answer 1

According to me, if we delete both third and second line, then the function goes in an infinite loop for every input except for an empty array input.

Execution is shown below:
- use "ms.sml";
[opening ms.sml]
val merge = fn : int list * int list -> int list
val split = fn : 'a list -> 'a list * 'a list
val mergesort = fn : 'a list -> int list
val it = () : unit
- mergesort([]);
val it = [] : int list
- mergesort([1]);

(* infinite loop *)

This is due to fact - everytime when mergesort reaches at single element level i.e., [a], it calls split function which splits it into [a] and []. [] is handled correctly by mergesort() but the same thing written above happens for [a] i.e., single element level. Hence repititive calls of mergesort() and split() lead to infinite loop.

Another observation, if we just remove the second line (case [a]) but keep the third line (case [a,b]) intact, then the inifinite loop thing doesnt occur and gives correct output for power of 2-sized arrays except 1 (size = 2,4,8,..) . Since [a,b] is handled correctly by third line.

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Thanks.