CSE 216 Homework I

OCaml | homework | Data structure | assignment作业 – 这是利用OCaml 进行训练的代写, 对OCaml 的编程流程进行训练解析, 是比较典型的OCaml 等代写方向, 这个项目是assignment代写的代写题目，OCaml 是非常小众的语言

This homework document consists of 3 pages. Carefully read the entire document before you start coding. Note: All functions, unless otherwise specified, should be polymorphic (i.e., they should work with any data type). For example, if you are writing a method that should work for lists, the type must be’a list, and notint list.

1 Recursion and Higher-order Functions (60 points)

In this section, you may not use any functions available in the OCaml library that already solves all or most of the question. For example, OCaml provides aList.revfunction, but you may not use that in this section.

1.Write a recursive functionpow, which takes two integer parametersxandn, and returnsxn. Also write (6)
a functionfloatpow, which does the same thing, but forxbeing a float (nis still an integer). You may
assume thatnwill always be non-negative.

2.Write a functioncompressto remove consecutive duplicates from a list. (6)
# compress ["a";"a";"b";"c";"c";"a";"a";"d";"e";"e";"e"];;

: string list = [“a”; “b”; “c”; “a”; “d”; “e”]

3.Write a functionremoveifof the type'a list -> ('a -> bool) -> 'a list, which takes a list and (6)
a predicate, and removes all the elements that satisfy the condition expressed in the predicate.
# remove_if [1;2;3;4;5] (fun x -> x mod 2 = 1);;

: int list = [2; 4]

4.Write a functionequivsof the type('a ->'a -> bool) ->'a list ->'a list list, which par- (6)
titions a list into equivalence classes according to the equivalence function.
# equivs (=) [1;2;3;4];;

: int list list = [[1];[2];[3];[4]]

equivs (fun x y -> (=) (x mod 2) (y mod 2)) [1; 2; 3; 4; 5; 6; 7; 8];;

: int list list = [[1; 3; 5; 7]; [2; 4; 6; 8]]

5.Some programming languages (like Python) allow us to quicklyslicea list based on two integersiand (6)
j, to return the sublist from indexi(inclusive) andj(not inclusive). We want such a slicing function
in OCaml as well.
Write a functionsliceas follows: given a list and two indices,iandj, extract the slice of the list
containing the elements from theith(inclusive) to thejth(not inclusive) positions in the original list.
# slice ["a";"b";"c";"d";"e";"f";"g";"h"] 2 6;;

: string list = [“c”; “d”; “e”; “f”]

Invalid index arguments should be handledgracefully. For example,
# slice ["a";"b";"c";"d";"e";"f";"g";"h"] 3 2;;

: string list = []

slice [“a”;”b”;”c”;”d”;”e”;”f”;”g”;”h”] 3 20;

: string list = [“d”;”e”;”f”;”g”;”h”];

6.Write a function calledcomposition, which takes two functions as its input, and returns their compo- (6)
sition as the output.

# let square_of_increment = composition square increment;;
val square_of_increment : int -> int = <fun>
# square_of_increment 4;; (* increments 4 to 5, and THEN computes square *)

: int = 25 7.Write a function calledequivon, which takes three inputs: two functionsfandg, and a listlst. It (6) returnstrueif and only if the functionsfandghave identical behavior on every element oflst.

let f i = i * i;;

val f : int -> int =

let g i = 3 * i;;

val g : int -> int =

equiv_on f g [3];;

: bool = true

equiv_on f g [1;2;3];;

: bool = false 8.Write a functions calledpairwisefilterwith two parameters: (i) a functioncmpthat compares two (6) elements of a specificTand returns one of them, and (ii) a listlstof elements of that same typeT. It returns a list that appliescmpwhile taking two items at a time fromlst. Iflsthas odd size, the last element is returned as is.

pairwisefilter min [14; 11; 20; 25; 10; 11];;

: int list = [11; 20; 10]

(* assuming that shorter : string * string -> string = already exists *)

pairwisefilter shorter [“and”; “this”; “makes”; “shorter”; “strings”; “always”; “win”];;

: string list = [“and”; “makes”; “always”; “win”] 9.Write thepolynomialfunction, which takes a list of tuples and returns the polynomial function corre- (6) sponding to that list. Each tuple in the input list consists of (i) the coefficient, and (ii) the exponent.

(* below is the polynomial function f(x) = 3x^3 – 2x + 5 *)

let f = polynomial [3, 3;; -2, 1; 5, 0];;