Description
CS-4337 – Organization of Programming Languages
De4ine and test the functions described below. In doing the assignment, you may assume
that the inputs to your functions have the correct data type. This means that you need not
check the inputs for validity (i.e. type checking). However, your function must behave
properly on all instances of valid input data types. You may de4ine auxiliary functions that
are called by your primary function. In some cases below you may be restricted to which
auxiliary functions you may use from the Racket standard library.
Your implementation of each function must have its function name spelled exactly as
it is in the description.
Your submission should consist of a Racket source code 4ile that is archived using a zip
utility. This may be accomplished by de4ining your functions in the top pane of the Dr.
Racket IDE and then using “Save De4initions”. Both your Racket source 4ile and zip 4ile
should be named using your NetID. Example: cid021000.rkt and cid021000.zip.
Upload this 4ile to eLearning.
You may 4ind Racket language help here:
• https://docs.racket-lang.org/reference/
• https://docs.racket-lang.org/guide/
1. my-reverse
De4ine your own Racket function that duplicates the functionality of reverse from the standard
library. You may not use either reverse or append as auxiliary functions. Your implementation
must be recursive.
Input: A list of elements of any data type, potentially heterogenous.
Output: A new list of the original elements in reverse order.
Example:
(my-reverse ‘(2 6 3 7))
‘(7 3 6 3)
(my-reverse ‘(3 2.71 “foo” 5))
‘(5 “foo” 2.71 3)
(my-reverse ‘(7))
‘(7)
(my-reverse ‘((1 2) 3 (4 5))
‘((4 5) 3 (1 2))
2. my-map
De4ine your own Racket function that duplicates the the functionality of map from the standard
library. You may not use the built-in map function as an auxiliary function. Your implementation
must be recursive.
Input: A function name (of a function that takes a single argument) and a list of elements of the
same data type compatible with the function.
Output: A new list of the original elements with the same function applied to each.
Example:
(my-map sqrt ‘(9 25 81 49))
‘(3 5 9 7)
(my-map double ‘(6 4 8 3))
‘(12 8 16 6)
(my-map sqr ‘(5 7))
‘(25 49)
3. function-3
De4ine a function that takes a named function as an argument and passes the number 3 to that
function. Your implementation must be recursive.
Input: A named function which takes a single number as an argument.
Output: The value returned by applying the named function to the number 3.
Example:
(function-3 sqrt)
1.7320508075688772
(function-3 sqr)
9
(function-3 add-one)
4
4. zipper
De4ine a function takes two lists as arguments and returns a single list of pairs (i.e. two-items lists.
The the 4irst pair should be the both 4irst items from the respective lists. The second pairs should be
the second items from the respective lists, and so on. If one list is longer than the other, extra
elements of the longer list are ignored. Your implementation must be recursive.
Input: Two lists of elements of any type, potentially heterogenous. The two lists do not have to
be the same length.
Output: A new list whose elements are each two-element sublists. The 4irst sublist is composed
of the 4irst elements from two input lists respectively, the second sublist is composed of the
second elements form the two input lists respectively, etc. If one list is longer than the other,
extra elements of the longer list are ignored.
Example:
(zipper ‘(1 2 3 4) ‘(a b c d))
‘((1 a) (2 b) (3 c) (4 d))
(zipper ‘(1 2 3) ‘(4 9 5 7))
‘((1 4) (2 9) (3 5))
(zipper ‘(3 5 6) ‘(“one” 6.18 #t “two”))
‘((3 “one”)(5 6.18)(6 #t))
(zipper ‘(5) ‘())
‘()
5. segregate
De4ine a function that takes a list of integers as an argument and returns a list containing two
sublists, the 4irst sublist containing the even numbers from the original list and the second sublist
containing the odd numbers from the original lists. You may not use the built-in filter , even?,
or odd? functions as auxiliary functions. You may de4ine your own auxiliary functions. Your
implementation must be recursive.
Input: A lists of integers.
Output: A new list with two sublists. The 4irst sublist contains the even numbers from the
original list and the second sublist contains the odd numbers.
Example:
(segregate ‘(7 2 3 5 8)
‘((2 8) (7 3 5))
(segregate ‘(3 -5 8 16 99))
‘((8 16) (3 -5 99))
(segregate ‘())
‘(() ())
6. is-member?
De4ine a function that takes two arguments, a list and a single value. Your function should return
true (#t) if the value is a member of the list and false (#f) if it does not. You may not use the builtin
member or element functions as auxiliary functions. Your implementation must be recursive.
Input: A list of elements of any data type, potentially heterogenous and a single atom of any
data type.
Output: A boolean value that indicates whether the input atom is a member of the input list.
Example:
(is-member? 6 ‘(4 8 6 2 1))
#t
(is-member? 7 ‘(4 8 6 2 1))
#f
(is-member? “foo” ‘(4 5 #f “foo” a))
#t
7. my-sorted?
De4ine a function that takes a list as an argument. It should return a boolean (i.e. #t or #f) indicating
whether the list is sorted in ascending order. You may not use the built-in sorted? function. Your
implementation must be recursive.
Input: A list of elements of homogenous data type, either numbers or strings.
Output: A boolean value that indicates whether the elements of the list are sorted in strictly
increasing order.
Example:
(my-sorted? ‘(2 5 6 9 11 34))
#t
(my-sorted? ‘(7 25 4 15 11 34))
#f
(my-sorted? ‘(“alpha” “beta” “gamma”))
#t
(my-sorted? ‘(“john” “zack” “bob”))
#f
8. my-flatten
De4ine your own Racket function that duplicates the the functionality of flatten from the
standard library. You may not use the built-in flatten function as an auxiliary function. It should
take a list containing zero or more sublists as an argument. Each sublist may contain an arbitrary
level of nesting. It should return a single list containing all of the items from all nested levels with no
sublists. You may not use the built-in flatten function as an auxiliary function. Your
implementation must be recursive.
Input: A single list which may contain an arbitrary number of elements and sublists, each
sublists may also contain an arbitrary number of elements and sublists, nested to an any depth.
Output: A new single-level list which contains all of the atomic elements from the input list.
Example:
(my-flatten ‘(1))
‘(1)
(my-flatten ‘((1 2) 3))
‘(1 2 3)
(my-flatten ‘(((4 3) 6)((7 2 9)(5 1))))
‘(4 3 6 7 2 9 5 1)
9. threshold
De4ine a function that takes a list of numbers and a number (the threshold). It should return a new
list that has the same numbers as the input list, but with all elements strictly greater than the
threshold number removed. You may not use the built-in filter function as an auxiliary function.
Your implementation must be recursive.
Input: A list of numbers and a single atomic number.
Output: A new list of numbers that contains only the numbers from the original list that are
strictly “less than” (<) the threshold number.
Example:
(threshold '(3 6.2 7 2 9 5.3 1) 6)
'(3 2 5.3 1)
(threshold '(1 2 3 4 5) 4)
'(1 2 3)
(threshold '(4 8 5 6 7) 6.1)
'(4 5 6)
(threshold '(8 3 5 7) 2)
'()
10. my-list-ref
De4ine your own Racket function that duplicates the the functionality of list-ref from the
standard library. You may not use the built-in list-ref function as an auxiliary function.
De4ine a function that takes a list and an integer. The function should return the list element at the
integer number (4irst list position is index “0”). If the integer is larger than the index of the last list
member, it should display an “index out of bounds” message. Your implementation must be
recursive.
Input: A list of elements of any data type, potentially heterogenous, and a single integer.
Output: A single element from the original list that is at the “index” indicated by the integer. The
4irst list position is position “0”, the second list position is “1”, etc. If the integer is greater than
the number of list elements, the function should return the string “index out of bounds”.
Example:
(my-list-ref '(4 7 9) 0)
4
(my-list-ref '(4 7 9) 1)
7
(my-list-ref '(4 7 9) 2)
9
(my-list-ref '(4 7 9) 3)
index out of bounds
OPTIONAL BONUS. deep-reverse
De4ine a function similar to the built-in reverse function, except that it acts recursively, reversing
the order the members of any nested sublists. You may not use the built-in reverse function as an
auxiliary function. However, you may use your own my-reverse function as an auxiliary function.
Input: A single list which may contain an arbitrary number of elements and sublists, each
sublists may also contain an arbitrary number of elements and sublists, nested to an any depth.
Output: A new list which contains all elements in reverse order, as well as recursively reverse
order all members of sublists.
Example:
(deep-reverse '(((4 3) 6)((7 2 9)(5 1))))
'(((1 5) (9 2 7)) (6 (3 4)))
(deep-reverse '((1 2) 3))
'(3 (2 1))
(deep-reverse '((4 5)))
'((5 4))
(deep-reverse '(3 6 9 12))
'(12 9 6 3)