Learn the basics of the Racket lists and various patterns of recursion:
You will again use DrRacket, which you should have downloaded and installed for the previous lab.
For this lab, you will need to implement the following functions recursively in Racket:
You must write all of these functions recursively (though you can use helper functions as needed).
You may not use higher-order functions like
filter, or any of the variants of
fold. You may not use functions that use or return indices, such as
You may not use anything that modifies a value in place such as
set! or list-modification operators.
(define (check-temps1 temps) ...)
temps is a list of numbers representing temperatures and the result is a boolean indicating whether all of the temperatures are with the range 5 to 95 inclusive.
(check-temps1 (list 80 92 56)) returns true, and
(check-temps1 (list 80 99 56)) returns false.
(define (check-temps temps low high) ...)
temps is a list of numbers representing temperatures and the result is a boolean indicating whether all of the temperatures are with the range
(check-temps some-list-of-temps 5 95) should work just like
Suggestion: Yes, you could code
check-temps1 to just call your more general
check-temps. But try to code
check-temps1 first to see the basic pattern, then think about how to generalize it to
(define (convert digits) ...)
digits is a non-empty list of digits (each between 0 and 9) and the result is the integer equivalent of these interpreted as a list of digits of a number in reverse order.
(convert (list 1 2 3)) should return the number 321.
You may not use
string→number or any other string-handling functions for this. Avoid using strings at all.
Hint: Don't try to figure out what position each digit is in as you process the list. (I.e., don't worry about “hundreds place”, “tens place”, etc.). Can you figure out how to write the conversion with a more straightforward recursion? What should recursing on the rest of the list return if the function works correctly? What's the relationship between that and the first thing in the list that will give you the correct result?
(define (duple lst) ...)
lst is a list of any type of values, and the result is a list of two-element lists that has each value duplicated.
(duple (list 1 2 3)) returns the list
( (1 1) (2 2) (3 3) ).
Hint: Be careful when to use
list and when to use
(define (average lst) ...)
lst is a non-empty list of numbers, and the result is the average of these numbers.
(average (list 1 2 3 4)) returns 5/2.
Hint: you are not required to compute the average in a single pass. Can you break it into simpler operations?
(define (convertFC temps) ...)
temps is a list of numbers representing temperatures in Fahrenheit, and the result is a list representing the same values in Celsius.
(convertFC (list 32 50 212)) returns
(0 10 100).
(define (eliminate-larger lst) ...)
lst is a list of numbers, and the result is the same list but with all values larger than any subsequent ones removed.
(eliminate-larger (list 1 2 3 9 4 5)) returns
(1 2 3 4 5).
Hint: try using a helper function.
Hint 2: consider trying to make the decision about whether to drop a particular item from the list after recursively calling eliminate-larger on the rest after that one – it's easier.
(define (get-nth lst n) ...)
lst is a list of arbitrary types and
n is a non-negative number less than the length of the list, and the result is the nth item of the list using zero-based indexing.
(get-nth (list 1 2 3 4) 2) returns the value 3.
Note: You must code this recursively and not use any other built-in Racket functions for such indexing, nor can you simply convert it to a vector and then do random access.
(define (find-item lst target) ...)
lst is a list of numbers and
target is a number, and the result is the position (using zero-based indexing) at which
target first appears in the list, or -1 if it doesn't appear.
(find-item (list 1 2 3 4) 3) returns the value 2, and
(find-item (list 1 2 3 4) 42) returns -1.
Hint: consider using an auxiliary variable.
You again do not need to bulletproof the code to enforce proper inputs. Your code only needs to return correct values given correct inputs. But you should be careful to think about what the correct output should be for the case where the input list is empty.
You may want to again use the Step button to walk through your code and watch the equivalent sequence of substitutions that are performed. This is particularly useful in tracing the recursion and watching what's happening to the parameters.
You may use auxiliary or helper functions as needed. For many of these the simplest solution is to use multiple functions instead of trying to cram it all through one recursive pass through the list. You might also have to recurse through the list multiple times, in which case it's easiest to use separate functions.