====Objective:====
Learn the basics of the Racket lists and various patterns of recursion:
* List operators
* Natural recursion
* Common patterns for recursive list-processing operations
* Using auxiliary parameters
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====Preparation:====
You will again use DrRacket, which you should have downloaded and installed for the previous lab.
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====Deliverables:====
For this lab, you will need to implement the following functions recursively in Racket:
* ''check-temps1''
* ''check-temps''
* ''convert''
* ''duple''
* ''average''
* ''convertFC''
* ''eliminate-larger''
* ''get-nth''
* ''find-item''
**
You must write all of these functions recursively (though you can use helper functions as needed).
You may not use higher-order functions like ''map'', ''filter'', or any of the variants of ''fold''. You may not use functions that use or return indices, such as ''index-of'' or ''list-ref''.
You may not use anything that modifies a value in place such as ''set!'' or list-modification operators.
**
=== check-temps1 ===
(define (check-temps1 temps) ...)
where ''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.
For example, ''(check-temps1 (list 80 92 56))'' returns true, and ''(check-temps1 (list 80 99 56))'' returns false.
=== check-temps ===
(define (check-temps temps low high) ...)
where ''temps'' is a list of numbers representing temperatures and the result is a boolean indicating whether all of the temperatures are with the range ''low'' to ''high'' inclusive.
For example, ''(check-temps some-list-of-temps 5 95)'' should work just like ''(check-temps1 some-list-of-temps)''.
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 ''check-temps''.
=== convert ===
(define (convert digits) ...)
where ''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.
For example, ''(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?
=== duple ===
(define (duple lst) ...)
where ''lst'' is a list of any type of values, and the result is a list of two-element lists that has each value duplicated.
For example, ''(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 ''cons''.
=== average ===
(define (average lst) ...)
where ''lst'' is a non-empty list of numbers, and the result is the average of these numbers.
For example, ''(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?
=== convertFC ===
(define (convertFC temps) ...)
where ''temps'' is a list of numbers representing temperatures in Fahrenheit, and the result is a list representing the same values in Celsius.
For example, ''(convertFC (list 32 50 212))'' returns ''(0 10 100)''.
=== eliminate-larger ===
(define (eliminate-larger lst) ...)
where ''lst'' is a list of numbers, and the result is the same list but with **all** values larger than **any** subsequent ones removed.
For example, ''(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.
=== get-nth ===
(define (get-nth lst n) ...)
where ''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.
For example ''(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.
=== find-item ===
(define (find-item lst target) ...)
where ''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.
For example, ''(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.
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====Notes:====
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.
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====Hints:====
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.