Summary: In this laboratory, you will explore some basic concepts in recursing over lists.
a. Discuss the self check with your partner.
b. Do the normal lab setup. That is
- Start DrRacket.
- Make sure that the
csc151package is up to date.
(require csc151)to the top of the definitions pane.
c. Add the procedures and associated documentation from the corresponding reading to the definitions pane. Be sure to include a short note as to the source of that code.
d. Create a list named
mixed-values that contains a dozen or so different
kinds of values. You will likely use an instruction like the following.
(define mixed-values (list 1 'two "three" 4.5 6/7 (list) (list 8) 9+10i ...))
Exercise 1: Testing the
a. Read through
sum so that you have a sense of how it accomplishes
b. Verify that
sum produces the same results as in the corresponding reading.
c. What value do you expect
sum to produce for the empty list?
d. Check your answer experimentally.
e. What value do you expect
sum to produce for a singleton list? (A “singleton list” is a list with only one value.)
f. Check your answer experimentally.
sum for a few other lists, too.
h. What do you expect the following to compute?
> (sum 1 2 3)
i. Check your answer experimentally.
Exercise 2: Selecting numbers
a. Reread the definition of
select-numbers to try to understand what it does.
Then copy the code into your definitions pane.
b. Determine which values in
mixed-values are numbers with
(map number? mixed-values).
c. Create a list of numbers with
d. Verify that all the resulting values are numbers, using a technique similar to the one that you used in step b.
Exercise 3: Counting values
length procedure, which computes the length of a list,
were not defined. We could define it by recursing through the list,
counting 1 for each value in the list. In some sense, this is much like
the definition of
sum, except that we use the value 1 rather than the
value of each element.
a. Using this idea, write a recursive procedure,
lst) that finds the length of a list. You may not use
length in defining
b. Check your answer on a few examples: the empty list, the list of values you created, and a few more lists of your choice.
Exercise 4: Product
Write a recursive procedure,
(product nums), that computes
the product of a list of numbers. You should feel free to use
as a template for
product. However, you should think carefully about
the base case.
Exercise 5: Counting special values
length procedure counts the number of values in a list. What if
we don’t want to count every value in a list? For example, suppose we
only want to count the numbers in a mixed list. In this case,
we still recur over the list, but we sometimes count 1 (when the
element is a number) and sometimes count 0 (when it is not).
a. Using this idea, write a procedure,
that, given a list, counts how many are numbers. Note: You should not
your solution. Instead, use the ideas behind some or all of these
functions in crafting your own recursive solution.
b. Check how your procedure functions on a variety of inputs. For example, you might start with the following
> (tally-numbers null) > (tally-numbers (list 1 2 3)) > (tally-numbers (list "a" "b" "c")) > (tally-numbers (list 1 "a" 2 "b" 3 "c")) > (tally-numbers mixed-values)
Exercise 6: The largest element in a list
Using recursion (hence, without
sort or any similar
procedure), write a procedure,
(largest lst), that finds the largest
value in a non-empty list of real numbers. You need not check the
precondition that the list is non-empty nor the precondition that it
contains only reals.
Exercise 7: A safer
largest using the Husk and Kernel strategy introduced in
the reading on preconditions.
For those with extra time
The following exercises will challenge you to extend the problem-solving strategies you’ve learned so far.
Extra 1: Finding skips
(a) Without using
index-of, write a procedure,
lst) that takes a list of symbols as a parameter and returns
the index of the first instance of the symbol
lst, if skip
appears in lst. Your procedure may return an error if the symbol
does not appear in the list.
> (find-first-skip (list 'hop 'skip 'and 'jump)) 1 > (find-first-skip (list 'skip 'hop 'jump 'skip 'and 'skip 'again)) 0 > (find-first-skip (list 'hop 'to 'work 'jump 'to 'school 'but 'never 'skip 'class)) 8
(b) Extend your
find-first-skip procedure so that, when the symbol
skip is not in the list, the procedure produces
#f rather than
> (find-first-skip (list 'hop 'to 'work 'jump 'to 'school 'but 'never 'skip 'class)) 8 > (find-first-skip (list 'hop 'and 'jump)) #f
Extra 2: Finding arbitrary values
Write a procedure,
(my-index-of val lst) that takes a
value and a list of values as its parameters and returns the index of
the first instance of
lst, if the value appears in the
list. If the value does not appear,
index-of should return
> (my-index-of 'skip (list 'hop 'skip 'and 'jump)) 1 > (index-of 5 (list 5 4 3 2 1 2 3 4 5)) 0 > (my-index-of "eraser" (list "pencils" "paper" "index cards" "markers" "ball-point pens")) #f
Extra 3: Riffling lists
Write and document a function
(riffle first second) that produces a new list containing alternating elements from the lists
first ... second. If one list runs out before the other, then the remaining elements should appear at the end of the new list.
> (riffle (list 'a 'b 'c) (list 'x 'y 'z)) (a x b y c z) > (riffle (list 'a 'b 'c) (iota 10)) (a 0 b 1 c 2 3 4 5 6 7 8 9)
Extra 4: Difference
sum procedure adds up all of the elements in a list. Suppose we
want to compute the difference of the values in the list. For example,
given the list
'(a b c d e), we want
a - b - c - d - e.
> (difference (list 5)) 5 > (difference (list 5 2)) 3 > (difference (list 5 2 1)) 2 > (difference (list 5 2 1 7)) -5 > (difference (list 5 2 1 7 8)) -13 > (difference (list 5 2 1 7 8 10)) -23
a. Come up with a strategy for implementing
b. Implement that strategy.