Lab: Processing homogeneous Lists

Held
Monday, 11 February 2019
Writeup due
Wednesday, 13 February 2019
Summary
We further explore Scheme’s list structures. Lists permit us to group data and process those data as a group. We also explore the procedures that we can use with lists, such as map, reduce, and sort.

Useful procedures and notation

Standard list notation

'(val1 val2 ... valn) - a list of n values.

Creating lists

(list exp1 exp2 ... expn) - create a list by evaluating each of the expressions and then joining together their values.

(make-list n val) - make a list of n copies of val.

(range n) - create a list of all the natural numbers strictly less than n (starting with 0).

Manipulating lists

(map fun lst) - apply the function to each element of the list. (map fun (list val1 val2 ... valn)) gives you (list (fun val1) (fun val2) ... (fun valn)).

(reduce fun lst) - reduce the list to a single value by repeatedly replacing each pair of neighboring values with the result of applying fun to that pair of values.

(map fun lst1 lst2) - create a new list by applying the function to corresponding pairs of elements from the two lists. You can also use map with more than two lists.

(tally-value lst val) - determine how many times val appears in lst.

(tally lst pred?) - determine the number of values in lst for which pred? holds.

Sorting

(sort nums <) - reorder the elements in a list of real numbers from smallest to largest.

(sort nums >) - reorder the elements a list of real numbers from largest to smallest.

(sort strings string-ci<?) - reorder the elements in a list of strings from alphabetically first to alphabetically last.

(sort strings string-ci>?) - reorder the elements in a list of strings from alphabetically last to alphabetically first.

Other list operations

(length lst) - Determine how many elements are in a list.

(reverse lst) - Create a new list with the elements in the opposite order.

(append lst1 lst2) - Join two lists together.

(take lst n) - Build a new list consisting of the first n elements of lst.

(drop lst n) - Build a new list consisting of all but the first n elements of lst.

(list-ref lst n) - Extract element n of the list. (Remember that lists start with element 0.)

(index-of val lst) - Determine the position of val in lst. (It turns out the position is how many values need to be dropped from lst to reach val.)

(indexes-of val lst) - Find all the indices of the value in the list.

Creating procedures

(o f g) - Create a new procedure that applies g and then applies f to the result.

(o f g h) - Create a new procedure that applies h, then g to the result of h, then f to the result of g.

(section f <> val) - Create a new procedure that takes one parameter and calls f on that parameter and val.

Preparation

a. Review the list of procedures above.

b. If you have not done so already, you may want to open a separate tab or window in your browser for the reading on list basics and the new reading on processing homogeneous lists.

c. Grab the latest version of the loudhum package by donig one of the following:

i. Open a terminal window and then type the following.

\$ /home/rebelsky/bin/csc151/update


ii. From the File menu in DrRacket, select Install Package and then enter https://github.com/grinnell-cs/loudhum.git.

d. In your definitions window, require the loudhum library.

(require loudhum)


; A list of movie ratings for The Large Illness
(define large-illness-ratings
(list 7 4 0.2 -3 6 5.5 5 6 -1.5 54/7 0))

; Some words, as strings
(define story-beginning
(list "Once" "upon" "a" "time" "in" "a" "land" "not" "so" "far" "away"))

; Some names, as symbols
(define names
(list 'millicent 'octavius))

; A few letters, as strings
(define letters
(list "a" "b" "c" "d" "e"))

; The words in Jane Eyre (plus whatever Project Gutenberg adds)
(define eyre-words (file->words "/home/rebelsky/Desktop/pg1260.txt"))


f. Add the names of about six other people (e.g., your group and the two groups nearest you) to the list of names.

Exercises

Exercise 1: Reviewing the self-check

a. Predict the results of evaluating each of the following expressions.

(list 2 1)
(make-list 1 2)
(make-list -1 2)
(map - (range 2))
(map - (range 2) (list 2 1))
(map range (list 2 1))


b. Check your predictions with DrRacket.

Exercise 2: Averaging ratings

Write a set of instructions that allow you to compute the average rating given The Large Illness.

Exercise 3: Rounding ratings

The ratings associated with The Large Illness include both whole numbers and fractional numbers. Suppose that “those on high” decide that only whole-number ratings are permitted.

a. Write an instruction that rounds each rating to the nearest integer. (Hint: You’ll want to use map and round.)

b. Write an instruction that rounds each rating down.

c. Write an instruction that rounds each rating up.

d. Determine the effects of each strategy on the average rating.

Exercise 4: Exploring word lengths

As you may recall from the preparation, story-beginning contains a short list of strings and eyre-words contains a much longer list of strings.

a. Write expressions that determine how many words are in each list.

b. Write an expression that determines the length of each word in story-beginning.

c. Write an expression that determines the average word length in story-beginning.

d. Write an expression that determines the average word length in eyre-words.

e. Write an expression that determines the longest word length in eyre-words.

Exercise 5: Tallying values

a. Write an expression that determines how many times the word “a” appears in story-beginning.

b. Write an expression that determines how many times the word “a” appears in eyre-words.

c. Write an exprssion that determines how many times the word “Eyre” appears in eyre-words.

d. Write an exprssion that determines how many times the word “Reed” appears in eyre-words.

e. Write expressions that determine how many times 4-letter, 5-letter, and 10-letter words appear in eyre-words.

Exercise 6: Experiments in reduction

a. Determine and then explain what the following procedure does.

(define combine
(lambda (s1 s2)
(string-append s1 " and " s2 " and " s1)))


b. What do you expect for the following?

> (reduce combine letters)


e. What do you expect if you type the same expression again?

g. What do you expect for the following?

> (reduce-left combine letters)
?
> (reduce-right combine letters)
?


Exercise 7: Sorting out sorting

a. Write an expression to sort the ratings from lowest to highest.

b. Write an expression to sort the ratings from highest to lowest.

c. Write an expression to alphabetically sort the words in story-beginning.

d. Write an expression to alphabetically sort the names. Note that the names are symbols, so you will need to do some conversion.

Exercise 8: Word choice

a. Write an expression to find the three alphabetically last words in story-beginning.

b. Write an expression to find the ten alphabetically last words in eyre-words.

Exercise 9: Finding words

a. In looking at the alphabetically last words in eyre-words, we discovered that zenith appears exactly once in Jane Eyre. Using index-of, determine which word it is. (That is, what word number.)

b. Using list-ref, determine what words come immediately before and after zenith.

c. In an earlier exercise, we noted that the word “Eyre” appears about 100 times in Jane Eyre. Using indexes-of, determine where those 100 appearances are.

d. What does the following expression do? (Conceptually.)

> (map (o (section list-ref eyre-words <>) add1) (list 100 200 300 400))


e. Using a similar expression, determine the words that immediately follow “Eyre”.

f. Using a similar expression, determine the words that immediately precede “Eyre”.

For those with extra time

If you find that you have extra time, you might consider any of the following problems.

Extra 1: Multiple tallies

In an exercise, you determined the number of 4, 5, and 10-character words that appear in Jane Eyre. Using map, tally-val, and range, write a single expression that determines how many 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12-letter words there are in Jane Eyre.

Extra 2: Inconsistent subtraction, revisited

Consider the following list.

(define ones (make-list 10 1))


a. How many different values do you think you can get from (reduce - ones)?