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The main purpose is to practice elementary recursive manipulation with lists. Lists can be decomposed by functions `car`

and `cdr`

. On the other hand, lists can be built by functions `cons`

, `list`

or `append`

. Also higher-order functions `filter`

and `map`

can be used as they were introduced in the second lecture (`map`

only applied to a single list).

**Exercise 1:** Write the function `(my-reverse lst)`

taking a list `lst`

and returning a list consisting of elements from `lst`

in the reverse order. E.g. `(my-reverse '(a b c)) ⇒ (c b a)`

. The function should use the tail recursion.

*Hint:* The idea is to use an accumulator `acc`

storing the intermediate result. We start with an empty accumulator and recursively deconstruct the list `lst`

element by element by means of `car,cdr`

and join them to the accumulator by `cons`

. The computation for `lst = '(a b c)`

and `acc = '()`

go as follows:

`(cdr lst)` | `(cons (car lst) acc)` |
---|---|

'(b c) | '(a) |

'(c) | '(b a) |

'() | '(c b a) |

(define (my-reverse lst [acc '()]) (if (null? lst) acc (my-reverse (cdr lst) (cons (car lst) acc))))Note that using the accumulator is a general concept.

**Exercise 2:** Write a function `(letter-frequencies str)`

which takes a string `str`

and returns a histogram of letters occurring in `str`

so that the most frequent characters come first. The histogram is just a list of pairs `(char . num)`

where `char`

is a character and `num`

is the number of its occurrences in `str`

. E.g. `(letter-frequencies “good”) ⇒ ((#\o . 2) (#\d . 1) (#\g . 1))`

. The string `str`

should be first converted into lowercase characters so that `#\A`

and `#\a`

represent the same character. Non-alphabetic characters should be removed.

*Idea:* The function `letter-frequencies`

is just a composition of several functions.

string-downcase -> string->list -> filter-alphabetic -> sort -> group-same -> join-lengths -> sort

- The function
`string-downcase`

translates all characters into lowercase letters and it is implemented in racket. - The function
`string->list`

is implemented as well and it decomposes a given string into a list of its characters. - Then non-alphabetic characters can be filter out by
`filter`

function using the predicate`char-alphabetic?`

. - To compute the number of occurrences of characters, we apply
`sort`

function which groups together the same characters, e.g.`(sort '(#\c #\z #\c) char<?) ⇒ (#\c #\c #\z)`

. The function`sort`

takes as its second argument a boolean function taking two arguments and comparing them. - The function
`group-same`

scans the input list and returns a list consisting of lists of the same consecutive characters, e.g.`(group-same '(#\c #\c #\z)) ⇒ ((#\c #\c) (#\z))`

. - The function
`join-lengths`

creates for each group of the same character a pair of the for (char . num) where the number of occurrences num is computed by function`length`

. - Finally, the output is sorted by numbers of occurrences.

The function `group-same`

is the only recursive function in our program. It has to keep as an intermediate result a partially built group of the same character. If the new character `(car l)`

coming from the list is the same as the current character in the group, the partial group is extended by this character. Once the new character `(car l)`

differs from the current character in the group, the partial group is closed, joined to the output and a new group is created.

(define (group-same lst) (define (iter l gr) (cond ([null? l] (list gr)) ([eqv? (car gr) (car l)] (iter (cdr l) (cons (car gr) gr))) (else (cons gr (iter (cdr l) (list (car l))))))) (if (null? lst) '() (iter (cdr lst) (list (car lst))))) (define (join-lengths grs) (map (lambda (g) (cons (car g) (length g))) grs)) (define (letter-frequencies str) (sort (join-lengths (group-same (sort (filter char-alphabetic? (string->list (string-downcase str))) char<?))) > #:key cdr)) ; Might be more readable: #| (define (letter-frequencies-2 str) (let* [(lowercase (string-downcase str)) (listified (string->list lowercase)) (alphabetic (filter char-alphabetic? listified)) (sorted-chars (sort alphabetic char<?)) (grouped (group-same sorted-chars)) (joined (join-lengths grouped)) (sorted-occurs (sort joined > #:key cdr))] sorted-occurs)) |#

If you wish, you can use function `file->string`

to check letter frequencies in any file, for instance in Shakespeare's Sonnets by calling `(letter-frequencies (file->string "sonnets.txt"))`

and comparing the result with the letter frequencies in English alphabet Wikipedia.

**Task 1:** Write a function `(average-list lst)`

taking a list of numbers `lst`

and returning their arithmetical average. E.g. `(average-lst '(1 2 3)) ⇒ 2`

. The function should be tail-recursive.

*Hint:* As the function should be tail-recursive, it has to use an accumulator storing a partial sum of elements from the list. Finally, the resulting sum is divided by the number of all elements in the list. For the number of elements in `lst`

, you can use the function `length`

.
Depending on your implementation function can return precise rational numbers like `(average-list '(0 1)) ⇒ 1/2`

. If you want to have the usual floating-point representation, use the function `exact->inexact`

transforming the result into imprecise floting-point representation.

(define (average-list lst) (define (iter l acc) (if (null? l) acc (iter (cdr l) (+ acc (car l))))) (exact->inexact (/ (iter lst 0) (length lst))))

**Task 2:** Taking an inspiration from the `group-same`

function, write a function `(split-list n lst)`

which takes a natural number `n`

and a list `lst`

and returns a list of lists consisting of `n`

-tuples of consecutive elements from `lst`

. E.g. `(split-list 2 '(a b 1 2 3 4)) => ((a b) (1 2) (3 4))`

. In case the number of elements is not divisible by `n`

, make the last list in the output shorter. E.g. `(split-list 3 '(a b 1 2)) => ((a b 1) (2))`

.

Using functions `split-list`

and `average-list`

from the previous task, write a function `(n-block-average n lst)`

which splits a given list of numbers `lst`

into `n`

-tuples of consecutive numbers and returns a list of averages of these `n`

-tuples. E.g. `(n-block-average 2 '(1 3 1 5)) ⇒ (2 3)`

.

*Hint:* The function `split-list`

needs two accumulators. The first accumulator keeps a partially built segment of consecutive elements and the second tracks how many elements we have to read from the list to complete the `n`

-tuple of consecutive elements.

(define (split-list n lst) (define (iter l k segment) (cond ([null? l] (list segment)) ([zero? k] (cons segment (iter l n '()))) (else (iter (cdr l) (- k 1) (append segment (list (car l))))))) (iter lst n '())) (define (n-block-average n lst) (map average-list (split-list n lst)))

courses/fup/tutorials/lab_2_-_lists.txt · Last modified: 2022/02/27 14:45 by xhorcik