How to reverse a list such that every sublist is also reversed? This is what I have so far:
(defun REV (L)
(cond
((null L) nil)
((listp L)
(append
(REV (cdr L))
(list (car L))))
(t
(append
(REV (cdr L))
(list (car L))))))
You are on the right track, but your last two conditions have the same action, which should give an indication that one of them is not doing what it should. Indeed, the second condition, the listp case, is not right, because when it's a list, you need to append the reverse of that list instead of the unmodified list. A possible solution:
(defun my-reverse (l)
(cond ((null l) nil)
((listp (car l)) (append (my-reverse (cdr l))
(list (my-reverse (car l)))))
(t
(append (my-reverse (cdr l))
(list (car l))))))
> (my-reverse '((1 2 3) (4 5 6)))
((6 5 4) (3 2 1))
As you can see, the only difference is that you test if the first element is a list, and if it is, you reverse the first element before appending it.
I'd write it this way:
(defun reverse-all (list)
(loop
with result = nil
for element in list
if (listp element)
do (push (reverse-all element) result)
else do (push element result)
finally (return result)))
Sounds like a homework problem :)
Looks like you started by writing the regular reverse code. I'll give you a hint: The second condition (listp L) isn't quite right (it'll always be true). You want to be checking if something else is a list.
dmitry_vk's answer (which probably is faster in most lisps than using append in the previous examples) in a more lispish way:
(defun reverse-all (list)
(let ((result nil))
(dolist (element list result)
(if (listp element)
(push (reverse-all element) result)
(push element result)))))
Or even:
(defun reverse-all (list)
(let ((result nil))
(dolist (element list result)
(push
(if (listp element) (reverse-all element) element)
result))))
Related
Essentially I am trying to remove the first and last element in a list. I have currently been able to determine how to remove the last element in the list but i'm struggling how to remove the first element in the list with the last element in the list.
Here is the code I have so far. Is there a way I can modify my code so I am able to include removing the first element in the list.
(define (rid L)
(cond
[(empty? L) '()]
[(empty? (rest L)) '()]
[(cons (first L) (rid (rest L)))]))
Here is the results I am expecting with my code
(check-expect (rid (list 1 2 3 4 5)) (list 2 3 4))
(check-expect (rid (list "cat" "dog" "giraffe")) (list "dog"))
Just for fun - In Racket you can solve this problem without using explicit recursion. Always try to use existing procedures to solve your problems:
(define (rid L)
(rest (drop-right L 1)))
(rid '(1 2 3 4 5 6))
=> '(2 3 4 5)
With many recursive algorithms, it is not uncommon to actually implement them with two procedures: one to set up the initial conditions and a second one to do the actual recursion, like so:
(define (rid-inner li)
(cond
[(empty? li) '()]
[(empty? (rest li)) '()]
[(cons (first li) (rid-inner (rest li)))]))
(define (rid1 L)
(define r (if (empty? L) '() (rest L)))
(rid-inner r))
With (define r (if (empty? L) '() (rest L))) we strip off the first element of the list; no recursion is actually necessary for this step. Then we define the same procedure you had before with a different name and call it with our new list that already has the first element stripped off. If you want the first element stripped off, just strip off the first element; don't overthink it :) .
In a language like Racket that allows closures and nested procedures, you don't actually even need to define both procedures at the top "global" module scope; just define your recursive procedure inside your initial procedure and call it from there. Example:
(define (rid2 L)
(define r (if (empty? L) '() (rest L)))
(define (rid-inner li)
(cond
[(empty? li) '()]
[(empty? (rest li)) '()]
[(cons (first li) (rid-inner (rest li)))]))
(rid-inner r))
Another, somewhat cleaner, way to do the above is to use a named let, which allows us to simultaneously set up our initial conditions, create a named procedure, and then call that procedure immediately from within itself. We do that like so:
(define (rid3 L)
(let rid-inner ([li (if (empty? L) '() (rest L))])
(cond
[(empty? li) '()]
[(empty? (rest li)) '()]
[(cons (first li) (rid-inner (rest li)))])))
To those unfamiliar with Racket, Scheme, or a related Lisp, the named let in rid3 may be more cryptic at first since it is really doing two or three things at once. You can find the docs for it here. Don't be fooled though, it works exactly the same as rid2. Named let exists precisely because this pattern is so common.
(define (rid L)
(if (< (length L) 3)
'()
(reverse (rest (reverse (rest L))))))
;;; recursion inside and more general
;;; you can setting which position 0~n-1 you want to remove
(define (rid-v2 L)
(local ((define remove-index-list (list 0 (- (length L) 1)))
(define (auxf L k)
(cond
[(empty? L) '()]
[(memq k remove-index-list) (auxf (rest L) (+ k 1))]
[else (cons (first L)
(auxf (rest L) (+ k 1)))])))
(auxf L 0)))
tail call recursive version
(define (rid lst (acc '()))
(cond ((empty? lst) acc)
((empty? (cdr lst)) (cdr (reverse acc)))
(else (rid (cdr lst) (cons (car lst) acc)))))
with elementar lisp (not the most efficient)
(define (rid1 lst)
(cdr (reverse (cdr (reverse lst))))
My program works with all lists except the improper lists (which have an atom in the cdr field of the last cons cell). Please help upgrade this program to work with the improper lists:
(define (ndelete lst)
(let recur ((i 1) (rest lst))
(cond ((null? rest) '())
((= i 2) (recur 1 (cdr rest)))
(else (cons (car rest) (recur (+ i 1) (cdr rest)))))))
You just need to fix your base condition, (null? rest). If you want to support improper lists, you should check for (not (pair? rest)) instead.
Of course, this has an annoying side-effect of making your function handle any object - not just lists. For any non-list object, it just returns nil. If that's a problem for you, you'll need to encapsulate your recursive function and make sure lst is in fact a list. Like so:
(define (ndelete lst)
(letrec ((recur (lambda (i rest)
(cond ((not (pair? rest)) '())
((= i 2) (recur 1 (cdr rest)))
(else (cons (car rest) (recur (+ i 1) (cdr rest))))))))
(if (pair? lst)
(recur 1 lst)
(raise (condition (make-error)
(make-message-condition `(,lst is not a pair)))))))
I want to write a recursive function that checks the list and either returns true if the list is in ascending order or NIL otherwise. If the list is empty it is still true. I am completely new to Lisp, so its still very confusing.
(defun sorted (x)
(if (null x)
T
(if (<= car x (car (cdr x)))
(sorted (cdr x))
nil)))
The recursive version:
(defun sorted (list)
(or (endp list)
(endp (cdr list))
(and (<= (first list) (second list))
(sorted (cdr list)))))
The more idiomatic loop-based predicate accepting a :test argument:
(defun sortedp (list &key (test #'<=))
(loop for (a b) on list
while b
always (funcall test a b)))
The version accepting a :key; we only call the key function once per visited element:
(defun sortedp (list &key (test #'<=) (key #'identity))
(loop for x in list
for old = nil then new
for new = (funcall key x)
for holdp = T then (funcall test old new)
always holdp))
Some tests:
(loop for k in '(()
((1))
((1) (2))
((2) (1))
((1) (2) (3))
((3) (2) (1)))
collect (sortedp k :test #'> :key #'car))
=> (T T NIL T NIL T)
This one also works with other kinds of sequences:
(defun sortedp (sequence &key (test #'<=) (key #'identity))
(reduce (lambda (old x &aux (new (funcall key x)))
(if (or (eq old t)
(funcall test old new))
new
(return-from sortedp nil)))
sequence
:initial-value t))
The above test gives:
(T 1 NIL 1 NIL 1)
... which is a correct result thanks to generalized booleans.
If you are doing your homework (seems so), then the above answers are fine. If you are just learning Lisp, and don't have constraints about recursivity, then the following might give you a glimpse about the power of Lisp:
(defun sorted (l)
(or (null l) (apply #'< l)))
The first problem with your solution is the base case You need to stop not at the end of the list, but when looking at the last to elements, as you need to elements to do the comparison. Also the parens are missing in the call to (car x)
(defun sorted (list)
(if (endp (cddr list))
(<= (car list) (cadr list))
(and (<= (car list) (cadr list))
(sorted (cdr list)))))
Bare in mind that recursive solutions are discouraged in CL
Let's say we have this list '( (4 (1 2)) (5 (5 5)) (7 (3 1)) (1 (2 3)))
I am trying to write smth in Scheme in order to get the second element for every element in the list.. So the result will look like '( (1 2) (5 5) (3 1) (2 3))
I have this code so far..
(define (second list1)
(if (null? (cdr list1))
(cdr (car list1))
((cdr (car list1))(second (cdr list1)))))
Here's a straightforward solution:
(define (seconds lst)
(map cadr lst))
In general, when you want to transform every element of a list, map is the way to go.
All you need to do is map the built-in function second onto the list lst:
(map second lst)
Your error is that you lack an operator, perhaps cons. If you look at the consequent:
((cdr (car list1))(second (cdr list1)))
So Scheme expects (cdr (car list)) to be a procedure since it's in operator position in the form, but since it isn't you get an error. In addition (cdr (car x)) == cdar wont take the second element in every element but the tail of each element. cadar is what you're lookig for.
(define (second list1)00+
(if (null? (cdr list1))
(cons (cadar list1) '())
(cons (cadar list1) (second (cdr list1)))))
It will fail for the empty list. To fix this you let the consequemt take care of every element and the base case only to stop:
(define (second list1)
(if (null? list1)
'()
(cons (cadar list1) (second (cdr list1)))))
The result for a list will be the same. There is a procedure called map. It supports several list arguments, but the implementation for one is:
(define (map fun lst)
(if (null? lst)
'()
(cons (fun (car lst)) (map fun (cdr lst)))))
Looks familiar? Both make a list based on each element, but map is generic. Thus we should try to make (fun (car lst)) do the same as (cadar lst).
(define (second lst)
(map cadr lst)) ; (cadr (car x)) == (cadar x)
There you have it. Chris beat me to it, but I'd like to comment one of the other answers that uses the abbreviation second. It's defined in racket/base and the library SRFI-1, but it's not mentioned in the last Scheme reports. I.e. some implementations might require an extra library to be imported for it to work.
im trying to write a function in Scheme where i accept a list and return all the different derangements (look below for definition) as a list of lists
derangement: A list where no item is in the same place as the original list
ex: '(a b c) -> '(cab)
any help is appreciated!
Compute all of the permutations of the input list and then filter out the ones that have an element in the same position as the input list. If you need more detail, leave a comment.
Edit 1:
Define (or maybe it's defined already? Good exercise, anyway) a procedure called filter that takes as its first argument a procedure p and a list l as its second argument. Return a list containing only the values for which (p l) returns a truthy value.
Define a procedure derangement? that tests if a list l1 is a derangement of l2. This will be handy when paired with filter.
The most obvious solution would be something like this:
(define filtered-permutations
(lambda (lst)
(filter
(lambda (permuted-list)
(deranged? permuted-list lst))
(permute lst))))
Since the number of derangements is considerably lower than then number of permutations, however, this is not very efficient. Here is a solution that mostly avoids generating permutations that are not derangements, but does use filter once, for the sake of simplicity:
(define deranged?
(lambda (lst1 lst2)
(if (null? lst1)
#t
(if (eq? (car lst1) (car lst2))
#f
(deranged? (cdr lst1) (cdr lst2))))))
(define derange
(lambda (lst)
(if (< (length lst) 2)
;; a list of zero or one elements can not be deranged
'()
(permute-helper lst lst))))
(define derange-helper
(lambda (lst template)
(if (= 2 (length lst))
(let ((one (car lst))
(two (cadr lst)))
(filter
(lambda (x)
(deranged? x template))
(list (list one two) (list two one))))
(let ((anchor (car template)))
(let loop ((todo lst)
(done '())
(result '()))
(if (null? todo)
result
(let ((item (car todo)))
(if (eq? item anchor)
;; this permutation would not be a derangement
(loop (cdr todo)
(cons item done)
result)
(let ((permutations
(map
(lambda (x)
(cons item x))
(derange-helper (append (cdr todo) done)
(cdr template)))))
(loop (cdr todo)
(cons item done)
(append result permutations)))))))))))