Remove duplicates in a MULTI-LEVEL list (using Common Lisp) without changing list's inner structure. This problem seems to be a hard nut and a big headache for me.
Source list:
(1 2 (6 5) 2 3 (5 4)) ==> Result: (1 (6) 2 3 (5 4))
Here's my not-working decision:
LispWokrs:
(defun F (l &optional (lst (remove-duplicates (flatten l))))
(cond
((null l) nil)
((atom (car l))
(if (member (car l) lst)
(cons (car l) (F (cdr l) (remove (car l) lst)))
(F (cdr l) lst)))
(t (cons (F (car l) lst) (F (cdr l) lst)))))
I tried to use lst for keeping a clear set (1 2 6 5 3 4) and I've been trying to remove an element from this set each time I add a new element.
But what I get is almost the same source sequence (parallel recursion...):
(f '(1 2 (6 5) 2 3 (5 4))) ==> (1 2 (6 5) 3 (5 4))
(f '(А ((B C E) D (B E A)))) ==> (А ((B C E) D (B E A)))
Then I searched over the net, but there was no decision for this problem.
Try this:
(defun multi-level-list-remove-duplicates (tree)
(let ((seen NIL))
(labels ((rec (l)
(cond
((null l) NIL)
((consp (car l)) (cons (rec (car l))
(rec (cdr l))))
((member (car l) seen) (rec (cdr l)))
(T (push (car l) seen)
(cons (car l) (rec (cdr l)))))))
(rec tree))))
This maintains a list of already-seen values in seen and removes these if seen again. The recursive function rec closes over this value and thus all the sub-lists share one seen variable for each call to multi-level-list-remove-duplicates.
Related
How do I recursively merge jumping pairs of elements of a list of lists? I need to have
'((a b c) (e d f) (g h i))
from
'((a b) c (e d) f (g h) i)
My attempt
(define (f lst)
(if (or (null? lst)
(null? (cdr lst)))
'()
(cons (append (car lst) (list (cadr lst)))
(list (append (caddr lst) (cdddr lst))))))
works if I define
(define listi '((a b) c (d e) f))
from which I obtain
((a b c) (d e f))
by doing simply
(f listi)
but it does not work for longer lists. I know I need recursion but I don't know where to insert f again in the last sentence of my code.
A simpler case that your algorithm fails: (f '((1 2) 3)) should result in '((1 2 3)), but yours results in an error.
We will define some terms first:
An "element" is a regular element, like 1 or 'a.
A "plain list" is simply a list of "element"s with no nested list.
E.g., '(1 2 3) is a plain list. '((1 2) 3) is not a plain list.
A "plain list" is either:
an empty list
a cons of an "element" and the next "plain list"
A "list of jumping pairs" is a list of even length where the odd index has a "plain list", and the even index has an element. E.g., '((1) 2 (a) 4) is a "list of jumping pairs". A "list of jumping pairs" is either:
an empty list
a cons of
a "plain list"
a cons of an "element" and the next "list of jumping pairs"
We are done with terminology. Before writing the function, let's start with some examples:
(f '()) equivalent to (f empty)
should output '()
equivalent to empty
(f '((1 2) 3)) equivalent to (f (cons (cons 1 (cons 2 empty))
(cons 3
empty)))
should output '((1 2 3))
equivalent to (cons (cons 1 (cons 2 (cons 3 empty)))
empty)
(f '((1 2) 3 (4) a)) equivalent to (f (cons (cons 1 (cons 2 empty))
(cons 3
(cons (cons 4 empty)
(cons 'a
empty)))))
should output '((1 2 3) (4 a))
equivalent to (cons (cons 1 (cons 2 (cons 3 empty)))
(cons (cons 4 (cons 'a empty))
empty))
So, f is a function that consumes a "list of jumping pairs" and returns a list of "plain list".
Now we will write the function f:
(define (f lst)
???)
Note that the type of lst is a "list of jumping pairs", so we will perform a case analysis on it straightforwardly:
(define (f lst)
(cond
[(empty? lst) ???] ;; the empty list case
[else ??? ;; the cons case has
(first lst) ;; the "plain list",
(first (rest lst)) ;; the "element", and
(rest (rest lst)) ;; the next "list of jumping pairs"
???])) ;; that are available for us to use
From the example:
(f '()) equivalent to (f empty)
should output '()
equivalent to empty
we know that the empty case should return an empty list, so let's fill in the hole accordingly:
(define (f lst)
(cond
[(empty? lst) empty] ;; the empty list case
[else ??? ;; the cons case has
(first lst) ;; the "plain list",
(first (rest lst)) ;; the "element", and
(rest (rest lst)) ;; the next "list of jumping pairs"
???])) ;; that are available for us to use
From the example:
(f '((1 2) 3)) equivalent to (f (cons (cons 1 (cons 2 empty))
(cons 3
empty)))
should output '((1 2 3))
equivalent to (cons (cons 1 (cons 2 (cons 3 empty)))
empty)
we know that we definitely want to put the "element" into the back of the "plain list" to obtain the resulting "plain list" that we want:
(define (f lst)
(cond
[(empty? lst) empty] ;; the empty list case
[else ;; the cons case has:
???
;; the resulting "plain list" that we want
(append (first lst) (cons (first (rest lst)) empty))
;; the next "list of jumping pairs"
(rest (rest lst))
;; that are available for us to use
???]))
There's still the next "list of jumping pairs" left that we need to deal with, but we have a way to deal with it already: f!
(define (f lst)
(cond
[(empty? lst) empty] ;; the empty list case
[else ;; the cons case has:
???
;; the resulting "plain list" that we want
(append (first lst) (cons (first (rest lst)) empty))
;; the list of "plain list"
(f (rest (rest lst)))
;; that are available for us to use
???]))
And then we can return the answer:
(define (f lst)
(cond
[(empty? lst) empty] ;; the empty list case
[else ;; the cons case returns
;; the resulting list of "plain list" that we want
(cons (append (first lst) (cons (first (rest lst)) empty))
(f (rest (rest lst))))]))
Pattern matching (using match below) is insanely useful for this kind of problem -
(define (f xs)
(match xs
;; '((a b) c . rest)
[(list (list a b) c rest ...)
(cons (list a b c)
(f rest))]
;; otherwise
[_
empty]))
define/match offers some syntax sugar for this common procedure style making things even nicer -
(define/match (f xs)
[((list (list a b) c rest ...))
(cons (list a b c)
(f rest))]
[(_)
empty])
And a tail-recursive revision -
(define (f xs)
(define/match (loop acc xs)
[(acc (list (list a b) c rest ...))
(loop (cons (list a b c) acc)
rest)]
[(acc _)
acc])
(reverse (loop empty xs)))
Output for each program is the same -
(f '((a b) c (e d) f (g h) i))
;; '((a b c) (e d f) (g h i))
(f '((a b) c))
;; '((a b c))
(f '((a b) c x y z))
;; '((a b c))
(f '(x y z))
;; '()
(f '())
;; '()
As an added bonus, this answer does not use the costly append operation
There is no recursive case in your code so it will just work statically for a 4 element list. You need to support the following:
(f '()) ; ==> ()
(f '((a b c) d (e f g) h)) ; ==> (cons (append '(a b c) (list 'd)) (f '((e f g) h)))
Now this requires exactly even number of elements and that every odd element is a proper list. There is nothing wrong with that, but onw might want to ensure this by type checking or by adding code for what should happen when it isn't.
Here is a task: a list is given, some of the elements are also lists. It's nescessary to replace the nested lists with the sum of the numbers in them, if all of them are even, using recursion. For example:
(1 2 NIL (2 4 6) 5 7) -> (1 2 NIL 12 5 7)
if the parent list matches the condition after the transformation:
(2 2 (4 4) (2 2)) -> (2 2 8 4) -> 16
Now i have the following code:
;; check for all list elements are even
(defun is-even-list (lst)
(cond ((null lst) t)
((and (numberp (car lst)) (evenp (car lst))) (is-even-list (cdr lst)))
(t nil)
)
)
;; list summing
(defun sum-list (lst)
(cond ((null lst) 0)
(t (+ (car lst) (sum-list (cdr lst))))
)
)
;; main func
(defun task (lst)
(cond ((null lst) nil)
((atom (car lst)) (cons (car lst) (task (cdr lst))))
((is-even-list (car lst)) (cons (list (sum-list (car lst))) (task (cdr lst))))
(t (cons (task (car lst)) (task (cdr lst))))
)
)
But now it processes only the “lowest” level of the list if it exists:
(2 4) -> (2 4)
(2 (2 4 6) 6) -> (2 12 6)
(2 (4 (6 8) 10) 12) -> (2 (4 14 10) 12)
(2 (4 6) (8 10) 12) -> (2 10 18 12)
How can i change this code to get "full" processing?
It's definitely not the best solution but it works:
(defun is-even-list (lst)
(cond ((null lst) t)
((and (numberp (car lst)) (evenp (car lst))) (is-even-list (cdr lst)))
(t nil)
)
)
(defun sum-list (lst)
(cond ((null lst) 0)
(t (+ (car lst) (sum-list (cdr lst))))
)
)
(defun test (lst)
(dotimes (i (list-length lst))
(cond
((not (atom (nth i lst))) (setf (nth i lst) (test (nth i lst))))
)
)
(cond
((is-even-list lst) (setf lst (sum-list lst)))
((not (is-even-list lst)) (setf lst lst))
)
)
Here's a solution which I think meets the requirements of the question: recursively sum a list each element of which is either an even number or a list meeting the same requirement. It also does this making only a single pass over the structure it is trying to sum. For large lists, it relies on tail-call elimination in the implementation which probably is always true now but is not required to be. sum-list-loop could be turned into something explicitly iterative if not.
(defun sum-list-if-even (l)
;; Sum a list if all its elements are either even numbers or lists
;; for which this function returns an even number. If that's not
;; true return the list. This assumes that the list is proper and
;; elements are numbers or lists which meet the same requirement but
;; it does not check this in cases where it gives up for other
;; reasons first: (sum-list-if-even '(2 "")) signals a type error
;; (but (sum-list-if-even '(1 "")) fails to do so)
(labels ((sum-list-loop (tail sum)
(etypecase tail
(null sum) ;all the elements of '() are even numbers
(cons
(let ((first (first tail)))
(etypecase first
(integer
;; Easy case: an integer is either an even number
;; or we give up immediately
(if (evenp first)
(sum-list-loop (rest tail) (+ sum first))
;; give up immediately
l))
(list
;; rerurse on the car ...
(let ((try (sum-list-if-even first)))
;; ... and check to see what we got to know if
;; we should recurse on the cdr
(if (not (eq try first))
(sum-list-loop (rest tail) (+ sum try))
l)))))))))
(sum-list-loop l 0)))
Allow me to show some improvements on your own answer.
First, use conventional formatting: no dangling parentheses, bodies indented two spaces, other argument forms aligned. Use appropriate line breaks.
(defun is-even-list (lst)
(cond ((null lst) t)
((and (numberp (car lst))
(evenp (car lst)))
(is-even-list (cdr lst)))
(t nil)))
(defun sum-list (lst)
(cond ((null lst) 0)
(t (+ (car lst)
(sum-list (cdr lst))))))
(defun test (lst)
(dotimes (i (list-length lst))
(cond ((not (atom (nth i lst)))
(setf (nth i lst) (test (nth i lst))))))
(cond ((is-even-list lst) (setf lst (sum-list lst)))
((not (is-even-list lst)) (setf lst lst))))
The first function checks two things: that every element is a number, and that every element is even. In this context, the first condition mainly means: no sublists.
(defun flat-all-even-p (list)
(and (every #'numberp list)
(every #'even list)))
The second function sums a list and assumes that all elements are numbers (sublists would signal an error here).
(defun sum (list)
(reduce #'+ list))
The third function does not test, it sums. Note that it only accidentally returns the answer, since setf returns the value it sets. Another problem is that you do index lookup on lists in a loop, which is very inefficient. Finally, you modify the list you were given, which will surprise your caller.
(defun sum-if-all-even (tree)
(if (listp tree)
(let ((recursed-tree (mapcar #'sum-if-all-even tree)))
(if (flat-all-even-p recursed-tree)
(sum recursed-tree)
recursed-tree))
tree)
I need a function that will do this:
Odd Length list
Input '(1 2 3 4 5) = '(1 (2 (3) 4) 5)
Even length list
Input '(1 2 3 4) = '(1 (2 () 3) 4)
It needs to use very minimal built in functions. I have spent hours trying to figure this out and I am completely out of ideas at this point.
Here is what I have:
(define (listInList L)
(define length (listLength L))
(define L2 (listInListHelper length L '() '()))
(define L3 (listInListHelper (- length 2) L L2 '()))
L3
)
(define (listInListHelper N L NL)
(cond
((= N 0) '()
((= N 1) (cons (list (car L)) NL))
(else (cons (cons (car L) (list (lastItem L))) NL)
(remove 1 L)))
)
)
(define (lastItem L)
(if (null? (cdr L))(car L)
(lastItem (cdr L)))
)
(define (remove N L)
(cond ((eq? N 0) (cdr L))
(else (cons (car L) (remove (- N 1)(cdr L))))))
This would be one way to do it, you need to tell me if it's minimal enough:
(define (f lst)
(define (helper lst rlst half)
(cond
((= half 0 ) null)
((= half 1/2) (list (car lst)))
(else (list (car lst)
(helper (cdr lst) (cdr rlst) (sub1 half))
(car rlst)))))
(helper lst (reverse lst) (/ (length lst) 2)))
testing:
> (f '(1 2 3 4 5))
'(1 (2 (3) 4) 5)
> (f '(1 2 3 4))
'(1 (2 () 3) 4)
I am trying to learn clisp and I have started learning how to manipulate lists recursively. I am unsure wether it is my logic or if I am just too unfamiliar with the constructs of lisp, for some I am able to do it i.e. for procedure (separate '(a 1 b 2 c 3 d 4)) => ((1 2 3 4) (a b c d)) by doing
(defun separate (lst)
(if (endp lst)
'(nil nil)
(let ((x (separate (cdr lst))))
(if (numberp (car lst))
(list (cons (car lst)
(car x)))
(list (car x)
(cons (car lst) (cadr x)))))))
but when I do the same approach for another procedure
(greater-than-n '(9 1 8 2 7 3 6 4) 5)
I would expect to get a list : ((9 8 7 6) (1 2 3 4))
but instead I get: ((9 8 7 6))
My program thus far is:
(defun greater-than-n (lst n)
(if (endp lst)
'(() ())
(let ((x (greater-than-n (cdr lst) n)))
(if (> (car lst) n)
(list (cons (car lst)
(car x)))
(list (car x)
(cons (car lst)
(car x)))))))
I appreciate any help or comments.
Your bug is in the
(list (cons (car lst)
(car x)))
form: you are returning a list of 1 element.
PS. Your functions seem like a textbook case for using multiple values instead of a list of values.
First off, if anyone can find a question where this has already been answered, let me know. All I can find are functions that remove duplicates.
Anyhow, I am trying to write a scheme function (delete V L) that takes a value and a list as arguments, and removes that value from the list and all its sublists. For example, given the following input:
> (deep-delete 3 '(1 2 3 (4 3) 5 (6 (3 7)) 8))
It would yield:
(1 2 (4) 5 (6 (7)) 8)
So far, this is what I have written, but I know that the if statement (which is to check to see if the element is a sub-list, which implies it too must be operated on) must be placed incorrectly. Also, I cannot wrap my brain around where I should be using cons and where I shouldn't, because I'm still confused about tracking the return values of the recursion. Can someone please take a look and explain what I'm doing wrong?
(define (delete V L)
(if (list? (car L)) (cons (delete V (car L) (cdr L)))
(cond
((null? L) L)
((equal? V (car L)) (delete V (cdr L)))
(else (cons (car L) (delete V (cdr L))))))))
I have a few comments on your code:
First, in your if statement you use (car L) without checking if L is empty.
Also, in line 2 of your code, you do: (delete V (car L) (cdr L)),
but cons takes two arguments, not three. And you forgot to recursively call delete on the cdr.
You wanted:
(cons (delete V (car L)) (delete V (cdr L)))
Why not use a single cond? Since there are several cases, using cond will make the recursive structure of your algorithm more apparent, and errors easier to catch.
See below.
(define (del V L)
(cond ((null? L) L)
((list? (car L))
(cons (del V (car L)) (del V (cdr L))))
((equal? V (car L)) (del V (cdr L)))
(else (cons (car L) (del V (cdr L))))))
This will recursively delete V from L.
(del 3 '(1 2 3 (4 3) 5 (6 (3 7)) 8))
==> (1 2 (4) 5 (6 (7)) 8)
This is quite easy to achieve with folding; here's an example in Racket using foldr:
(define (deep-delete elt lst (test equal?))
(foldr (lambda (e r)
(if (list? e)
(cons (deep-delete elt e test) r)
(if (test elt e) r (cons e r))))
null
lst))
testing
> (deep-delete 3 '(1 2 3 (4 3) 5 (6 (3 7)) 8))
'(1 2 (4) 5 (6 (7)) 8)
This removes subtrees from a tree (including atomic ones):
(define (remove-element needle haystack)
(let rec ((haystack haystack))
(cond
((equal? needle haystack) '())
((not (pair? haystack)) haystack)
((equal? needle (car haystack)) (rec (cdr haystack)))
((equal? needle (cdr haystack)) (cons (rec (car haystack)) '()))
(else (cons (rec (car haystack))
(rec (cdr haystack)))))))
(remove-element 'atom 'atom) ; => ()
(remove-element '(1 2 3) '((1 2 3) 1 2 3)) ; => ()
(remove-element '(1 2 3) '((1 2 3) 4 5 6)) ; => (4 5 6)
(remove-element '(1 2 3) '(3 2 1 2 3)) ; ==> (3 2)
(remove-element '3 '((1 2 3) 1 2 3)) ; ==> ((1 2) 1 2)
(remove-element '(1 2 3) '(1 2 3 4)) ; ==> (1 2 3 4)