How do i make this transform in lisp? - list

I need to make a function that transforms 2 list in one in lisp?Can you please help me?
(A B C) (X Y Z) --> ((A.X) (B.Y) (C.Z))
This is the example

For the case you asked :
CL-USER> (mapcar #'cons '(1 2 3) '(a b c))
((1 . A) (2 . B) (3 . C))
If you want to generalize :
CL-USER> (mapcar #'list '(1 2 3) '(a b c) '(x y z))
((1 A X) (2 B Y) (3 C Z))
In a function :
(defun foo (&rest l)
(apply #'mapcar #'list l))
Which gives:
CL-USER> (foo '(1 2 3) '(a b c) '(x y z))
((1 A X) (2 B Y) (3 C Z))

Related

Using nested car with cons in a lisp function

I'm making a recursive lisp function that takes two lists and makes a sublist of index pairs
ex: put in (A B C D) and (1 2 3 4) and get ((1 A) (2 B) (3 C) (4 D))
However, I'm having trouble using car along with cons to make said sublist. Here's my code:
(DEFUN zipper (a b)
(if (= (OR (list-length a) (list-length b)) 0)
(setq c NIL)
(progn (zipper (cdr a) (cdr b))
(cons '((car a) (car b)) c))
)
)
I played around for a little and it appears using car to create lists just doesn't work most of the time. Additionally, I'm using CLISP. Any ideas?
Thanks!
The general idea goes into the right direction. There are a bunch of problems, though. Let's have a look.
(DEFUN zipper (a b)
(if (= (OR (list-length a) (list-length b)) 0)
(setq c NIL)
(progn (zipper (cdr a) (cdr b))
(cons '((car a) (car b)) c))
)
)
First indentation:
(DEFUN zipper (a b)
(if (= (OR (list-length a) (list-length b)) 0)
(setq c NIL)
(progn (zipper (cdr a) (cdr b))
(cons '((car a) (car b)) c)) ; <--
)
)
Next dangling parentheses:
(DEFUN zipper (a b)
(if (= (OR (list-length a) (list-length b)) 0)
(setq c NIL)
(progn (zipper (cdr a) (cdr b))
(cons '((car a) (car b)) c))))
Return the empty list in IF for the true case:
(defun zipper (a b)
(if (= (OR (list-length a) (list-length b)) 0)
nil
(progn (zipper (cdr a) (cdr b))
(cons '((car a) (car b)) c))))
Now cons to the result in the false case:
(defun zipper (a b)
(if (= (OR (list-length a) (list-length b)) 0)
nil
(cons '((car a) (car b))
(zipper (cdr a) (cdr b)))))
What remains to be done?
see the comment by 'rsm': replace the quote with a call to list.
don't use list-length. Use null instead. It checks if a list is empty. list-length would traverse the input whole lists on each call -> inefficient.
If you call list-length at each step of recursion, you are going to traverse both lists entirely each time, which gives your zipper function a quadratic time complexity with respect to the sum of your lists' sizes:
(zipper '(1 2 3) '(4 5 6))
=> (list-length (1 2 3))
=> (list-length (2 3))
=> (list-length (3))
=> (list-length ())
=> (list-length (4 5 6))
=> (list-length (4 5))
=> (list-length (5))
=> (list-length ())
(zipper '(2 3) '(5 6))
=> (list-length (2 3))
...
=> (list-length (5 6))
...
...
This is inefficient and not necessary here. Since you are already visiting both lists, you can directly check if any of them is empty using null or endp, which take constant time. You return NIL as soon as one of the list is empty, which is by the way the default behaviour of mapcar. Notice also that mapcar can work on multiple lists at the same time, for example:
(mapcar #'+ '(1 2) '(5 8))
=> (6 10)
If you know a function that takes (at least) two arguments and return a list, then you could mapcar that function over your lists and have a list of lists.
The zip function from other languages such as Python and Haskell is a special case of mapcar.
The traditional zip function can be achieved via:
> (mapcar #'list list1 list2 ... listn)
Such that for this case:
> (mapcar #'list '(A B C D) '(1 2 3 4))
((A 1) (B 2) (C 3) (D 4))
To swap the order of the pairs as you indicated, simply change the function passed to mapcar accordingly:
> (mapcar #'(lambda (x y) (list y x)) '(A B C D) '(1 2 3 4))
((1 A) (2 B) (3 C) (4 D))
Checkout the documentation for mapcar for more details.
zip function with arbitrary number of lists
(defun zip (&rest lists)
(apply #'mapcar #'list lists))
Shortest list determines depth of zipping.
CL-USER> (zip '(1 2 3) '(a b c) '("a" "b" "c"))
((1 A "a") (2 B "b") (3 C "c"))
CL-USER> (zip '(1 2 3) '(a b c) '("a" "b" "c" "d"))
((1 A "a") (2 B "b") (3 C "c"))
You could do something such as this:
(defun zipper (a b)
(if (or (null a) (null b))
nil
(cons (list (car b) (car a)) (our-combiner (cdr a) (cdr b)))))
We can check if either of the lists is null, so that we could stop when one of the lists runs out (similar to how mapcar will stop applying a function to lists when one of the lists runs out). We can then cons a nested list with the car's of the lists in each recursive call. Your output would be:
CL-USER> (zipper '(a b c d) '(1 2 3 4))
((1 A) (2 B) (3 C) (4 D))
CL-USER>
We could also use mapcar as it will iterate over both lists and returns the result of applying the function to both lists (unlike mapc). This is fewer lines of code, and since it will return when some list runs out, there's no need for a conditional:
(defun zipper (a b)
(mapcar #'list b a))

Combining list of list

Hello i have to programm this fucntion in lisp:
(defun combine-list-of-lsts (lst)...)
So when executing the function i should get
(combine-list-of-lsts '((a b c) (+-) (1 2 3 4)))
((A + 1) (A + 2) (A + 3) (A + 4) (A-1) (A-2) (A-3) (A-4) (B + 1) (B + 2) (B + 3) (B + 4) (B-1) (B-2) (B-3) (B-4)(C + 1) (C + 2) (C + 3) (C + 4) (C-1) (C-2) (C-3) (C-4))
What i have now is:
(defun combine-list-of-lsts (lst)
(if (null (cdr lst))
(car lst)
(if (null (cddr lst))
(combine-lst-lst (car lst) (cadr lst))
(combine-lst-lst (car lst) (combine-list-of-lsts (cdr lst))))))
Using this auxiliar functions:
(defun combine-lst-lst (lst1 lst2)
(mapcan #'(lambda (x) (combine-elt-lst x lst2)) lst1))
(defun combine-elt-lst (elt lst)
(mapcar #'(lambda (x) (list elt x)) lst))
But what i get with this:
((A (+ 1)) (A (+ 2)) (A (+ 3)) (A (+ 4)) (A(-1)) (A(-2)) (A(-3)) (A(-4))...)
I dont know how to make this but without the parenthesis
The first thing is to look at this case:
(combine-list-of-lsts '((a b c)))
What should that be? Maybe not what your function returns...
Then I would look at the function combine-list-of-lsts. Do you need two IF statements?
Then look at combine-elt-lst. Do you really want to use LIST? It creates a new list. Wouldn't it make more sense to just add the element to the front?
Usually, when you want to reduce mutliple arguments into single result, you need function #'reduce. Your combination of lists has name cartesian n-ary product.
Following function:
(defun cartesian (lst1 lst2)
(let (acc)
(dolist (v1 lst1 acc)
(dolist (v2 lst2)
(push (cons v1 v2) acc)))))
creates cartesian product of two supplied lists as list of conses, where #'car is an element of lst1, and #'cdr is an element of lst2.
(cartesian '(1 2 3) '(- +))
==> ((3 . -) (3 . +) (2 . -) (2 . +) (1 . -) (1 . +))
Note, however, that calling #'cartesian on such product will return malformed result - cons of cons and element:
(cartesian (cartesian '(1 2) '(+ -)) '(a))
==> (((1 . +) . A) ((1 . -) . A) ((2 . +) . A) ((2 . -) . A))
This happens, because members of the first set are conses, not atoms. On the other hand, lists are composed of conses, and if we reverse order of creating products, we could get closer to flat list, what is our goal:
(cartesian '(1 2)
(cartesian '(+ -) '(a)))
==> ((2 + . A) (2 - . A) (1 + . A) (1 - . A))
To create proper list, we only need to cons each product with nil - in other words to create another product.
(cartesian '(1 2)
(cartesian '(+ -)
(cartesian '(a) '(nil))))
==> ((2 + A) (2 - A) (1 + A) (1 - A))
Wrapping everything up: you need to create cartesian product of successive lists in reversed order, having last being '(nil), what can be achieved with reduce expression. Final code will look something like this:
(defun cartesian (lst1 lst2)
(let (acc)
(dolist (v1 lst1 acc)
(dolist (v2 lst2)
(push (cons v1 v2) acc)))))
(defun combine-lsts (lsts)
(reduce
#'cartesian
lsts
:from-end t
:initial-value '(nil)))
There is one more way you can try,
(defun mingle (x y)
(let ((temp nil))
(loop for item in x do
(loop for it in y do
(cond ((listp it) (setf temp (cons (append (cons item 'nil) it) temp)))
(t (setf temp (cons (append (cons item 'nil) (cons it 'nil)) temp))))))
temp))
Usage:(mingle '(c d f) (mingle '(1 2 3) '(+ -))) =>
((F 1 +) (F 1 -) (F 2 +) (F 2 -) (F 3 +) (F 3 -) (D 1 +) (D 1 -) (D 2 +)
(D 2 -) (D 3 +) (D 3 -) (C 1 +) (C 1 -) (C 2 +) (C 2 -) (C 3 +) (C 3 -))

Adding values to a list in a sort of "overlapped" way

I'll explain in math, here's the transformation I'm struggling to write Scheme code for:
(f '(a b c) '(d e f)) = '(ad (+ bd ae) (+ cd be af) (+ ce bf) cf)
Where two letters together like ad means (* a d).
I'm trying to write it in a purely functional manner, but I'm struggling to see how. Any suggestions would be greatly appreciated.
Here are some examples:
(1mul '(0 1) '(0 1)) = '(0 0 1)
(1mul '(1 2 3) '(1 1)) = '(1 3 5 3)
(1mul '(1 2 3) '(1 2)) = '(1 4 7 6)
(1mul '(1 2 3) '(2 1)) = '(2 5 8 3)
(1mul '(1 2 3) '(2 2)) = '(2 6 10 6)
(1mul '(5 5 5) '(1 1)) = '(5 10 10 5)
(1mul '(0 0 1) '(2 5)) = '(0 0 2 5)
(1mul '(1 1 2 3) '(2 5)) = '(2 7 9 16 15)
So, the pattern is like what I posted at the beginning:
Multiply the first number in the list by every number in the second list (ad, ae, af) and then continue along, (bd, be, bf, cd, ce, cf) and arrange the numbers "somehow" to add the corresponding values. The reason I call it overlapping is because you can sort of visualize it like this:
(list
aa'
(+ ba' ab')
(+ ca' bb' ac')
(+ cb' bc')
cc')
Again,
(f '(a b c) '(d e f)) = '(ad (+ bd ae) (+ cd be af) (+ ce bf) cf)
However, not just for 3x3 lists, for any sized lists.
Here's my code. It's in racket
#lang racket
(define (drop n xs)
(cond [(<= n 0) xs]
[(empty? xs) '()]
[else (drop (sub1 n) (rest xs))]))
(define (take n xs)
(cond [(<= n 0) '()]
[(empty? xs) '()]
[else (cons (first xs) (take (sub1 n) (rest xs)))]))
(define (mult as bs)
(define (*- a b)
(list '* a b))
(define degree (length as))
(append
(for/list ([i (in-range 1 (+ 1 degree))])
(cons '+ (map *- (take i as) (reverse (take i bs)))))
(for/list ([i (in-range 1 degree)])
(cons '+ (map *- (drop i as) (reverse (drop i bs)))))))
The for/lists are just ways of mapping over a list of numbers and collecting the result in a list. If you need, I can reformulate it just maps.
Is this a good candidate for recursion? Not sure, but here's a
a direct translation of what you asked for.
(define (f abc def)
(let ((a (car abc)) (b (cadr abc)) (c (caddr abc))
(d (car def)) (e (cadr def)) (f (caddr def)))
(list (* a d)
(+ (* b d) (* a e))
(+ (* c d) (* b e) (* a f))
(+ (* c e) (* b f))
(* c f))))
Is it correct to assume, that you want to do this computation?
(a+b+c)*(d+e+f) = a(d+e+f) + b(d+e+f) + c(d+e+f)
= ad+ae+af + bd+be+bf + cd+ce+cf
If so, this is simple:
(define (f xs ys)
(* (apply + xs) (apply + ys))
If you are interested in the symbolic version:
#lang racket
(define (f xs ys)
(define (fx x)
(define (fxy y)
(list '* x y))
(cons '+ (map fxy ys)))
(cons '+ (map fx xs)))
And here is a test:
> (f '(a b c) '(d e f))
'(+ (+ (* a d) (* a e) (* a f))
(+ (* b d) (* b e) (* b f))
(+ (* c d) (* c e) (* c f)))

applying list of functions to list in common lisp

I have a list of functions, a list of elements, and I'd like to apply all the functions on all the elements then append all the resulting lists together. I did it as follow
(defun apply-functions(funcs elements)
(if (null funcs)
nil
(append (mapcar #'(lambda (x) (funcall (car funcs) x)) elements) (apply-functions (rest funcs) elements))))
It works as intended, but I don't like it. Is there a cleaner, more concise way of doing it?. I am new to lisp, and still getting used to the lispish style of doing things.
I don't know if you like loop macro (and I don't want to spoil anyone), but try this:
(defun apply-functions (fs es)
(loop for f in fs appending (mapcar f es)))
This is the same idea as yours, just shorter:
(defun apply-functions (functions elements)
(mapcan #'(lambda (x) (mapcar x elements)) functions))
I would define a function, call-each that returns a new function,
returning the list of calling each function on it's argument:
(defun call-each (fns)
(lambda (arg)
(mapcar (lambda (fn)
(funcall fn arg))
fns)))
(funcall (call-each (list #'third #'second #'first)) '(a b c))
;=> (C B A)
cl has the function mapcan which is basically nconc + mapcar :
(mapcan #'reverse '((a b c)
(e f g)
(h i j)))
;=> (C B A G F E J I H)
(mapcan (call-each (list #'identity #'1+)) '(1 3 5 7 9))
;=> (1 2 3 4 5 6 7 8 9 10)
unfortunately, nconc, which mapcan uses, is destructive:
(let ((data '((a b c)
(d e f)
(g h i))))
;;here be dragons
(list (mapcan #'identity data)
data))
;=> ((A B C D E F G H I) ((A B C D E F G H I) (D E F G H I) (G H I)))
alexandria to the rescue:
(let ((data '((a b c)
(d e f)
(g h i))))
;;safe version
(list (alexandria:mappend #'identity data)
data))
;=> ((A B C D E F G H I) ((A B C) (D E F) (G H I)))
note that using mapcan is more efficient, but unless you know exactly where
your data is coming from, and who owns it, mappend is the way to go.
so you could write:
(defun apply-functions (fs es)
(when fs
(alexandria:mappend (call-each fs) es))
(apply-functions (list #'identity #'1+) '(1 3 5 7 9))
;=> (1 2 3 4 5 6 7 8 9 10)

Building a 2D List

Looking for a function that would do something akin to the following:
(foo 3 2) => '( ( (1 1) (1 2) (1 3) )
( (2 1) (2 2) (2 3) ) )
Would there be any built-in function in DrRacket that accomplishes that?
The main tool that you want to use to get such things in Racket is the various for loops. Assuming that you want to create a list-based matrix structure, then this is one way to get it:
#lang racket
(define (foo x y)
(for/list ([i y])
(for/list ([j x])
(list (add1 i) (add1 j)))))
And since people raised the more general question of how to make foo create a matrix of any dimension, here's a generalized version that works with any number of arguments, and still returns the same result when called as (foo 3 2):
#lang racket
(define (foo . xs)
(let loop ([xs (reverse xs)] [r '()])
(if (null? xs)
(reverse r)
(for/list ([i (car xs)])
(loop (cdr xs) (cons (add1 i) r))))))
(Note BTW that in both cases I went with a simple 0-based iteration, and used add1 to get the numbers you want. An alternative way would be to replace
(for/list ([i x]) ... (add1 i) ...)
with
(for/list ([i (in-range 1 (add1 x)]) ... i ...)
)
Code:
(define (foo-makey const max data)
(let* ((i (length data))
(newy (- max i))
(newpair (cons const newy)))
(if (= max i)
data
(foo-makey const max
(cons newpair data)))))
(define (foo-makex xmax ymax data)
(let* ((i (length data))
(newx (- xmax i)))
(if (= xmax i)
data
(foo-makex xmax ymax
(cons (foo-makey newx ymax '()) data)))))
(define (foo x y)
(foo-makex y x '()))
Output:
> (foo 3 2)
'(((1 . 1) (1 . 2) (1 . 3)) ((2 . 1) (2 . 2) (2 . 3)))
I can't answer your question as-is because I don't understand how the nested lists should work for >2 arguments. AFAIK there is no built-in function to do what you want.
To start you off, here is some code that generates output without nested lists. As an exercise try adjusting the code to do the nested listing. And see if there's a way you can make the code more efficient.
;;can take in any number of arguments
(define (permutations . nums)
(foldl
(lambda (current-num acc)
(append-map
(lambda (list-in-acc)
(for/list ((i (build-list current-num (curry + 1))))
(append list-in-acc (list i))))
acc))
(list (list))
(reverse nums)))
Example 1:
> (permutations 3 2)
'((1 1) (1 2) (1 3) (2 1) (2 2) (2 3))
Example 2:
> (permutations 10)
'((1) (2) (3) (4) (5) (6) (7) (8) (9) (10))
Example 3:
> (permutations 2 3 4)
'((1 1 1)
(1 1 2)
(1 2 1)
(1 2 2)
(1 3 1)
(1 3 2)
(2 1 1)
(2 1 2)
(2 2 1)
(2 2 2)
(2 3 1)
(2 3 2)
(3 1 1)
(3 1 2)
(3 2 1)
(3 2 2)
(3 3 1)
(3 3 2)
(4 1 1)
(4 1 2)
(4 2 1)
(4 2 2)
(4 3 1)
(4 3 2))
(define (build-2d row col)
(build-list row (lambda(x) (build-list col (lambda(y) (list (+ x 1) (+ y 1))))))