I need to extract the main diagonal from a square matrix
(1 2 3)
(4 5 6) -> (1 5 9)
(7 8 9)
I have the following code and I need to replace the ... with the appropriate functions.
(define (diag m)
(if (null? m) '()
(cons (... m)
(diag (map ... (... m))))))
Input: (diag '((1 2 3) (4 5 6) (7 8 9)))
Output: (1 5 9)
Any ideas? Thank you!
First of all I created a function that returns n-th element of list (I am not sure if you can use built-in function for it, that's why I created my own bicycle):
(define (nthItem l item currentItem)
(if (null? l) '()
(if (= currentItem item) (car l)
(nthItem (cdr l) item (+ currentItem 1)))))
Then I created a function that you need. I added a parameter "i" that contains current position on a diagonal:
(define (diagPrivate m i)
(if (null? m) '()
(cons (nthItem (car m) i 0)
(diagPrivate (cdr m) (+ i 1)))))
For better appearance I created a wrapper for this function (that looks like your initial function):
(define (diag m)
(diagPrivate m 0))
So you are asking, given you have the list '((1 2 3) (4 5 6) (7 8 9)) how do I get the value 1 from it?
Then you are asking given the same list, how do I get ((4 5 6) (7 8 9)) from it.
Then given that result how do I make a new list using map that only takes the rest of each element list so that the result is ((5 6) (8 9))
The question code looks like came from SO as an answer with VERY easy challenge on how to complete it. Am I right?
The answer is of course just list accessors every beginner schemer should know: cdr x 2 and caar, not necessarily in that order.
Using Racket which is a Scheme dialect:
(define diag '((1 2 3) (4 5 6) (7 8 9)))
(define (getDiagonal l)
(let loop ((l l)
(ol '())
(n 0))
(cond
[(empty? l) (reverse ol)]
[(loop (rest l)
(cons (list-ref (first l) n) ol)
(add1 n))])))
(getDiagonal diag)
Output:
'(1 5 9)
There is for/list loop in Racket which also can be used here:
(for/list ((i (length diag)))
(list-ref (list-ref diag i) i))
Related
I was trying to make a recursive function to split a list into two lists according the number of elements one wants.
Ex:
(split 3 '(1 3 5 7 9)) ((1 3 5) (7 9))
(split 7 '(1 3 5 7 9)) ((1 3 5 7 9) NIL)
(split 0 '(1 3 5 7 9)) (NIL (1 3 5 7 9))
My code is like this:
(defun split (e L)
(cond ((eql e 0) '(() L))
((> e 0) (cons (car L) (car (split (- e 1) (cdr L))))))))
I don't find a way to join the first list elements and return the second list.
Tail recursive solution
(defun split (n l &optional (acc-l '()))
(cond ((null l) (list (reverse acc-l) ()))
((>= 0 n) (list (reverse acc-l) l))
(t (split (1- n) (cdr l) (cons (car l) acc-l)))))
Improved version
(in this version, it is ensured that acc-l is at the beginning '()):
(defun split (n l)
(labels ((inner-split (n l &optional (acc-l '()))
(cond ((null l) (list (reverse acc-l) ()))
((= 0 n) (list (reverse acc-l) l))
(t (inner-split (1- n) (cdr l) (cons (car l) acc-l))))))
(inner-split n l)))
Test it:
(split 3 '(1 2 3 4 5 6 7))
;; returns: ((1 2 3) (4 5 6 7))
(split 0 '(1 2 3 4 5 6 7))
;; returns: (NIL (1 2 3 4 5 6 7))
(split 7 '(1 2 3 4 5 6 7))
;; returns ((1 2 3 4 5 6 7) NIL)
(split 9 '(1 2 3 4 5 6 7))
;; returns ((1 2 3 4 5 6 7) NIL)
(split -3 '(1 2 3 4 5 6 7))
;; returns (NIL (1 2 3 4 5 6 7))
In the improved version, the recursive function is placed one level deeper (kind of encapsulation) by using labels (kind of let which allows definition of local functions but in a way that they are allowed to call themselves - so it allows recursive local functions).
How I came to the solution:
Somehow it is clear, that the first list in the result must result from consing one element after another from the beginning of l in successive order. However, consing adds an element to an existing list at its beginning and not its end.
So, successively consing the car of the list will lead to a reversed order.
Thus, it is clear that in the last step, when the first list is returned, it hast to be reversed. The second list is simply (cdr l) of the last step so can be added to the result in the last step, when the result is returned.
So I thought, it is good to accumulate the first list into (acc-l) - the accumulator is mostly the last element in the argument list of tail-recursive functions, the components of the first list. I called it acc-l - accumulator-list.
When writing a recursive function, one begins the cond part with the trivial cases. If the inputs are a number and a list, the most trivial cases - and the last steps of the recursion, are the cases, when
the list is empty (equal l '()) ---> (null l)
and the number is zero ----> (= n 0) - actually (zerop n). But later I changed it to (>= n 0) to catch also the cases that a negative number is given as input.
(Thus very often recursive cond parts have null or zerop in their conditions.)
When the list l is empty, then the two lists have to be returned - while the second list is an empty list and the first list is - unintuitively - the reversed acc-l.
You have to build them with (list ) since the list arguments get evaluated shortly before return (in contrast to quote = '(...) where the result cannot be evaluated to sth in the last step.)
When n is zero (and later: when n is negative) then nothing is to do than to return l as the second list and what have been accumulated for the first list until now - but in reverse order.
In all other cases (t ...), the car of the list l is consed to the list which was accumulated until now (for the first list): (cons (car l) acc-l) and this I give as the accumulator list (acc-l) to split and the rest of the list as the new list in this call (cdr l) and (1- n). This decrementation in the recursive call is very typical for recursive function definitions.
By that, we have covered all possibilities for one step in the recursion.
And that makes recursion so powerful: conquer all possibilities in ONE step - and then you have defined how to handle nearly infinitely many cases.
Non-tail-recursive solution
(inspired by Dan Robertson's solution - Thank you Dan! Especially his solution with destructuring-bind I liked.)
(defun split (n l)
(cond ((null l) (list '() '()))
((>= 0 n) (list '() l))
(t (destructuring-bind (left right) (split (1- n) (cdr l))
(list (cons (car l) left) right)))))
And a solution with only very elementary functions (only null, list, >=, let, t, cons, car, cdr, cadr)
(defun split (n l)
(cond ((null l) (list '() '()))
((>= 0 n) (list '() l))
(t (let ((res (split (1- n) (cdr l))))
(let ((left-list (car res))
(right-list (cadr res)))
(list (cons (car l) left-list) right-list))))))
Remember: split returns a list of two lists.
(defun split (e L)
(cond ((eql e 0)
'(() L)) ; you want to call the function LIST
; so that the value of L is in the list,
; and not the symbol L itself
((> e 0)
; now you want to return a list of two lists.
; thus it probably is a good idea to call the function LIST
; the first sublist is made of the first element of L
; and the first sublist of the result of SPLIT
; the second sublist is made of the second sublist
; of the result of SPLIT
(cons (car L)
(car (split (- e 1)
(cdr L)))))))
Well let’s try to derive the recursion we should be doing.
(split 0 l) = (list () l)
So that’s our base case. Now we know
(split 1 (cons a b)) = (list (list a) b)
But we think a bit and we’re building up the first argument on the left and the way to build up lists that way is with CONS so we write down
(split 1 (cons a b)) = (list (cons a ()) b)
And then we think a bit and we think about what (split 0 l) is and we can write down for n>=1:
(split n+1 (cons a b)) = (list (cons a l1) l2) where (split n b) = (list l1 l2)
So let’s write that down in Lisp:
(defun split (n list)
(ecase (signum n)
(0 (list nil list))
(1 (if (cdr list)
(destructuring-bind (left right) (split (1- n) (cdr list))
(list (cons (car list) left) right))
(list nil nil)))))
The most idiomatic solution would be something like:
(defun split (n list)
(etypecase n
((eql 0) (list nil list))
(unsigned-integer
(loop repeat n for (x . r) on list
collect x into left
finally (return (list left r))))))
When written this way the error says: 4 parts after if:
(define (rolling-window l size)
(if (< (length l) size) l
(take l size) (rolling-window (cdr l) size)))
and when there's another paranthesis to make it 3 parts:
(define (rolling-window l size)
(if (< (length l) size) l
((take l size) (rolling-window (cdr l) size))))
then it says: application: not a procedure;
How to write more than one expression in if's else in racket/scheme?
Well that's not really the question. The question is "How to build a rolling window procedure using racket?". Anyway, it looks like you're probably coming from another programming language. Processing linked lists can be a little tricky at first. But remember, to compute the length of a list, you have to iterate through the entire list. So using length is a bit of an anti-pattern here.
Instead, I would recommend you create an auxiliary procedure inside your rolling-window procedure which builds up the window as you iterate thru the list. This way you don't have to waste iterations counting elements of a list.
Then if your aux procedure ever returns and empty window, you know you're done computing the windows for the given input list.
(define (rolling-window n xs)
(define (aux n xs)
(let aux-loop ([n n] [xs xs] [k identity])
(cond [(= n 0) (k empty)] ;; done building sublist, return sublist
[(empty? xs) empty] ;; reached end of xs before n = 0, return empty window
[else (aux-loop (sub1 n) (cdr xs) (λ (rest) (k (cons (car xs) rest))))]))) ;; continue building sublist
(let loop ([xs xs] [window (aux n xs)] [k identity])
(cond ([empty? window] (k empty)) ;; empty window, done
([empty? xs] (k empty)) ;; empty input list, done
(else (loop (cdr xs) (aux n (cdr xs)) (λ (rest) (k (cons window rest)))))))) ;; continue building sublists
(rolling-window 3 '(1 2 3 4 5 6))
;; => '((1 2 3) (2 3 4) (3 4 5) (4 5 6))
It works for empty windows
(rolling-window 0 '(1 2 3 4 5 6))
;; => '()
And empty lists too
(rolling-window 3 '())
;; => '()
Here is an alternative:
#lang racket
(define (rolling-window n xs)
(define v (list->vector xs))
(define m (vector-length v))
(for/list ([i (max 0 (- m n -1))])
(vector->list (vector-copy v i (+ i n)))))
(rolling-window 3 '(a b c d e f g))
(rolling-window 3 '())
(rolling-window 0 '(a b c))
Output:
'((a b c) (b c d) (c d e) (d e f) (e f g))
'()
'(() () () ()) ; lack of spec makes this ok !
Following modification of OP's function works. It includes an outlist for which the initial default is empty list. Sublists are added to this outlist till (length l) is less than size.
(define (rolling-window l size (ol '()))
(if (< (length l) size) (reverse ol)
(rolling-window (cdr l) size (cons (take l size) ol))))
Testing:
(rolling-window '(1 2 3 4 5 6) 2)
(rolling-window '(1 2 3 4 5 6) 3)
(rolling-window '(1 2 3 4 5 6) 4)
Output:
'((1 2) (2 3) (3 4) (4 5) (5 6))
'((1 2 3) (2 3 4) (3 4 5) (4 5 6))
'((1 2 3 4) (2 3 4 5) (3 4 5 6))
Any improvements on this one?
(define (rolling-window l size)
(cond ((eq? l '()) '())
((< (length l) size) '())
((cons (take l size) (rolling-window (cdr l) size)))))
I have a small exercise in Lisp:
Write a function test-delta with parameters delta and lst, which will
check if the difference between successive elements in lst is smaller than
delta. Write the function in two ways:
recursively
using a mapping function
I have no problem writing that function recursively, but I don't know which mapping function I should use. All the standard mapping functions work with only one element of the list at a time. reduce cannot be used either, because I do not have some operation to use between successive elements. What function could I use here?
All standard functions are working only with one element at time.
Reduce function cannot be use either
because i do not have some operation to use between to elements.
There's already an answer by uselpa showing that you can do this with reduce, but it feels a bit awkward to me to bend reduce to this case.
It's much more natural, in my opinion, to recognize that the standard mapping functions actually let you work with multiple lists. I'll show mapcar and loop first, and then every, which I think is the real winner here. Finally, just for completeness, I've also included maplist.
mapcar
The standard mapcar can take more than one list, which means that you can take elements from two different lists at once. Of particular note, it could take a list and (rest list). E.g.,
(let ((list '(1 2 3 4 5 6)))
(mapcar 'cons
list
(rest list)))
;=> ((1 . 2) (2 . 3) (3 . 4) (4 . 5) (5 . 6))
loop
You can use loop to do the same sort of thing:
(loop
with l = '(1 2 3 4 5 6)
for a in l
for b in (rest l)
collect (cons a b))
;=> ((1 . 2) (2 . 3) (3 . 4) (4 . 5) (5 . 6))
There are some other variations on loop that you can use, but some of them have less conventient results. E.g., you could loop for (a b) on list, but then you get a (perhaps) unexpected final binding of your variables:
(loop for (a b) on '(1 2 3 4 5 6)
collect (list a b))
;=> ((1 2) (2 3) (3 4) (4 5) (5 6) (6 NIL))
This is similar to what maplist will give you.
every
I think the real winners here, though, are going to the be every, some, notevery, and notany functions. These, like mapcar can take more than one list as an argument. This means that your problem can simply be:
(let ((delta 4)
(lst '(1 2 4 7 9)))
(every (lambda (x y)
(< (abs (- x y)) delta))
lst
(rest lst)))
;=> T
(let ((delta 2)
(lst '(1 2 4 7 9)))
(every (lambda (x y)
(< (abs (- x y)) delta))
lst
(rest lst)))
;=> NIL
maplist
You could also do this with maplist, which works on successive tails of the list, which means you'd have access to each element and the one following. This has the same 6 NIL at the end that the second loop solution did, though. E.g.:
(maplist (lambda (tail)
(list (first tail)
(second tail)))
'(1 2 3 4 5 6))
;=> ((1 2) (2 3) (3 4) (4 5) (5 6) (6 NIL))
reduce can be used:
(defun testdelta (delta lst)
(reduce
(lambda (r e)
(if (< (abs (- r e)) delta)
e
(return-from testdelta nil)))
lst)
t)
or, without return-from (but possibly slower):
(defun testdelta (delta lst)
(and
(reduce
(lambda (r e)
(and r (if (< (abs (- r e)) delta) e nil)))
lst)
t))
Given two lists, return a list whose elements are lists of size two, such that for the i-th list, the first element is the i-th element of the first original list, and the second element is the i-th element of the second original list. If one list is smaller than the other, the resulting list is of the smallest size; and so if one of the lists is empty, return an empty list. For example:
> (zip '(1 2) '(3 4))
'((1 3) (2 4))
> (zip '(1 2 3) '())
'()
> (zip '() '(4 5 6))
'()
> (zip '(8 9) '(3 2 1 4))
'((8 3) (9 2))
> (zip '(8 9 1 2) '(3 4))
'((8 3) (9 4))
Try so:
(map cons '(1 2 3) '(a b c))
or so:
(map list '(1 2 3) '(a b c))
(define zip (lambda (l1 l2) (map list l1 l2)))
->(zip '(1 2 3) '(x y z))
'((1 x) (2 y) (3 z))
Because you didn't post the code you've written, I'm guessing this is homework. I'll give you some hints to get started, this is the general structure of the solution, fill-in the blanks - it'll be much more fun if you reach the correct answer by your own means!
(define (zip lst1 lst2)
(cond ((<???> lst1) ; if the first list is empty
<???>) ; then return the empty list
((<???> lst2) ; if the second list is empty
<???>) ; then also return the empty list
(else ; otherwise
(cons (list ; cons a list with two elements:
<???> ; the first from the first list
<???>) ; and the first from the second list
(zip <???> <???>))))) ; advance recursion over both lists
I tested the above implementation with the sample inputs, and the results are as expected:
(zip '(1 2) '(3 4))
=> '((1 3) (2 4))
(zip '(1 2 3) '())
=> '()
(zip '() '(4 5 6))
=> '()
(zip '(8 9) '(3 2 1 4))
=> '((8 3) (9 2))
(zip '(8 9 1 2) '(3 4))
=> '((8 3) (9 4))
If you've solved the problem for the first element then you can recurse on the rest of the list:
(define (zip l1 l2)
(if (or (null? l1) (null? l2))
'()
(cons (list (car l1) (car l2))
(zip (cdr l1) (cdr l2)))))
provided you handle the base case where either list is empty.
> (zip '(1 2 3 4) '(a b))
((1 a) (2 b))
> (zip '() '(a b))
()
If we accept Racket functions, and also relax the requirement of returning 2-tuples in favor of a more general zip, then I would check out for/list. Here are examples zipping or interleaving two or three lists, stopping at the shortest list.
(define l1 '(a b c))
(define l2 '(1 2 3))
(define l3 '(true false))
;; → '((a 1 true) (b 2 false))
(for/list ([i l1] [j l2] [k l3])
(list i j k))
;; → '((a 1) (b 2) (c 3))
(for/list ([i l1] [j l2])
(list i j))
;; → '()
(for/list ([i l1] [j l2] [k null])
(list i j k))
If your map implementation stops at the shortest list, then zip can be defined with map, Scheme's list procedure and apply. Here's a hint:
(define (zip . lsts)
(apply <??> <??> lsts))
SRFI-1's map is sufficient. So in Racket you add (require (only-in srfi/1 map))
Today, I came across the same exercise and did my own implementation which is different from all the ones people posted here. All the other answers are great. I really liked the most voted one from #Alinsoar.
Definitely, the other answers are actually better than my implementation. But I will post it anyway. Maybe, this can help someone trying to learn Racket.
(define (shorter-list xs ys)
(if (> (length xs) (length ys))
ys
xs))
(define (zip xs ys)
(cond [(null? (shorter-list xs ys)) null]
[true (cons (list (car xs) (car ys)) (zip (cdr xs) (cdr ys)))]))
Am in on the right track for programming the knapsack problem in scheme? My program doesn't have to account for objects "values" , only their weights. The goal is to take the best combination of items so that I have approximately half of the weight in my bag.
(define (split-equip wlst)
(define (sum lst)
(define (sum-h accum lst1)
(if (null? lst)
(/ accum (length lst))
(sum-h (+ (car lst1) accum) (cdr lst1))))
(sum-h 0 lst))
(define (split-equip-h)
(let ((target-w (/ (sum wlst) 2)))
I am tempted to write my program to output a list with all of the different combinations of weights possible and then traversing the list until I find the best set of weights, but not sure how to implement this.
Since this is already your second attempt at this (the first question was deleted), I'll show you a solution in Racket. You should read it like pseudo-code and translate it into the Scheme variant you have been taught.
Disclaimer: I suck at these kind of exercises. That should be another reason for you to understand and reformulate this. But the results of my code still seem correct.
Here's the code:
#lang racket
(define (knapsack lst)
(define half (/ (apply + lst) 2)) ; compute half of total
(printf "list : ~a\nhalf : ~a\n" lst half)
(define (combs lst1 (lst2 null)) ; compute all the combinations
(if (null? lst1)
(if (null? lst2)
null
(list (reverse lst2)))
(append
(combs (cdr lst1) lst2) ; case 1 -> we don't carry the iten
(combs (cdr lst1) (cons (car lst1) lst2))))) ; case 2 -> we do
(for/fold ((delta half) (res null)) ((c (in-list (combs lst)))) ; determine the best fit
(let* ((sm (apply + c)) (newdelta (abs (- half sm))))
(cond
((< newdelta delta) (values newdelta (list c)))
((= newdelta delta) (values delta (cons c res)))
(else (values delta res))))))
(time
(let-values (((delta res) (knapsack (cdr (range 0 24 3)))))
(printf "result: ~a\ndelta : ~a\n" res delta)))
and here's what it says:
list : (3 6 9 12 15 18 21)
half : 42
result: ((3 6 12 21) (3 6 15 18) (3 9 12 18) (3 18 21) (6 9 12 15) (6 15 21) (9 12 21) (9 15 18))
delta : 0
cpu time: 6 real time: 5 gc time: 0
Hope this helps. Don't hesitate to ask questions if there's something you don't get!