I want to show the result of my function as a list not as a number.
My result is:
(define lst (list ))
(define (num->base n b)
(if (zero? n)
(append lst (list 0))
(append lst (list (+ (* 10 (num->base (quotient n b) b)) (modulo n b))))))
The next error appears:
expected: number?
given: '(0)
argument position: 2nd
other arguments...:
10
I think you have to rethink this problem. Appending results to a global variable is definitely not the way to go, let's try a different approach via tail recursion:
(define (num->base n b)
(let loop ((n n) (acc '()))
(if (< n b)
(cons n acc)
(loop (quotient n b)
(cons (modulo n b) acc)))))
It works as expected:
(num->base 12345 10)
=> '(1 2 3 4 5)
Related
I have been writing a code that returns a list with all prime numbers less than or equal to n in the Scheme language.
Example,3 -> 2,3 10 -> 1,3,5,7 11->2,3,5,7,11
Actually, the codes below works.However, when I put 1 for n, the code should show (), but it shows 2. I think that it is because I put 2 on the second line. But I put the 2 for the other test case.
I tried to fix the code, but it did not work.
Are there any points where I can fix?
(define (primes n)
(let loop((result `(2))
(i 3))
(cond ((> i n)(reverse result))
(else (loop
(if (divide-any? i result) result (cons i result))
(+ i 2))))))
(define (divide? n1 n2)
(zero? (modulo n1 n2)))
(define (divide-any? n ls)
(do ((ls ls (cdr ls)))
((or (null? ls)
(divide? n (car ls)))
(not (eqv? '() ls)))))
Yes, the function primes is partial - it only works for certain values.
You can fix it quite simply:
(define (primes n)
(if (<= n 1)
'()
(let loop((result `(2))
(i 3))
(cond ((> i n)(reverse result))
(else (loop
(if (divide-any? i result) result (cons i result))
(+ i 2)))))))
I'm having problems with this problem because i don't know how to make a list with recursivity using generators. The idea is to create a function that receives a generator that generates n numbers and returns a list with those numbers.
This is my code
;GENERATOR THAT GENERATES "INFINITE NUMBERS OF FIBONACCI"
(define (fib)
(let ((a 0) (b 1))
(lambda ()
(let ((ret a))
(set! a b)
(set! b (+ ret b))
ret))))
;RETURNS A GENERATOR THAT GENERATES NUMBERS OF FIBONACCI UP TO N
(define (taking n g)
(let ((i 1))
(lambda ()
(if (> i n)
#f
(begin
(set! i (+ i 1))
(g))))))
Your definitions are fine! You just need to call them correctly to see it.
> (define t (taking 10 (fib)))
> (t)
0
> (t)
1
> (t)
1
> (t)
2
> (t)
3
> (t)
5
>
UPDATE
(define (generator->list n g)
(if (= n 0)
'()
(cons (g) (generator->list (- n 1) g))))
(generator->list 10 (fib))
So something like this:
(define (to-list gen)
(let loop ((l '()))
(let ((r (gen)))
(if r
(loop (cons r l))
(reverse! l)
))))
Untested. What this does is build up a list in reverse consing the truthy items. When it gets a falsy item, it stops and returns the reverse of the accumulation list.
Hi I am trying to implement a program in scheme shifting a list k times to the left.
For example:
(shift-k-left ’(1 2 3) 2)
’(3 1 2)
I have managed to implement a code that do shift left once here:
(define shift-left
(lambda (ls)
(if (null? ls)
'()
(append (cdr ls)
(cons (car ls)
'())))))
I want to use shift left as a function on shift-k-left.
Here is a solution using circular-list from srfi/1.
(require srfi/1)
(define (shift xs k)
(define n (length xs))
(take (drop (apply circular-list xs) k) n))
Using your shift-left to shift k times:
If k is 0: do nothing
If k is not 0: shift k-1 times, and then shift-left the result.
That is,
(define (shift-left-k ls k)
(if (= k 0)
ls
(shift-left (shift-left-k ls (- k 1)))))
You may want to adjust to do something sensible for negative k.
The idea is to count down n while consing the cars of r to p and the cdrs to r then the base case becomes append r to the reverse of p. If we run into a null? r we reverse p and continue this wraps the rotation:
(define (shift-k-left l n)
; assume that n >= 0
(let loop ((n n) (p '()) (r l))
(if (= n 0)
(append r (reverse p))
(if (null? r)
(loop n '() (reverse p))
(loop (- n 1) (cons (car r) p) (cdr r))))))
Here is something similar:
(define (addn value n)
(let loop ((value value) (n n))
(if (zero? n)
value
(loop (add1 value) (- n 1)))))
(addn 5 3)
; ==> 8
Now you could make an abstraction:
(define (repeat proc)
(lambda (v n)
...))
(define addn (repeat add1))
(addn 5 3)
; ==> 8
(define shift-k-left (repeat shift-left))
(shift-k-left ’(1 2 3) 2)
; ==> (3 1 2)
Needless to say repeat looks a lot like add1 does.
NB: The naming is off. Your implementation is more "rotate" than "shift".
shift-left is actually more like cdr than your implemenation.
I'm trying to print the first 2 numbers in a list coded in Scheme. I'm having a bit of trouble doing this. I get an error when I run the procedure. Any suggestions on how I can get this to work
(define (print-two-nums n nums)
( list-ref nums(+ (cdr nums) n)))
( print-two-nums 2'(5 5 4 4))
It looks like you were wavering between the ideas of "print two numbers" and "print n numbers." If you really want just the two first numbers of a list, you can write:
(define (print-two-nums nums)
(print (list (car nums) (cadr nums))))
But for the more general first n numbers, you can use:
(define (print-n-nums n nums)
(print (take nums n)))
To print the first n numbers, you could use this simple procedure
(define (print-n-nums L n) (cond
((or (= 0 n) (null? L)) '())
(else (cons (car L) (print-n-nums (cdr L) (- n 1))))))
(print-n-nums (list 1 2 3) 2)
;Output: (1 2)
You could further abstract the cons operation and define print-n-nums as a higher order procedure to carry out the desired operation. For example, if we wanted to add the first n numbers of a list, we could define the following procedure. Here OPERATION is a function that we pass to the list-operator function. Thus, here we want to perform the + operation. In the case above, we want to perform the cons operation. The initial parameter is just how we want to handle the edge case.
(define (list-operator L n OPERATION initial) (cond
((or (= 0 n) (null? L)) initial)
(else (OPERATION (car L) (list-operator (cdr L) (- n 1) OPERATION initial)))))
(list-operator (list 1 2 3) 2 + 0)
;Output: 3
Now, if you wanted the product of the first 2 numbers, you would just do
(list-operator (list 1 2 3) 2 * 1)
A k-ary necklace of length n is an ordered list of length n whose items are drawn from an alphabet of length k, which is the lexicographically first list in a sort of all lists sharing an ordering under rotation.
Example:
(1 2 3) and (1 3 2) are the necklaces of length 3 from the alphabet {1 2 3}.
More info:
http://en.wikipedia.org/wiki/Necklace_(combinatorics)
I'd like to generate these in Scheme (or a Lisp of your choice). I've found some papers...
Savage - A New Algorithm for Generating Necklaces
Sawada - Generating Bracelets in Constant Amortized Time
Sawada - Generating Necklaces with Forbidden Substrings
...but the code presented in them is opaque to me. Mainly because they don't seem to be passing in either the alphabet or the length (n) desired. The scheme procedure I'm looking for is of the form (necklaces n '(a b c...)).
I can generate these easy enough by first generating k^n lists and then filtering out the rotations. But it's terribly memory-inefficient...
Thanks!
The FKM algorithm for generating necklaces. PLT Scheme. Not so hot on the performance. It'll take anything as an alphabet and maps the internal numbers onto whatever you provided. Seems to be correct; no guarantees. I was lazy when translating the loops, so you get this weird mix of for loops and escape continuations.
(require srfi/43)
(define (gennecklaces n alphabet)
(let* ([necklaces '()]
[alphavec (list->vector alphabet)]
[convert-necklace
(lambda (vec)
(map (lambda (x) (vector-ref alphavec x)) (cdr (vector->list vec))))]
[helper
(lambda (n k)
(let ([a (make-vector (+ n 1) 0)]
[i n])
(set! necklaces (cons (convert-necklace a) necklaces))
(let/ec done
(for ([X (in-naturals)])
(vector-set! a i (add1 (vector-ref a i)))
(for ([j (in-range 1 (add1 (- n i)))])
(vector-set! a (+ j i)
(vector-ref a j)))
(when (= 0 (modulo n i))
(set! necklaces (cons (convert-necklace a) necklaces)))
(set! i n)
(let/ec done
(for ([X (in-naturals)])
(unless (= (vector-ref a i)
(- k 1))
(done))
(set! i (- i 1))))
(when (= i 0)
(done))))))])
(helper n (length alphabet))
necklaces))
I would do a two step process. First, find each combination of n elements from the alphabet. Then, for each combination, pick the lowest value, and generate all permutations of the remaining items.
Edit: Here is some code. It assumes that the input list is already sorted and that it contains no duplicates.
(define (choose n l)
(let ((len (length l)))
(cond ((= n 0) '(()))
((> n len) '())
((= n len) (list l))
(else (append (map (lambda (x) (cons (car l) x))
(choose (- n 1) (cdr l)))
(choose n (cdr l)))))))
(define (filter pred l)
(cond ((null? l) '())
((pred (car l)) (cons (car l) (filter pred (cdr l))))
(else (filter pred (cdr l)))))
(define (permute l)
(cond ((null? l) '(()))
(else (apply append
(map (lambda (x)
(let ((rest (filter (lambda (y) (not (= x y))) l)))
(map (lambda (subperm) (cons x subperm))
(permute rest))))
l)))))
(define (necklaces n l)
(apply
append
(map
(lambda (combination)
(map (lambda (permutation)
(cons (car combination) permutation))
(permute (cdr combination))))
(choose n l))))
(display (choose 1 '(1 2 3 4 5))) (newline)
(display (choose 2 '(1 2 3 4 5))) (newline)
(display (permute '(1 2))) (newline)
(display (permute '(1 2 3))) (newline)
(display (necklaces 3 '(1 2 3 4))) (newline)
(display (necklaces 2 '(1 2 3 4))) (newline)
Example: (1 2 3) and (1 3 2) are the necklaces of length 3 from the alphabet {1 2 3}.
You forgot (1 1 1) (1 1 2) (1 1 3) (1 2 2) (1 3 3) (2 2 2) (2 2 3) (2 3 3) (3 3 3). Necklaces can contain duplicates.
If you were only looking for necklaces of length N, drawn from an alphabet of size N, that contain no duplicates, then it's pretty easy: there will be (N-1)! necklaces, and each necklace will be of the form (1 :: perm) where perm is any permutation of {2 .. N}. For example, the necklaces of {1 .. 4} would be (1 2 3 4) (1 2 4 3) (1 3 2 4) (1 3 4 2) (1 4 2 3) (1 4 3 2). Extending this method to deal with no-duplicates necklaces of length K < N is left as an exercise for the reader.
But if you want to find real necklaces, which may contain duplicate elements, then it's not so simple.
As a first idea, you can do the obvious, but inefficient: step through all combinations and check if they are a necklace, i.e. if they are the lexically smallest rotation of the elements (formal definition on p 5 in above paper). This would be like the way you proposed, but you would throw away all non-necklaces as soon as they are generated.
Other than that, I think that you will have to understand this article (http://citeseer.ist.psu.edu/old/wang90new.html):
T. Wang and C. Savage, "A new algorithm for generating necklaces," Report
TR-90-20, Department of Computer Science, North Carolina State University
(1990).
It is not too hard, you can break it down by implementing the tau and sigma functions as described and then applying them in the order outlined in the article.