I know how to get the first n elements in a list,
(define (countup n ls)
(cond
[(zero? n) '()]
[else (cons (first ls) (countup (sub1 n) (rest ls)))]))
but how can I do something like this for the last n elements in a list (without using list-ref)?
If I call (countup 3 '(a b c d e)), I get (list a b c). I need to be able to enter (counter 3 '(a b c d e)) and get (list c d e).
I need error messages in case the number n given is bigger than the list's length.
Just use the built-in take-right procedure, it does exactly what you need:
(take-right '(a b c d e) 3)
=> '(c d e)
Or you can implement it from scratch, using primitive procedures:
(define (counter n lst)
(define (move n lst)
(if (zero? n)
lst
(move (sub1 n) (rest lst))))
(define (trim-left lst rst)
(if (empty? rst)
lst
(trim-left (rest lst) (rest rst))))
(trim-left lst (move n lst)))
It also works as expected:
(counter 3 '(a b c d e))
=> '(c d e)
I guess I would use a local fn to chop of items from the left and then return the remaining items. The following also returns '() if asked to return a Negative number of items. You may want to treat this as an error as well. #f signals an error in your input ie trying to take more items than the list contains
(define (counter n loN)
(define (acc loN c)
(cond [(null? loN) '()]
[(> c 0) (acc (cdr loN) (sub1 c))]
[else loN]))
;in
(let ((c (- (length loN) n)))
(cond ; [(>= 0 n) #f]
[(positive? c) (acc loN c)]
[else #f])))
(check-equal? (counter 3 '(a b c d e)) '(c d e))
(check-equal? (counter 6 '(a b c d e)) #f)
(check-equal? (counter -3 '(a b c d e)) '())
(check-equal? (counter 0 '(a b c d e)) '())
Related
I am stuck up in a Scheme program for about 5 hours. The program that I am working on should take two lists as input and then compute the number of times the pattern within the first list appears on the second list.
For example : > (patt '(b c) '(a b c d e b c)) ==> answer = 2
(patt '(a b c) '(a b c a b c d e a b c c c)) ==> answer = 3
(patt '((a b) c) '(a b (a b) c d e b c)) ==> answer = 1
Below is the code that I have till now.
(define (patt lis1 lis2)
(cond
((null? lis1) 0)
((null? lis2) 0)
[(and (> (length lis1) 1) (eq? (car lis1) (car lis2))) (patt (cdr lis1) (cdr lis2))]
((eq? (car lis1) (car lis2)) (+ 1 (patt lis1 (cdr lis2))))
(else (patt lis1 (cdr lis2)))
))
Can someone please help me solve this. Thanks!
Consider the subproblem of testing if a list starts with another list.
Then do this for every suffix of the list. Sum up the count of matches.
If you want non overlapping occurrences, you can have the prefix match, return the suffix of the list so that you can skip over the matching part.
Also use equals? for structural equality, not eq? which is for identity.
You need to divide the problem into parts:
(define (prefix? needle haystack)
...)
(prefix? '() '(a b c)) ; ==> #t
(prefix? '(a) '(a b c)) ; ==> #t
(prefix? '(a b c) '(a b c)) ; ==> #t
(prefix? '(a b c d) '(a b c)) ; ==> #f
(prefix? '(b) '(a b c)) ; ==> #t
(define (count-occurences needle haystack)
...)
So with this you can imagine searching for the pattern (count-occurences '(a a) '(a a a a)). When it is found from the first element you need to search again on the next. Thus so that the result is 3 for the (a a a a) since the matches overlap. Every sublist except when it's the empty list involves using prefix?
Good luck!
(define (patt list1 list2)
(let ([patt_length (length list1)])
(let loop ([loop_list list2]
[sum 0])
(if (>= (length loop_list) patt_length)
(if (equal? list1 (take loop_list patt_length))
(loop (cdr loop_list) (add1 sum))
(loop (cdr loop_list) sum))
sum))))
After giving this homework problem a little time to marinate, I don't see the harm in posting additional answers -
(define (count pat xs)
(cond ((empty? xs)
0)
((match pat xs)
(+ 1 (count pat (cdr xs))))
(else
(count pat (cdr xs)))))
(define (match pat xs)
(cond ((empty? pat)
#t)
((empty? xs)
#f)
((and (list? pat)
(list? xs))
(and (match (car pat) (car xs))
(match (cdr pat) (cdr xs))))
(else
(eq? pat xs))))
(count '(a b c) '(a b c a b c d e a b c c c)) ;; 3
(count '((a b) c) '(a b (a b) c d e b c)) ;; 1
(count '(a a) '(a a a a)) ;; 3
I have created a function that takes a list as input and returns either a list or a atom. I want to apply this function to a deep list, starting with the inner lists, then finish once the function has been run on the outer list.
Can somebody give me some direction on this?
A sample input would be (a b (c (d e))) z) the function should compute on (d e) first with a result of say f. then the function should compute on (c f) with a result of say g then similarly on (a b g z) to produce an output of h.
An example function could be:
(define sum
(lambda (l)
(if (not (pair? l))
0
(+ (car l) (sum (cdr l))))))
Where input would be (1 2 (3 4) 5) > 15
Assuming your example transformation, expressed as a Scheme procedure:
(define (transform lst)
(case lst
(((d e)) 'f)
(((c f)) 'g)
(((a b g z)) 'h)
(else (error (~a "wot? " lst)))))
then what you are looking for seems to be
(define (f lst)
(transform
(map (lambda (e)
(if (list? e) (f e) e))
lst)))
Testing:
> (f '(a b (c (d e)) z))
'h
Here is an example:
(define product
(lambda (l)
(cond
[(number? l) l]
[(pair? l) (* (product (car l)) (product (cdr l)))]
[else 1])))
> (product '(1 2 (3 4) 5))
120
The program is suppose to pick out every third atom in a list.
Notice that the last atom 'p' should be picked up, but its not.
Any suggestions as to why the last atom is not being selected.
(define (every3rd lst)
(if (or (null? lst)
(null? (cdr lst)))
'()
(cons (car lst)
(every3rd (cdr(cdr(cdr lst)))))))
(every3rd '(a b c d e f g h i j k l m n o p))
Value 1: (a d g j m)
Thanks
You're missing a couple of base cases:
(define (every3rd lst)
(cond ((or (null? lst) (null? (cdr lst))) lst)
((null? (cdr (cdr lst))) (list (car lst)))
(else (cons (car lst)
(every3rd (cdr (cdr (cdr lst))))))))
See how the following cases should be handled:
(every3rd '())
=> '()
(every3rd '(a))
=> '(a)
(every3rd '(a b))
=> '(a)
(every3rd '(a b c))
=> '(a)
(every3rd '(a b c d))
=> '(a d)
(every3rd '(a b c d e f g h i j k l m n o p))
=> '(a d g j m p)
Fixing your code (covering the base cases)
It's worth noting that Scheme defines a number of c[ad]+r functions, so you can use (cdddr list) instead of (cdr (cdr (cdr list))):
(cdddr '(a b c d e f g h i))
;=> (d e f g h i)
Your code, as others have already pointed out, has the problem that it doesn't consider all of the base cases. As I see it, you have two base cases, and the second has two sub-cases:
if the list is empty, there are no elements to take at all, so you can only return the empty list.
if the list is non-empty, then there's at least one element to take, and you need to take it. However, when you recurse, there are two possibilies:
there are enough elements (three or more) and you can take the cdddr of the list; or
there are not enough elements, and the element that you took should be the last.
If you assume that <???> can somehow handle both of the subcases, then you can have this general structure:
(define (every3rd list)
(if (null? list)
'()
(cons (car list) <???>)))
Since you already know how to handle the empty list case, I think that a useful approach here is to blur the distinction between the two subcases, and simply say: "recurse on x where x is the cdddr of the list if it has one, and the empty list if it doesn't." It's easy enough to write a function maybe-cdddr that returns "the cdddr of a list if it has one, and the empty list if it doesn't":
(define (maybe-cdddr list)
(if (or (null? list)
(null? (cdr list))
(null? (cddr list)))
'()
(cdddr list)))
> (maybe-cdddr '(a b c d))
(d)
> (maybe-cdddr '(a b c))
()
> (maybe-cdddr '(a b))
()
> (maybe-cdddr '(a))
()
> (maybe-cdddr '())
()
Now you can combine these to get:
(define (every3rd list)
(if (null? list)
'()
(cons (car list) (every3rd (maybe-cdddr list)))))
> (every3rd '(a b c d e f g h i j k l m n o p))
(a d g j m)
A more modular approach
It's often easier to solve the more general problem first. In this case, that's taking each nth element from a list:
(define (take-each-nth list n)
;; Iterate down the list, accumulating elements
;; anytime that i=0. In general, each
;; step decrements i by 1, but when i=0, i
;; is reset to n-1.
(let recur ((list list) (i 0))
(cond ((null? list) '())
((zero? i) (cons (car list) (recur (cdr list) (- n 1))))
(else (recur (cdr list) (- i 1))))))
> (take-each-nth '(a b c d e f g h i j k l m n o p) 2)
(a c e g i k m o)
> (take-each-nth '(a b c d e f g h i j k l m n o p) 5)
(a f k p)
Once you've done that, it's easy to define the more particular case:
(define (every3rd list)
(take-each-nth list 3))
> (every3rd '(a b c d e f g h i j k l m n o p))
(a d g j m)
This has the advantage that you can now more easily improve the general case and maintain the same interface every3rd without having to make any changes. For instance, the implementation of take-each-nth uses some stack space in the recursive, but non-tail call in the second case. By using an accumulator, we can built the result list in reverse order, and return it when we reach the end of the list:
(define (take-each-nth list n)
;; This loop is like the one above, but uses an accumulator
;; to make all the recursive calls in tail position. When
;; i=0, a new element is added to results, and i is reset to
;; n-1. If i≠0, then i is decremented and nothing is added
;; to the results. When the list is finally empty, the
;; results are returned in reverse order.
(let recur ((list list) (i 0) (results '()))
(cond ((null? list) (reverse results))
((zero? i) (recur (cdr list) (- n 1) (cons (car list) results)))
(else (recur (cdr list) (- i 1) results)))))
It is because (null? '()) is true. you can debug what's happening with following code
(define (every3rd lst)
(if (begin
(display lst)
(newline)
(or (null? lst)
(null? (cdr lst))))
'()
(cons (car lst)
(every3rd (cdr(cdr(cdr lst)))))))
(every3rd '(a b c d e f g h i j k l m n o p))
(newline)
(display (cdr '(p)))
(newline)
(display (null? '()))
(newline)
(display (null? (cdr '(p))))
(newline)
this gives following result.
(a b c d e f g h i j k l m n o p)
(d e f g h i j k l m n o p)
(g h i j k l m n o p)
(j k l m n o p)
(m n o p)
(p)
()
#t
#t
Im want to make a function where rootcheck has a list L as input, L always is 3 atoms (a b c) where a is coefficient of x^2, b coef of x and c is the constant. it checks if the equation is quadratic, using discriminant (b^2 - 4ac) and should output this (num 'L) where num is the number of roots and L is a list that contains the roots themselves (using quadratic formula), L is empty in case of no roots. here is my code:
(define roots-2
(lambda (L)
(let ((d (- (* (cdr L) (cdr L)) (4 (car L) (caddr L))))))
(cond ((< d 0) (cons(0 null)))
((= d 0) (cons(1 null)))
(else((> d 0) (cons(2 null)))))
))
its giving me no expression in body error.
also I tried to code the quadratic function and even tried some that are online, one compiled fint but gave me an error when I inserted input this is the code for the quadratic function, NOT MINE!
(define quadratic-solutions
(lambda (a b c) (list (root1 a b c) (root2 a b c))))
(define root1
(lambda (a b c) (/ (+ (- b) (sqrt (discriminant a b c)))
(* 2 a))))
(define root2
(lambda (a b c) (/ (- (- b) (sqrt (discriminant a b c)))
(*2 a))))
(define discriminant
(lambda (a b c) (- (square b) (* 4 (* a c)))))
There are several mistakes in the code:
Some parentheses are incorrectly placed, use a good IDE to detect such problems. This is causing the error reported, the let doesn't have a body
You forgot to multiply in the 4ac part
You're incorrectly accessing the second element in the list
The else part must not have a condition
The output list is not correctly constructed
This should fix the errors, now replace null with the actual call to the function that calculates the roots for the second and third cases (the (< d 0) case is fine as it is):
(define roots-2
(lambda (L)
(let ((d (- (* (cadr L) (cadr L)) (* 4 (car L) (caddr L)))))
(cond ((< d 0) (list 0 null))
((= d 0) (list 1 null))
(else (list 2 null))))))
for the quadractic function part, I found a code online and tweaked it to provide both roots of a quadratic equation. returns a list of both roots
(define (solve-quadratic-equation a b c)
(define disc (sqrt (- (* b b)
(* 4.0 a c))))
(list (/ (+ (- b) disc) (* 2.0 a))
(/ (- (- b) disc) (* 2.0 a))
))
(rotate '(a b c d e)) should return ( (a b c d e) (b c d e a) (c d e a b) (d e a b c) (e a b c d) )
Here I have implemented the logic in shceme but i am facing problem can anyone help me out sovling this
Here is my code
(define (rotate lst)
(define (iter l cycles result)
(cond
((= cycles 0) (cons lst result))
((< cycles 0) result)
(else (let ((cycled (cycle l)))
(iter cycled (- cycles 1) (append result (list cycled)))))))
(iter lst (- (length lst) 1) ()))
(rotate '(a b c d e))
You weren't that far:
(define (rotate lst)
(define (iter lst cycles res)
(cond
((= cycles 0) (reverse res))
(else (iter (append (cdr lst) (list (car lst)))
(- cycles 1)
(cons lst res)))))
(iter lst (length lst) null))
No need to make the distinction between cycles = 0, cycles > 0 and cycles < 0; one base case and one recursive case are enough
What is (cycle l)? Is it defined somewhere else?