Basic LISP recursion, enumerate values greater than 3 - recursion

I need a recursive LISP function that enumerates the number of elements in any list of numbers > 3. I'm not allowed to use lets, loops or whiles and can only use basic CAR, CDR, SETQ, COND, CONS, APPEND, PROGN, LIST...
This is my attempt at the function:
(defun foo (lst)
(COND ((null lst) lst)
(T (IF (> (CAR lst) 3)
(1+ (foo (CDR lst)))
(foo (CDR lst)) ) ) ) )
The function call:
(foo '(0 1 2 3 4 5 6))

Your code is pretty close to correct, just a small mistake in the base case:
For the empty list you return the empty list. So if you have the list (6), you add 6 to foo of the empty list, which is the empty list. That does not work because you can't add a number to a list.
You can easily fix it by making foo return 0 instead of lst when lst is empty.
As a style note: Mixing cond and if like this, seems a bit redundant. I would write it like this, using only cond instead:
(defun foo (lst)
(cond
((null lst)
0)
((> (car lst) 3)
(1+ (foo (cdr lst))))
(T
(foo (cdr lst)))))

Some stylistic points:
There's no need to put some Lisp built-ins in uppercase. It's not 1958 anymore!
But if you are going to put built-ins in uppercase, why not DEFUN and NULL?
You have an if inside the last branch of your cond. This is redundant. Since the purpose of cond is testing conditions, why not use it?
There's no need to space out your closing parentheses like that. No-one counts parentheses these days, we have parenthesis-matching editors.
Lisp has separate namespaces for functions and values, so you don't have to call your argument lst to avoid conflicting with the built-in function list.
If you were programming this for real, of course you'd use count-if:
(count-if #'(lambda (x) (> x 3)) '(0 1 2 3 4 5 6))
==> 3

One save you can have on duplication of the recursive call:
(defun foo (l)
(if (null l) 0 ; if list is empty, return 0
(+ (if (> (car l) 3) 1 0) ; else +1 if condition is satisfactory
(foo (cdr l))))) ; plus the result from the rest

Related

Racket macro that recursively processes a list argument

I'm trying to write a macro that recursively 'unwraps' the values of a list into individual values. For example, unwrap '(1 2 3)) would produce (separately):
(car '(1 2 3)) ; 1
(car (cdr '(1 2 3)) ; 2
(car (cdr (cdr '(1 2 3)) ; 3
This would be used like (+ (unwrap '(1 2 3))) ==> (+ 1 2 3). (I know you can use the standard libary apply for this, but I'm trying to write my own version).
My problem is that in writing the macro, I don't know how to recursively process the list argument passed into the unwrap macro. Here's what I've tried:
(define-syntax (unwrap stx)
(syntax-case stx ()
[(_ lst)
#`(begin (car lst) ; error at the last step since (car '()) is invalid
(unwrap (cdr lst)))]))
or
(define-syntax (unwrap stx)
(syntax-case stx ()
[(_ lst)
#`(if (null? lst)
'()
(car (unwrap (cdr lst))))])) ; infinite loops
These are both obviously wrong, but essentially I don't know write a macro that check the value of the input list (or matches against an empty list pattern) and returns something different in either scenario. It's also possible I'm approaching this entirely wrong, so any help would be greatly appreciated. Thank you!
You want
(+ (unwrap '(1 2 3))) ==> (+ 1 2 3)
but this is impossible. You are asking for unwrap to macroexpand to three disconnected forms, which is not allowed. Any macro must expand into exactly one form. So as you say in your question, for the example you gave, apply is the right answer.
For other possible usages, the answer is to back up a step and ask why you think this unwrap function would be useful: what cases do you hope to use it in? Then design a different solution, that works within the constraints of the language.

Common lisp recursive macro in matrix addition

I have to write a recursive macro for list addition in Common Lisp (homework). What I have so far is :
(defmacro matrix-add-row (r1 r2 sum_row)
(if (not (and r1 r2)) `sum_row
(progn
`(matrix-add-row (cdr r1) (cdr r2) (cons sum_row (+ (car r1) (car r2))))
(reverse sum_row)
)
)
)
I call this function with
(matrix-add-row `(1 2) `(3 4) ())
and as an output I get unvaluated code instead of numbers (which leads going to infinite loop).
How to put , ` properly (or call the macro properly)?
Firstly, to me this seems a rather bizarre thing to do with a macro. I assume the point is that you use the macro to transform (matrix-add-row '(1 2) '(3 4)) to an explicit list of sums like (list (+ 1 3) (+ 2 4)).
Also, what you have written has several problems which look like you don't quite understand how the backtick works. So I think the easiest way to help is to solve an example for you.
Since this is homework, I'm going to solve a different (but similar) question. You should be able to take the answer and use it for your example. Suppose I want to solve the following:
Write a macro, diffs, which computes all differences of pairs of successive elements in a list. For example,
(diffs '(1 2 3)) should expand to (list (- 2 1) (- 3 2)), which will then evaluate to (1 1).
Note that my macro won't do the actual subtraction, so I can use it even if I don't know some of the numbers until runtime. (The reason I think this sort of question is a bit weird is that it does need to know the length of the list at compile time).
My solution is going to be used as a macro with one argument but if I want to use recursion I'll need to pass in an accumulator too, which I can start with nil. So I write something like this:
(defmacro diffs (lst &optional accumulator)
...)
Now what do I do with lst? If lst is nil, I want to bottom out and just return the accumulator, with a call to list at the front, which will be code to make my list. Something like this:
(defmacro diffs (lst &optional accumulator)
(cond
((null lst)
;; You could write `(list ,#accumulator) instead, but that seems
;; unnecessarily obfuscated.
(cons 'list accumulator))
(t
(error "Aargh. Unhandled"))))
Let's try it!
CL-USER> (diffs nil)
NIL
Not hugely exciting, but it looks plausible. Now use macroexpand, which just does the expansion without the evaluation:
CL-USER> (macroexpand '(diffs nil))
(LIST)
T
And what if we'd already got some stuff from a recursion?
CL-USER> (macroexpand '(diffs nil ((- a b) (- b c))))
(LIST (- A B) (- B C))
T
Looks good! Now we need to deal with the case when there's an actual list there. The test you want is consp and (for my example) it only makes sense when there's at least two elements.
(defmacro diffs (lst &optional accumulator)
(cond
;; A list of at least two elements
((and (consp lst) (consp (cdr lst)))
(list 'diffs (cdr lst)
(cons (list '- (cadr lst) (car lst)) accumulator)))
;; A list with at most one element
((listp lst)
(cons 'list accumulator))
(t
(error "Aargh. Unhandled"))))
This seems almost to work:
CL-USER> (macroexpand '(diffs (3 4 5)))
(LIST (- 5 4) (- 4 3))
T
but for two problems:
The list comes out backwards
The code is a bit horrible when we actually construct the recursive expansion
Let's fix the second part first by using the backtick operator:
(defmacro diffs (lst &optional accumulator)
(cond
;; A list of at least two elements
((and (consp lst) (consp (cdr lst)))
`(diffs ,(cdr lst)
,(cons `(- ,(cadr lst) ,(car lst)) accumulator)))
;; A list with at most one element
((listp lst)
(cons 'list accumulator))
(t
(error "Aargh. Unhandled"))))
Hmm, it's not actually much shorter, but I think it's clearer.
For the second part, we could proceed by adding each item to the end of the accumulator rather than the front, but that's not particularly quick in Lisp because lists are singly linked. Better is to construct the accumulator backwards and then reverse it at the end:
(defmacro diffs (lst &optional accumulator)
(cond
;; A list of at least two elements
((and (consp lst) (consp (cdr lst)))
`(diffs ,(cdr lst)
,(cons `(- ,(cadr lst) ,(car lst)) accumulator)))
;; A list with at most one element
((listp lst)
(cons 'list (reverse accumulator)))
(t
(error "Aargh. Unhandled"))))
Now we get:
CL-USER> (macroexpand '(diffs (3 4 5)))
(LIST (- 4 3) (- 5 4))
T
Much better!
Two last things. Firstly, I still have an error clause in my macro. Can you see how to trigger it? Can you think of a better behaviour than just outputting an error? (Your macro is going to have to deal with the same problem)
Secondly, for debugging recursive macros like this, I recommend using macroexpand-1 which just unfolds one level at once. For example:
CL-USER> (macroexpand-1 '(diffs (3 4 5)))
(DIFFS (4 5) ((- 4 3)))
T
CL-USER> (macroexpand-1 *)
(DIFFS (5) ((- 5 4) (- 4 3)))
T
CL-USER> (macroexpand-1 *)
(LIST (- 4 3) (- 5 4))
T
There are two problems with your logic. First you are calling reverse on each iteration instead of at the end of the iteration. Then you are accumulating the new values, through cons, in the cdr of the cons cell as opposed to the car.
Also I don't see why this have to be a macro so using a function.
(defun matrix-add-row (r1 r2 sum-row)
(if (or (endp r1) (endp r2))
(reverse sum-row)
(matrix-add-row (cdr r1)
(cdr r2)
(cons (+ (car r1) (car r2))
sum-row))))
(matrix-add-row '(1 2) '(3 4) ())
;; => (4 6)

Adding numbers from a list (e.g. asdf125dkf will return 8)

I need a function that will take in a list of characters and numbers, and then return the numbers added up (ignoring the characters). This is what I have so far:
(define (adder lst)
(cond
((null? lst)
0)
((number? (car lst))
(+(adder (car lst)) (adder (cdr lst))))
((char? (car lst))
((adder(cdr lst))))
))
(display (adder '(asd12sdf)))
Running it on codepad.org just displays void. I know the code is wrong because it looks wrong, but I have no idea how to fix it... How do I have the function keep track of the first number it finds and add it to the next one it finds, while skipping all characters?
In your second cond case, there's no reason to run adder on (car lst). Just adding (car list) itself to the recursive step should work.
For the last line, don't test (char? (car lst)). Just make the last line the else clause, meaning that anything BUT a number will go to the else line.
The reason you're getting void is because your input doesn't satisfy any of the cond conditions, and you have no else, so the answer is nothing (i.e. (void)).
The last mistake is in the input you're giving it. '(asd12sdf) is literally a list with one symbol named "asd12sdf". I think you want to give it '(a s d 1 2 s d f) (a list of 6 symbols and 2 numbers) which should result in 3. Notice that there's a very important difference between the symbol 'a and the character #\a.
It looks like you have the logic down, so your problem doesn't seem to be functional languages, just Scheme's syntax.
Edit: and in the last line, you have ((adder(cdr lst))) which has one too many parens wrapped around it. That will cause Scheme to attempt to evaluate the result of adder (which is a number) as a procedure (error!).
You should observe that this function is more or less sum which can be defined simply by using fold.
(define (adder lst)
(fold + 0 lst))
What does fold do? Basically, it's defined like so:
(define (fold f initial lst)
(if (null? lst)
initial
(fold f (f (car lst) initial) (cdr lst))))
(In other words, it calls f, a function of 2 arguments, on each element of lst, using the car of the lst as the first argument, and the accumulated result as the second argument to f.)
The issue here which you need to address is that + doesn't know how to operate on non-numeric values. No problem, you've already dealt with that. What happens if it's a character instead? Well, you're not adding anything to the total value, so replace it with a 0. Therefore, your solution is as simple as:
(define (adder lst)
(fold your-new-protected-+ 0 lst))
In Common Lisp:
(reduce #'+ '(1 #\a #\b 2 1 2 #\c #\d 4)
:key (lambda (item) (if (numberp item) item 0)))
or
(loop for item in '(1 #\a #\b 2 1 2 #\c #\d 4)
when (numberp item) sum item)

How would one interleave elements of 2 lists in LISP?

Given 2 lists, how can you produce an output of a 3rd list which has its elements as an interleaved set of L1 and L2? If they are uneven length, nil should be inserted for holes. On a second note, how can I reverse a list? I am super new to LISP and simply modifying existing code... I'd really love to have a good explanation, not just code.
First, I guess you use Common Lisp, as it is the one most used in Lisp courses. So, my examples will be in CL. If you use Scheme, you will get almost the same code. If modern Clojure, it will need some changes, through an idea will be the same.
Interleave
To interleave 2 lists you must go through both of them, collecting elements by turns. You can use loop statement or recursion for this. I'll use recursion since it has more functional style and may be used in any lisp, not only CL. Also note, that there's a feature called tail recursion, which lets you write recursive function that will be compiled to a loop.
So, base skeleton for our function will be:
(defun interleave (l1 l2)
??????
(interleave ?????))
To collect items in recursive functions you will need to return them from each call and then cons together (for a tail recursion you must have one more parameter, which will accumulate values). So, the end of the function will be (cons current-value (interleave ????)).
Also you must alternate lists to take elements from with each other. You may have additional parameter, but you also may just swap them in a recursive call. So, code becomes:
(defun interleave (l1 l2)
?????
(cons current-value (interleave l2 l1)))
Any recursion must stop somewhere. In this case, it must stop when both lists are empty (nil).
This is one condition (let give it number 1), and there are some more conditions:
2. if the list to take from is empty, and the other one is not, we must take nil instead.
3. if both lists are not empty, take first element as a current-value and proceed with it's tail.
There's only one more condition that 2 lists can be in: list to take from is not empty, and the second one is. But in fact we don't care about this and may go forward with a rule number 3.
So, the code (and this is the final one):
(defun interleave (l1 l2)
(cond ((and (eql l1 nil) (eql l2 nil)) nil) ;; rule #1
((eql l1 nil) (cons nil (interleave l2 l1))) ;; rule #2, current value is nil
(true (cons (first l1) (interleave l2 (rest l1)))))) ;; rule #3 in all other cases
Reverse
I'll show two implementations of this function: one with cond and another with built-in reduce function which is extremely useful in practice.
First approach for cond version is to go through the all list with a recursive calls and then go back, collecting elements:
(defun reverse-1-1 (li)
(if (eql li nil)
nil
(append (reverse-1-1 (rest li))
(list (first li)))))
But this is extremely inefficient, since append is O(n), and you must pass n elements, so the final complexity is O(n^2).
To reduce it you may use one more argument to the function (and make it tail recursive, if compiler lets you):
(defun reverse-1-2 (li)
(reverse-aux li nil))
(defun reverse-aux (li accumulator)
(if (eql li nil)
accumulator
(reverse-aux (rest li) (cons (first li) accumulator))))
That's you use one more parameter to collect your elements in while passing through the list, and then just return this accumulator.
There's one more interesting option. Lisp has extremely powerful function reduce (in other functional languages it is sometimes called fold, foldr, foldl or something like that). You may find description for it here, and I'll just show an example:
(defun reverse-2 (li)
(reduce #'cons li :from-end t :initial-value nil))
:from-end tells function to go through the the list from the end, and :initial-value tells to use as the very first reduced argument nil.
Note: in some implementations reduce with option :from-end true may first reverse list by itself, so if you need to create it from scratch or use the most efficient version, use reverse-1-2 instead.
In Common Lisp:
(defun merge-lists (lst1 lst2)
(let ((m (max (length lst1) (length lst2))))
(flatten (mapcar (lambda (a b) (list a b))
(append-nulls lst1 m)
(append-nulls lst2 m)))))
Examples:
(merge-lists '(1 2 3 4) '(5 6 7 8)) ;; => (1 5 2 6 3 7 4 8)
(merge-lists '(1 2 3 4) '(5 6 7)) ;; => (1 5 2 6 3 7 4 NULL)
(merge-lists '(1 2) '(5 6 7 8)) ;; => (1 5 2 6 NULL 7 NULL 8)
The helper functions flatten and append-nulls:
(defun flatten (tree)
(let ((result '()))
(labels ((scan (item)
(if (listp item)
(map nil #'scan item)
(push item result))))
(scan tree))
(nreverse result)))
(defun append-nulls (lst n)
(if (< (length lst) n)
(dotimes (i (- n (length lst)))
(setq lst (append lst (list 'null)))))
lst)
The answer above:
(defun interleave (l1 l2)
(cond ((and (eql l1 nil) (eql l2 nil)) nil) ;; rule #1
((eql l1 nil) (cons nil (interleave l2 l1))) ;; rule #2, current value is nil
(true (cons (first l1) (interleave l2 (rest l1)))))) ;; rule #3 in all other cases
If one of your lists is longer than the other, you will get something like (1 2 3 4 nil 5).
Replace:
((eql l1 nil) (cons nil (interleave l2 l1)))
with:
((null l1) l2)
:P
An example of a more idiomatic solution in Common Lisp:
(defun interleave (a b)
(flet ((nil-pad (list on-list)
(append list (make-list (max 0 (- (length on-list) (length list)))))))
(loop for x in (nil-pad a b)
for y in (nil-pad b a)
append (list x y))))

Scheme accumulative recursion with lists

How can I pass a list as a parameter to a function adding elements to it recursively,and have it unmodified when it comes out of recursion?
I want to use the list at each level of recursion with the list having the values added by deeper recursion levels.
To be more specific I want to do a DFS search on a graph and I want to store in the list the nodes I visited.
One method of doing this is just to return the list so you have access to it at higher levels of recursion.
Another method is to have your list be stored in a variable outside of the recursion. In other words not stored on the stack. Since it is not a good idea to use a global variable for this we need to have some local recursion.
The following code is a foolish way to reverse a list but it does illustrate the technique I am talking about.
(define (letrecreverse lst)
(letrec ((retlist '())
(reverse (lambda (lst)
(if (null? lst)
'()
(begin
(set! retlist (cons (car lst) retlist))
(reverse (cdr lst)))))))
(reverse lst)
retlist))
(letrecreverse '(1 2 3 4))
;outputs '(4 3 2 1)
Can you adopt this technique for your purposes?
If you build a new list by consing a value onto an old list, that old list is unmodified.
(define old '(1 2 3))
(define new (cons 55 old))
new
>(55 1 2 3)
old
>(1 2 3)
The 'tail' of the first cons in "new" is the list "old". But old hasn't changed.
(cdr new)
> (1 2 3)
If I understood your question correctly, this could be one solution:
;; Just a helper to print the current list.
(define (show list)
(display "list = ")
(display list)
(newline)
(flush-output))
;; Maximum depth of recursion
(define max-recur 5)
;; Original list is backed-up here.
(define orig-list null)
(define (recur list depth)
(if (null? orig-list)
(set! orig-list list))
(cond ((< depth max-recur)
(show list)
(recur (cons (random max-recur) list) (add1 depth)))
(else orig-list)))
Sample run:
> (recur '(1) 0)
list = (1)
list = (1 1)
list = (2 1 1)
list = (3 2 1 1)
list = (4 3 2 1 1)
(1) ;; In the end you get the original list back.

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