I have trouble with doing quicksort in Lisp.
My objective is:
If a list contains 0 or 1 element, it is already sorted. Otherwise sort it as follows: First get the pivot, which is the first element of the list. Now go through the rest of the list (by using DOLIST), compare each element with the pivot. If an element is less than or equal to the pivot, put it in the left-sublist, otherwise put it in the right-sublist (by using CONS or APPEND). Then call Qsort to sort left-sublist and right-sublist. Finally, combine left-sublist, pivot, and right-sublist into one sorted list.
This is my code:
(defun qsort (x)
(if (>= 1 (length x))
(format t"~%~s is already sorted" x)
((let (pivot (first x))
(dolist (i x )
(if (>= pivot (nth i x))
(list y (nth i))
(list z (nth i))))
(appned y z)))))
yet I seem to hit the wall by getting
Badly formed lambda: (LET (PIVOT (FIRST X)) (DOLIST (I X PIVOT) (IF (>= PIVOT (NTH I X)) (LIST PIVOT (NTH I)) (LIST PIVOT (NTH I)))))
from the compiler.
I hope you can help. Thank you.
Why are there two layers of parentheses around LET?
Why is there a layer of parentheses missing inside LET around the bindings?
Why do you call (nth i x) ? Why with i?
Why do you call NTH with one argument, when it takes two?
What function is APPNED? There is no function of that name.
(>= x 1) is (plusp x)
and more...
Related
In my else condition I have two statements to execute. The first one ought to append my calculation to my return-list and the second one calls my recursive procedure again.
The problem is that my append procedure is being ignored so I am just returning an empty list.
(define (calcit x lst)
(cond ((= x 0)
retlst)
(else (append (list (floor (/ x (first lst)))) retlst)
(calcit (modulo x (first lst)) (rest lst)))))
You need to do something with the data you are creating. You probably want to have the first element consed on the result of the list you get from the recursion:
(define (calcit x lst)
(if (= x 0)
'() ;; base case
(cons (floor (/ x (first lst)))
(calcit (modulo x (first lst)) (rest lst)))))
When creating lists in Scheme with recursion try to avoid append. Using append is an anti pattern. Learn how Scheme lists work and train to know it intimately. eg '((2 3) (4 5)) if I ask you how to get 5 from that you should think d a d a and answer cadadr almost right away.
I want to test this list whether it's palindrome or not by comparing first element with last element , second element with before the last element and so on
(setq l '(1 5 7 8 8 7 5 1))
(defun f (l)
(cond ((null l) 0)
((atom l) l)
(if (equal (car l) (car(cdr l))))
Is there a reason for this way of comparing them? If not, it would be easier to use the reverse function:
(defun palindrome-p (l)
(equal l (reverse l)))
The #Pascal solution reverses the entire list to check if it is palindrome, but this is not necessary. Why not reverse only half of it?
(defun palindrome-p (l)
(let* ((half (floor (length l) 2))
(secondhalf (reverse (nthcdr half l))))
(loop for x in l
for y in secondhalf
always (eq x y))))
This solution (which, I have to admit, is more “common-lispy” and less “lispy”) allocates only half of memory of the solution that reverses the entire list, and in CCL, on my laptop, for long lists uses less then half time.
Another option that conses only half the list:
(defun palindrome-p (list)
(let* ((length (length list))
;; The following lists will NOT include the middle element if length is odd
(half-length (ceiling length 2))
(tail (nthcdr half-length list))
(reversed-head (nreverse (butlast list half-length))))
(equal tail reversed-head)))
The thing about this option is that you get two lists of similar length, you don't have to worry about whether iteration stops at the smallest one, and it's easier to adapt and debug later for other purposes.
Yet another option that is usually disregarded is to copy the whole list into a vector. Most implementations take 1 or 2 architecture words (32-bit/64-bit) to represent a cons, thus the worst case for a list is:
2 × length words
These same implementations take about 1 to 2 words for the vector's header, plus 1 word per element, thus the worst case for a vector is:
2 + length words
What I mean is, you'll have about the same memory allocation cost for consing half of the list compared to copying the whole list into a vector.
The compromise is to find out when the header is no longer much of an overhead compared to consing and (n)reversing the list, or from accessing the nth element of a not-that-small list.
If this threshold is found, I'd redefine it as follows, making it accept a sequence:
;; Mere example, I did not research this on any implementation
(defconstant +list-to-vector-overhead-threshold+ 8)
(defun palindrome-p (sequence)
(if (and (consp sequence)
(not (null (nthcdr +list-to-vector-overhead-threshold+ sequence))
(palindrome-p (concatenate 'vector sequence)
(let ((length (length sequence)))
(dotimes (i (floor length 2))
(when (not (equal (elt sequence i) (elt sequence (- length i 1))))
(return nil)))
t)))
PS: Here's some implementations' object sizes found by experimentation (meaning, I might be wrong about these numbers) with 32-bit implementations:
Allegro CL
List: 2 × length words
Vector: 2 + length words, 2 words aligned (i.e. in 32-bit, 8-byte aligned)
Clozure CL
List: 2 × length words
Vector: 1 + length words, 2 words aligned (i.e. in 32-bit, 8-byte aligned)
LispWorks
List: 3 × length words
Vector: 2 + length words
SBCL
List: 2 × length words
Vector: 2 + length words
; Get the reverse of a list
(defun revList (l)
(cond
((null (cdr l)) l)
(t (append (revList (cdr l)) (list(car l) ) ))
)
)
; Check whether a given a list is a palindrome
(defun palindrome (l)
(cond ((null l) t)
((equal (car l) (car (last l)))(palindrome (cdr (revList (cdr l)))))
)
)
This implements a recursive function that returns (t) if a string (represented as a flat list of atoms) is a palindrome and (nil) otherwise. you can use the built-in "reverse" lisp function instead of "revList".
(defun palind (l1)
(if (equal l1 (reverse l1))
'palindrome
'no-palindrome))
I have two lists as follows:
(x y z) & (2 1)
and I want to have a result like:
((x y) (z))
The relation of the lists is quite clear. So basically I want to rearrange the members of the first list into a list of lists with two (length of second list) lists.
I have tried running two dotimes iterations to do this:
(let ((result) (list1* list1))
(dotimes (n (length list2) result)
(progn (setq result
(append result
(list (let ((result2))
(dotimes (m (nth n list2) result2)
(setq result2
(append result2
(list (nth m list1*)))))))))
(setq list1*
(subseq list1* 0 (nth n list2))))))
The idea is that I make the first list of the expected result (x y), and then I want to update the (x y z) list so that the x any y are removed and I only have (z). Then the loop runs again to get the (z) list in the expected result. This does not work correctly and results in:
((x y) (x))
which means apparently the second command for progn which is basically updating the list1* is not working. Clearly there must be a correct and better way of doing this and I was wondering whether anyone can help with this. Also explain why it is not possible to have the solution explained?
If I see that right, your problem is in (subseq list1* 0 (nth n list2)), which returns the part of the list that you do not want.
I have the following to offer:
(defun partition-list (list lengths)
(mapcar (lambda (length)
(loop :repeat length
:collect (pop list)))
lengths))
This is a bit simplistic, of course, as it does not handle unexpected input, such as (length list) being smaller than (reduce #'+ lengths), but it can be expanded upon.
Just for the sake of example, an alternative using iterate:
(defun partition-list (list by)
(iter:iter
(iter:for element in list)
(iter:for i from 1)
(iter:generating measure in by)
(iter:collect element into sublist)
(when (= (or measure (iter:next measure)) i)
(iter:collect sublist)
(iter:next measure)
(setf i 0 sublist nil))))
I apologize for the bad English..
I have a task to write a function called "make-bag" that counts occurences of every value in a list
and returns a list of dotted pairs like this: '((value1 . num-occurences1) (value2 . num-occurences2) ...)
For example:
(make-bag '(d c a b b c a))
((d . 1) (c . 2) (a . 2) (b . 2))
(the list doesn't have to be sorted)
Our lecturer allows us to us functions MAPCAR and also FILTER (suppose it is implemented),
but we are not allowed to use REMOVE-DUPLICATES and COUNT-IF.
He also demands that we will use recursion.
Is there a way to count every value only once without removing duplicates?
And if there is a way, can it be done by recursion?
First of, I agree with Mr. Joswig - Stackoverflow isn't a place to ask for answers to homework. But, I will answer your question in a way that you may not be able to use it directly without some extra digging and being able to understand how hash-tables and lexical closures work. Which in it's turn will be a good exercise for your advancement.
Is there a way to count every value only once without removing duplicates? And if there is a way, can it be done by recursion?
Yes, it's straight forward with hash-tables, here are two examples:
;; no state stored
(defun make-bag (lst)
(let ((hs (make-hash-table)))
(labels ((%make-bag (lst)
(if lst
(multiple-value-bind (val exists)
(gethash (car lst) hs)
(if exists
(setf (gethash (car lst) hs) (1+ val))
(setf (gethash (car lst) hs) 1))
(%make-bag (cdr lst)))
hs)))
(%make-bag lst))))
Now, if you try evaluate this form twice, you will get the same answer each time:
(gethash 'a (make-bag '(a a a a b b b c c b a 1 2 2 1 3 3 4 5 55)))
> 5
> T
(gethash 'a (make-bag '(a a a a b b b c c b a 1 2 2 1 3 3 4 5 55)))
> 5
> T
And this is a second example:
;; state is stored....
(let ((hs (make-hash-table)))
(defun make-bag (lst)
(if lst
(multiple-value-bind (val exists)
(gethash (car lst) hs)
(if exists
(setf (gethash (car lst) hs) (1+ val))
(setf (gethash (car lst) hs) 1))
(make-bag (cdr lst)))
hs)))
Now, if you try to evaluate this form twice, you will get answer doubled the second time:
(gethash 'x (make-bag '(x x x y y x z z z z x)))
> 5
> T
(gethash 'x (make-bag '(x x x y y x z z z z x)))
> 10
> T
Why did the answer doubled?
How to convert contents of a hash table to an assoc list?
Also note that recursive functions usually "eat" lists, and sometimes have an accumulator that accumulates the results of each step, which is returned at the end. Without hash-tables and ability of using remove-duplicates/count-if, logic gets a bit convoluted since you are forced to use basic functions.
Well, here's the answer, but to make it a little bit more useful as a learning exercise, I'm going to leave some blanks, you'll have to fill.
Also note that using a hash table for this task would be more advantageous because the access time to an element stored in a hash table is fixed (and usually very small), while the access time to an element stored in a list has linear complexity, so would grow with longer lists.
(defun make-bag (list)
(let (result)
(labels ((%make-bag (list)
(when list
(let ((key (assoc (car <??>) <??>)))
(if key (incf (cdr key))
(setq <??>
(cons (cons (car <??>) 1) <??>)))
(%make-bag (cdr <??>))))))
(%make-bag list))
result))
There may be variations of this function, but they would be roughly based on the same principle.
I'm trying to write a function in Common Lisp similar to the built in position function, that returns a list of the positions of all elements in the haystack that match the needle, as opposed to just the first. I've come up with a few possible solutions (for example recursively searching for the next element using a cdr-from function on the position and adding the result to the previous position) but none of the approaches I've come up with so far seem particularly elegant.
Can anyone suggest what would be the best way of approaching this, as I'm currently struggling.
The obvious way to solve the problem is just to look at each element of the list in turn, and each time one compares as equal to the needle collect its position into an output list. Getting the position is very easy in this case, because we are starting from the beginning of haystack; we can use a variable to count the current position starting from 0.
So if we describe the full algorithm in a sentence, we'd say something like "to find all the positions of a needle in a haystack, for each element in the haystack, and the position starting from 0, when the element is equal to the needle, collect the position."
The LOOP facility is basically the right thing to break out when you want to do iterative processing. Even though its syntax is complicated to describe formally, after some experience you can pretty much just put the English-language description of the algorithm in the body of LOOP and it will work.
(defun all-positions (needle haystack)
(loop
for element in haystack
and position from 0
when (eql element needle)
collect position))
Take this one with a grain of salt (and be sure to load Alexandria beforehand):
(defun positions (item sequence &key (test #'eql))
(mapcar #'car
(remove item (map 'list #'cons (alexandria:iota (length sequence)) sequence)
:test-not test
:key #'cdr)))
That said, it does have the advantage of working on arbitrary sequences:
CL-USER> (positions 'x #(x x y y x x y y))
(0 1 4 5)
CL-USER> (positions 5 (list 5.0 -1 5 5.0 -1) :test #'=)
(0 2 3)
CL-USER> (positions #\l "Hello")
(2 3)
If you want a recursive function, rather than a (loop ...) based one, you could use something like:
(defun all-positions (needle haystack)
(labels ((f (n h c r)
(if (null h)
r
(if (eql (car h) n)
(f n (cdr h) (1+ c) (cons c r))
(f n (cdr h) (1+ c) r))))))
(reverse (f needle haystack 0 nil)))
Here's another (not necessarily better) way to do it.
(defun get-positions (needle haystack)
(let ((result nil))
(dotimes (i (length haystack))
(if (eq (nth i haystack) needle)
(push i result)))
(nreverse result)))