Define a SCHEME procedure, named (tree-sort l), which takes a list of numbers and outputs the same
list, but in sorted order. Your procedure should sort the list by
(a) inserting the numbers into a binary search tree and, then,
(b) extracting from the binary search tree a list of the elements in sorted order.
To get started, write a procedure called (insert-list L T) which takes a list of numbers L and a binary
search tree T, and returns the tree that results by inserting all numbers from L into T. (Place the argument
L first, so a call to your function should have the form (insert-list L T), where L is a list and T is a
(perhaps empty) binary search tree.)
Then write a function called sort-extract which takes a binary search tree and outputs the elements of
the tree in sorted order. (We did this in class!)
Finally, put these two functions together to achieve (tree-sort l). (Note, all three of these functions
will be graded, so your solutions must consist of three top-level functions, insert-list, sort-extract,
and tree-sort.)
(define (insert-list insert-elements T)
(if (null? insert-elements)
T
(insert-list (cdr insert-elements)
(insert-list (car insert-elements) T))))
(insert-list (list 12) (list 15 (list) (list)))
mcdr: contract violation
expected: mpair?
given: 12
You are getting contract violations because you are calling insert-list with the car which is 12. Since it is not null? you'll try to do car and cdr of it. What is the cdr of 12?
Also for me it seems strange that you are not calling the procedure to add an element to a tree from insert-list. I can't think of any good reason to combine those two procedures in one.
If you had a procedure that takes a value and a tree and returns a tree with that value added you can do this:
(define (insert-list lst tree)
(foldl insert tree lst))
Eg.
(insert-list '(5 2 4) '()) ; ==>
(insert 4 (insert 2 (insert 5 '())))
Related
I'm trying to check if a parameter before use it in a function with racket. This parameter must be a list of lists.
I have tried:
(andmap (lambda (x) (not (and (list? x) (not (pair? x))))) lst)
with:
(define lst '('(a) '(b) '(c)))
But it fails because (pair? '(a)) is true. With pair? I'm trying to avoid (a . 1) dotted pairs because (list? (a . 1)) is also true.
How can I check if a list is a list of lists and doesn't contains dotter pairs?
Three things:
To check if a list is a list of lists, you can simply write
(define (list-of-lists? v)
(and (list? v) (andmap list? v)))
which first checks if the value is a list, then checks if all its elements are lists.
If you are doing this because a function should only accept a list of lists, and other values are illegal, then you should make things easier for yourself by using Racket’s contract system instead of doing the validation yourself:
(require racket/contract)
(define/contract (f lst-of-lsts)
(-> (listof list?) any/c)
#| do something here |#)
You, like many people exposed to it for the first time, seem to have some confusion about how quote works. You probably mean to write '((a) (b) (c)), not '('(a) '(b) '(c)). Please read What is the difference between quote and list?, or just use the list function.
i'm having a problem with this lisp function. I want to create a function that receives two lists, and verifies if the elements of the first list (all of them) occur in the second list, it returns True if this happens.
Currently i have the following code:
(defun ocorre-listas (l1 l2)
(dolist (elem1 l1)
(dolist (elem2 l2)
(if (equal elem1 elem2)
t))))
It's not working, as expected. Should i try to do it just with a simple recursion? I'm really not getting how i can iterate both lists in search of equal elements.
I decided to try without the dolists. This is what i have now, it's still not working.
(defun ocorre-listas (l1 l2)
(cond ((null l1) nil)
((null l2) nil)
((if (/= (first l1)(first l2)) (ocorre-listas l1 (rest l2))))
(t (if (= (first l1) (first l2)) (ocorre-listas (rest l1)(rest l2))))))
I get a warning saying that "t" is an undefined function. Also, every example i try returns null. What am i doing wrong ?
In the second piece of code, if the first list is empty then all of its elements are in the second one.
You don't need the ifs since you are inside a cond
After test if the lists are empty, you'll only need to test if the first element of the first list is in the second one and call the function again with the first list without this element
Instead of trying to do everything in one function, consider splitting it into two (or more) functions, e.g.
One that takes a number and the second list, and tests whether the number appears in the list
Another that iterates over the numbers in the first list, and for each one tests (using the first function) whether it appears in the second list.
As well as DOLIST, consider using MAPCAR and FIND-IF (assuming they are allowed in this assignment.)
So you need to check if every element of l1 is a member of l2. These are both functions in the Common Lisp standard library, so if you're allowed to use them, you can build a simple solution with them.
See the common lisp subsetp
predicate and its implementation:
CL-USER> (subsetp '(1 2 3) '(1 2 3 4)
T
To be able to work on both lists at the same time, the trick is probably to sort the lists before starting the recursion. Then it should be a simple matter of comparing the first element, and applying the same function to the rest of the list recursively, with some CAR/CDR magic added of course...
While there are many ways to do this, I would recommend using a hash table to avoid O(n^2) complexity. Using a hash table, you can achieve O(n) complexity.
here is a union function
(defun my-union (a b)
(let ((h (make-hash-table :test #'equal)))
(mapcar (lambda (x) (setf (gethash x h) x)) a)
(mapcan (lambda (x) (when (gethash x h) (list x))) b)))
here is a function testing for IDENTICAL elements in boths lists
(defun same-elements (a b)
(apply #'= (mapcar #'length (list (my-union a b) a b))))
here is a function making sure a is a subset of b (what you asked)
(defun subset (a b)
(same-elements (my-union a b) a))
I am trying to figure out how to find duplicate atom in possibly nested lists. I have been trying to figure this out all day. If you could please give me the logic, that would be great because I really want to learn.
basically
(findDup '(a b b)) would return t
(findDup '(a c ((d (f a)) s))) would also return t
The easiest and most efficient way would be the following (pseudocode):
Create a data structure (such as Common Lisp's hash table) to remembering which atoms were seen
Create a recursive sub-function that does the actual traversing - walking the nested lists and adding all new atoms to the data structure, and if one is already there, returning true
If the list is sorted or can be sorted, this is a simple solution:
(defun find-duplicates (lst)
(let ((dup-list nil))
(sort lst)
(mapcon (lambda (l) (when (eq (car l) (cadr l)) (push (car l) dup-list))) lst)
dup-list ))
This should take care of the first case:
(defun find-duplicates (lst)
(let ((h (make-hash-table))
(dupes))
(mapcar #'(lambda (x)
(if (gethash x h)
(push x dupes)
(setf (gethash x h) t)))
lst)
dupes))
If the list is empty/without an atomic car however deeply you go (e.g. (car (car (car ...))) recursively), then the answer is false.
You want to find the first atom of the list, and see if that atom occurs anywhere else in the list. You can do that with a function like member-of?—something similar is discussed in The Little Schemer, but basically you just test all the atoms in the list, and recur on lists, against that atom.
Then if that atom is in the list, you can return true.
Else, you'll try again (recur on) with the cdr of the list.
I'd start with a wrapper function that creates a hash table and passes the hash table and the list to a second function (alternatively, use a &optional argument, if you're using Common Lisp).
Then, the following pseudo-code should be enough:
If we're looking at an empty list, there are no duplicates
If the head is a list, we can return the logical OR of "inspect the head" and "inspect the tail"
If the head is an atom, it's a duplicate if it's already in the hash table. If not, add it to the hash table and inspect the tail for duplicates.
Let us say I have a list ((3 4 5) (d e f) (h i j) (5 5 5 5))
How can I get the last element of each list in such a way that the output would look like this (5 f j 5)?
Assuming this is about Common Lisp, there is a function last which returns a list containing the last item of a list. If you use this function with mapcan, which applies a given function to each element of a list and returns the concatenated results, you'll get what you want.
Note though that accessing the last element of a list is an O(N) operation, so if this isn't just homework after all, you might want to consider if you can't solve the real problem more efficiently than taking the last item of each list (maybe use another datastructure instead).
This, like most early LISPy homework problems is an exercise in thinking recursively and/or thinking in terms of induction. The way to start is to ask yourself simple questions that you can answer easily.
For example, if you had been asked to write something that gave you the first element in each list, I would thing about it this way:
Given a list of lists:
What is first-element of every list in the list '()? (easy - null)
What is first-element of every list in the list '(a)? (easy - a, or maybe an error)
What is first-element of every list in the list '((a))? (easy - (a))
What is first-element of any list in the form '(anything), where anything is a list? (easy - (first anything))
What is the first element of every list in the form '(anything morestuff)? (easy - (cons (first anything) (first-element morestuff)) )
What is first of an atom? either the atom or an error (depends on your point of view)
What is first of null? nil.
What is first of a list? (car list)
From here we can start writing code:
;; here's first, meeting questions 6-8
(define first (lambda (l)
(cond
((null? l) nil) ; Q7
((atom? l) l) ; Q6
(t (car l))))) ; Q8
;; with first we can write first-element, meeting questions 1-5
(define first-element (lambda (l)
(cond
((null? l) nil) ; Q1
((atom? l) (first l)) ; Q2
(t (cons (first (car l) (first-element (cdr l)))))))) ; Q4-5
Now this isn't your homework (intentionally). You should play with this and understand how it works. Your next goal should be to find out how this differs from your assignment and how to get there.
With respect to MAPCAR? Don't worry about it. You need to learn how to solve recursive problems first. Then you can worry about MAPCAR. What is the point of this assignment? To help you learn to think in this mode. Dang near everything in LISP/Scheme is solved by thinking this way.
The reason I went with all the questions to break it down into the parts that I'm worried about. If I'm given the task "how do I do foo on every item in a list?" I should answer the questions: How do I do handle null? How do handle an atom? How do I do handle on the first element on the list? How do I handle everything else? Once I've answered that, then I figure out how to actually do foo. How do I do foo on null? How do I do foo on an atom? How do I do foo on a list?
(defun get-last-lists (s)
(setq rt 'nil)
(loop for i from 0 to (- (length s) 1)
do (setq rt (append rt (last (nth i s)))))
(print rt))
as a beginner of lisp, i post my solution.
Write a procedure that returns the last element of a list, then learn a little about the built-in MAP (a.k.a. MAPCAR) procedure and see if any lightbulbs go off.
probably it is already solved, but I figured this out
; SELECT-FROM-INNER-LIST :: [list] -> [list]
(DEFUN SFIL (lst)
(COND ((NULL lst) NIL)
((LISTP (FIRST lst)) (APPEND (LAST (FIRST lst)) (SFIL (REST lst))))
))
Now, this works for legit list...so if you call function SFIL with correct list.... if not, it will return NIL
hopefully this will be helpful, for anyone who finds it
Given a list, I'm trying to return a new one that has only the items that appear more than once in the first list I receive as a parameter.
I have done the following:
(defun myf (lista)
(if (endp lista)
nil
(if (member (first lista) (rest lista))
(append (list (first lista)) (myf (rest lista)))
(myf (rest lista)))))
If I run the following: (myf '(A A B A B C)), it returns (A A B).
How can I make it return items only once (i.e., not have double "A")?
Once you've found that a letter is in the list more than once, you don't need to check it again, so you don't need it in the rest of the list. So you could modify the remaining list...
Note: this answer intentionally somewhat vague, since it's for homework and all. :)
The problem seems to be that you are checking to see if the first element of the list is in the tail of the list and appending it to the result list. The problem comes up when you come to the second instance of A, which when checked says yes it is in the tail because there is a 3rd instance of A in the list. If the input list had 4 A's then it would return 3 of them.
So to solve this need to check if A is already a member of the result list. That is, if first lista is not a member of list then append first lista to list.
Vincent, Gishu and Jerry hinted that you need to check if the item is already in the result list before appending to it, while Derek hinted that you could modify the original list when you see that an item is repeated.
Read the documentation of the functions adjoin and remove here:
http://www.lispworks.com/documentation/HyperSpec/Body/f_adjoin.htm
http://www.lispworks.com/documentation/HyperSpec/Body/f_rm_rm.htm
The HyperSpec is a very useful reference, add it your bookmarks.
Those two functions do not modify their arguments, but instead return the result as a new list. There are other functions that DO modify their arguments and thus might be more efficient, but at this point perhaps you shouldn't worry about them.
OK, I hope that by the time I have written this you have figured it out. If not, keep trying, that's the only way you'll really learn.
Now I'd like to talk to you about another approach, and that is about carrying the result through the recursive calls.
Our function repeated will do nothing but call a helper function repeatedr which will do the actual work, passing to it an initial empty result '():
(defun repeated (lst)
(repeatedr lst '()))
Now let's define the helper function, it receives two parameters: the list to search for duplicates, and the result list where we will accumulate the duplicate items.
(defun repeatedr (lst result)
(if (null lst)
result
(if (member (first lst) (rest lst))
(repeatedr (rest lst) (adjoin (first lst) result))
(repeatedr (rest lst) result))))
When the condition (member (first lst) (rest lst)) holds true we will adjoin the first item to the result, and the result of that adjoining will be passed to the recursive call as the second parameter; otherwise we just pass the result as is to the recursive call.
When the list is finally empty (if (null lst) we will return the result.
> (repeated '(a a b a b c))
(B A)
Notice that the result is (B A) and maybe you were expecting it to be (A B). Try to follow the execution of the recursive calls and the values of the parameters at each call with pen and paper, that will be a good exercise, and you'll have to play with adjoin to understand its behaviour. If you want to get the result reversed you can modify the function like this:
(defun repeatedr (lst result)
(if (null lst)
(reverse result)
(if (member (first lst) (rest lst))
(repeatedr (rest lst) (adjoin (first lst) result))
(repeatedr (rest lst) result))))
This reverses the result when the recursion finishes.
Now, what about the suggestion of removing the duplicate elements from the list before going forward? We could have written our function like this:
(defun repeatedr (lst result)
(if (null lst)
result
(if (member (first lst) (rest lst))
(repeatedr (remove (first lst) lst) (cons (first lst) result))
(repeatedr (rest lst) result))))
Try to play with remove at the REPL:
> (remove 'a '(a b c d a e f b a d))
(B C D E F B D)
Notice that we are no longer adjoining to the result, instead we just create a new "cons cell" with (cons (first lst) result). cons and adjoin do the same thing, except that adjoin will add the value only if it is not already present in the list.
Hope this gives you something to play with.
The problem seems to be that you're not checking if the element exists in the output list before appending to it.
Right now, for each element in the list, you're adding that element to the result if its not contained in the remainder of the list.
To get the result you apparently want, you'd add each element in the list to the result if it's not yet contained in the result.
If order is not a concern then you can also do:
(defun my-fun-no-order (lst)
(loop for (item . rest) on lst
when (= (count item rest) 0)
collect item))
Here we iterate over a list spitting it into the current item being iterated over and the rest of the items yet to be examined. The when clause determines the situation under which we collect the item.