I have a function that takes a number such as 36, and reverses it to say '(6 3)
Is there anyway to combine that 6 3 to make it one number?
Here is the code that I have written.
(define (number->rdigits num)
(if (rdigits (/ (- num (mod num 10)) 10)))))
(define reversible?
(lambda (n)
(cond
[(null? n) #f]
[else (odd? (+ n (list (number->rdigits n))))])))
Thanks!
You can do this using an iterative function that takes each element of the list in turn, accumulating a result. For example:
(define (make-number lst)
(define (make a lst)
(if (null? lst)
a
(make (+ (* 10 a) (car lst)) (cdr lst))))
(make 0 lst))
(display (make-number '(6 3)))
The make function uses an accumulator a and the rest of the digits in lst to build up the final result one step at a time:
a = 0
a = 0*10 + 6 = 6
a = 6*10 + 3 = 63
If you had more digits in your list, this would continue:
a = 63*10 + 5 = 635
a = 635*10 + 9 = 6359
A less efficient implementation that uses a single function could be as follows:
(define (make-number lst)
(if (null? lst)
0
(+ (* (expt 10 (length (cdr lst))) (car lst)) (make-number (cdr lst)))))
This function needs to calculate the length of the remainder of the list for each iteration, as well as calling the expt function repeatedly. Also, this implementation is not properly tail recursive so it builds up multiple stack frames during execution before unwinding them all after it reaches its maximum recursion depth.
Related
I'm trying to write a function in Scheme that returns the first n elements in a list. I'm want to do that without loops, just with this basic structure below.
What I've tried is:
(define n-first
(lambda (lst n)
(if (or(empty? lst) (= n 0))
(list)
(append (car lst) (n-first (cdr lst) (- n 1))))))
But I'm getting an error:
append: contract violation
expected: list?
given: 'in
I've tried to debug it and it looks that the tail of the recursion crashes it, meaning, just after returning the empty list the program crashes.
When replacing "append" operator with "list" I get:
Input: (n-first '(the cat in the hat) 3)
Output:
'(the (cat (in ())))
But I want to get an appended list.
A list that looks like (1 2 3) i constructed like (1 . (2 . (3 . ()))) or if you're more familiar with cons (cons 1 (cons 2 (cons 3 '()))). Thus (list 1 2 3)) does exactly that under the hood. This is crucial information in order to be good at procedures that works on them. Notice that the first cons cannot be applied before the (cons 2 (cons 3 '())) is finished so a list is always created from end to beginning. Also a list is iterated from beginning to end.
So you want:
(define lst '(1 2 3 4 5))
(n-first lst 0) ; == '()
(n-first lst 1) ; == (cons (car lst) (n-first (- 1 1) (cdr lst)))
(n-first lst 2) ; == (cons (car lst) (n-first (- 2 1) (cdr lst)))
append works like this:
(define (append lst1 lst2)
(if (null? lst1)
lst2
(cons (car lst1)
(append (cdr lst1) lst2))))
append is O(n) time complexity so if you use that each iteration of n parts of a list then you get O(n^2). For small lists you won't notice it but even a medium sized lists of a hundred thousand elements you'll notice append uses about 50 times longer to complete than the cons one and for large lists you don't want to wait for the result since it grows exponentially.
try so
(define first-n
(lambda (l)
(lambda (n)
((lambda (s)
(s s l n (lambda (x) x)))
(lambda (s l n k)
(if (or (zero? n)
(null? l))
(k '())
(s s (cdr l) (- n 1)
(lambda (rest)
(k (cons (car l) rest))))))))))
(display ((first-n '(a b c d e f)) 4))
(display ((first-n '(a b)) 4))
In scheme you must compute mentally the types of each expression, as it does not have a type checker/ type inference included.
I'm stuck on a homework question and could use any hints or suggestions. I need to find the n largest numbers in a list using Scheme. I am trying to do this by creating helper functions that are called by the main function. So far I have this:
(define (get_max_value L)
(if (null? L)
'()
(apply max L)
)
(define (biggest_nums L n)
(if (null? n)
'()
(cons (get_max_value L) (biggest_nums L (- n 1)))
)
)
When I type (biggest_num '(3 1 4 2 5) 3) at the command prompt drRacket just hangs and doesn't even return an error message. Where am I going wrong?
The simplest solution is to first sort the numbers in ascending order and then take the n first. This translates quite literally in Racket code:
(define (biggest_nums L n)
(take (sort L >) n))
It works as expected:
(biggest_nums '(3 1 4 2 5) 3)
=> '(5 4 3)
Two mains problems with your code:
L always stays the same. L doesn't decrease in size when you make the recursive call, so the max will always be the same number in every recursive call.
You don't ever check n to make sure it contains the correct amount of numbers before returning the answer.
To solve these two problems in the most trivial way possible, you can put a (< n 1) condition in the if, and use something like (cdr L) to make L decrease in size in each recursive call by removing an element each time.
(define (biggest-nums n L)
(if (or (empty? L)
(< n 1))
'()
(cons (apply max L) (biggest-nums (- n 1) (cdr L)))))
So when we run it:
> (biggest-nums 3 '(1 59 2 10 33 4 5))
What should the output be?
'(59 33 10)
What is the actual output?
'(59 59 33)
OK, so we got your code running, but there are still some issues with it. Do you know why that's happening? Can you step through the code to figure out what you could do to fix it?
Just sort the list and then return the first n elements.
However, if the list is very long and n is not very large, then you probably don't want to sort the whole list first. In that case, I would suggest something like this:
(define insert-sorted
(lambda (item lst)
(cond ((null? lst)
(list item))
((<= item (car lst))
(cons item lst))
(else
(cons (car lst) (insert-sorted item (cdr lst)))))))
(define largest-n
(lambda (count lst)
(if (<= (length lst) count)
lst
(let loop ((todo (cdr lst))
(result (list (car lst))))
(if (null? todo)
result
(let* ((item (car todo))
(new-result
(if (< (car result) item)
(let ((new-result (insert-sorted item result)))
(if (< count (length new-result))
(cdr new-result)
new-result))
result)))
(loop (cdr todo)
new-result)))))))
The function below is intended to compare every number in a list (2nd parameter) with the first parameter and for every num in the list that is greater than the second param, count it and return the total amount of elements in the list that were greater than the 'threshold'
The code I have doesn't run because I have tried to learn how recursion in Dr. Racket works, but I can't seem to understand. I am just frustrated so just know the code below isn't supposed to be close to working; functional programming isn't my thing, haha.
(define (comp-list threshold list-nums)
(cond [(empty? list-nums) 0]
[(cons? list-nums) (let {[my-var 0]}
(map (if (> threshold (first list-nums))
threshold 2) list-nums ))]))
The following doesn't use lambda of foldl (and is recursive) - can you understand how it works?
(define (comp-list threshold list-nums)
(cond [(empty? list-nums) 0]
[else
(cond [(> (car list-nums) threshold) (+ 1 (comp-list threshold (cdr list-nums)))]
[else (comp-list threshold (cdr list-nums))])]))
Tested:
> (comp-list 1 '(1 1 2 2 3 3))
4
> (comp-list 2 '(1 1 2 2 3 3))
2
> (comp-list 3 '(1 1 2 2 3 3))
0
map takes a procedure as first argument and applied that to every element in the given list(s). Since you are counting something making a list would be wrong.
foldl takes a procedure as first argument, the starting value as second and one or more lists. It applies the procedure with the elements and the starting value (or the intermediate value) and the procedure get to decide the next intermediate value. eg. you can use it to count a list:
(define (my-length lst)
(foldl (lambda (x acc) (+ acc 1))
0
lst))
(my-length '(a b c)) ; ==> 3
You can easily change this to only count when x is greater than some threshold, just evaluate to acc to keep it unchanged when you are not increasing the value.
UPDATE
A recursive solution of my-length:
(define (my-length lst)
;; auxiliary procedure since we need
;; an extra argument for counting
(define (aux lst count)
(if (null? lst)
count
(aux (cdr lst)
(+ count 1))))
;; call auxiliary procedure
(aux lst 0))
The same alteration to the procedure to foldl have to be done with this to only count in some circumstances.
(define (comp-list threshold list-nums)
(cond
[(empty? list-nums) ; there are 0 elements over the threshold in an empty list
0]
[(cons? list-nums) ; in a constructed list, we look at the the first number
(cond
[(< threshold (first list-nums))
(+ 1 ; the first number is over
(comp-list threshold (rest list-nums))] ; add the rest
[else
(comp-list threshold (rest list-nums))])])) ; the first number is lower
A simple functional start
#lang racket
(define (comp-list threshold list-nums)
(define (my-filter-function num)
(< num threshold))
(length (filter my-filter-function list-nums)))
Replacing define with lambda
#lang racket
(define (comp-list threshold list-nums)
(length (filter (lambda (num) (< num threshold))
list-nums)))
Racket's implementation of filter
In DrRacket highlighting the name of a procedure and right clicking and selecting "jump to definition in other file" will allow review of the source code. The source code for filter is instructive:
(define (filter f list)
(unless (and (procedure? f)
(procedure-arity-includes? f 1))
(raise-argument-error 'filter "(any/c . -> . any/c)" f))
(unless (list? list)
(raise-argument-error 'filter "list?" list))
;; accumulating the result and reversing it is currently slightly
;; faster than a plain loop
(let loop ([l list] [result null])
(if (null? l)
(reverse result)
(loop (cdr l) (if (f (car l)) (cons (car l) result) result)))))
I'm working on implementing a bubble sorting algorithm in Scheme, and I must say that the functional way of programming is a strange concept and I am struggling a bit to grasp it.
I've successfully created a function that will bubble up the first largest value we come across, but that's about all it does.
(bubbleH '(5 10 9 8 7))
(5 9 8 7 10)
I am struggling with the helper function that is required to completely loop through the list until no swaps have been made.
Here's where I am at so far, obviously it is not correct but I think I am on the right track. I know that I could pass in the number of elements in the list myself, but I am looking for a solution different from that.
(define bubbaS
(lambda (lst)
(cond (( = (length lst) 1) (bubba-help lst))
(else (bubbaS (bubba-help lst))))))
Using the bubble-up and bubble-sort-aux implementations in the possible-duplicate SO question I referenced...
(define (bubble-up L)
(if (null? (cdr L))
L
(if (< (car L) (cadr L))
(cons (car L) (bubble-up (cdr L)))
(cons (cadr L) (bubble-up (cons (car L) (cddr L)))))))
(define (bubble-sort-aux N L)
(cond ((= N 1) (bubble-up L))
(else (bubble-sort-aux (- N 1) (bubble-up L)))))
..., this is simple syntactic sugar:
(define (bubbleH L)
(bubble-sort-aux (length L) L))
With the final bit of syntactic sugar added, you should get exactly what you specified in your question:
(bubbleH '(5 10 9 8 7))
=> (5 7 8 9 10)
You can tinker with everything above in a repl.it session I saved & shared.
Here's my own tail-recursive version.
The inner function will bubble up the largest number just like your bubbleH procedure. But instead of returning a complete list, it will return 2 values:
the unsorted 'rest' list
the largest value that has bubbled up
such as:
> (bsort-inner '(5 1 4 2 8))
'(5 2 4 1)
8
> (bsort-inner '(1 5 4 2 8))
'(5 2 4 1)
8
> (bsort-inner '(4 8 2 5))
'(5 2 4)
8
Now the outer loop just has to cons the second value returned, and iterate on the remaining list.
Code:
(define (bsort-inner lst)
(let loop ((lst lst) (res null))
(let ((ca1 (car lst)) (cd1 (cdr lst)))
(if (null? cd1)
(values res ca1)
(let ((ca2 (car cd1)) (cd2 (cdr cd1)))
(if (<= ca1 ca2)
(loop cd1 (cons ca1 res))
(loop (cons ca1 cd2) (cons ca2 res))))))))
(define (bsort lst)
(let loop ((lst lst) (res null))
(if (null? lst)
res
(let-values (((ls mx) (bsort-inner lst)))
(loop ls (cons mx res))))))
For a recursive version, I prefer one where the smallest value bubbles in front:
(define (bsort-inner lst)
; after one pass, smallest element is in front
(let ((ca1 (car lst)) (cd1 (cdr lst)))
(if (null? cd1)
lst ; just one element => sorted
(let ((cd (bsort-inner cd1))) ; cd = sorted tail
(let ((ca2 (car cd)) (cd2 (cdr cd)))
(if (<= ca1 ca2)
(cons ca1 cd)
(cons ca2 (cons ca1 cd2))))))))
(define (bsort lst)
(if (null? lst)
null
(let ((s (bsort-inner lst)))
(cons (car s) (bsort (cdr s))))))
Write a procedure (first-half lst) that returns a list with the first half of its elements. If the length of the given list is odd, the returned list should have (length - 1) / 2 elements.
I am given these program as a example and as I am new to Scheme I need your help in solving this problem.
(define list-head
(lambda (lst k)
(if (= k 0)
'()
(cons (car lst)(list-head (cdr lst)(- k 1)))))))
(list-head '(0 1 2 3 4) 3)
; list the first 3 element in the list (list 0 1 2)
Also the expected output for the program I want is :
(first-half '(43 23 14 5 9 57 0 125))
(43 23 14 5)
This is pretty simple to implement in terms of existing procedures, check your interpreter's documentation for the availability of the take procedure:
(define (first-half lst)
(take lst (quotient (length lst) 2)))
Apart from that, the code provided in the question is basically reinventing take, and it looks correct. The only detail left to implement would be, how to obtain the half of the lists' length? same as above, just use the quotient procedure:
(define (first-half lst)
(list-head lst (quotient (length lst) 2)))
It looks like you are learning about recursion? One recursive approach is to walk the list with a 'slow' and 'fast' pointer; when the fast pointer reaches the end you are done; use the slow pointer to grow the result. Like this:
(define (half list)
(let halving ((rslt '()) (slow list) (fast list))
(if (or (null? fast) (null? (cdr fast)))
(reverse rslt)
(halving (cons (car slow) rslt)
(cdr slow)
(cdr (cdr fast))))))
Another way to approach it is to have a function that divides the list at a specific index, and then a wrapper to calculate floor(length/2):
(define (cleave_at n a)
(cond
((null? a) '())
((zero? n) (list '() a))
(#t
((lambda (x)
(cons (cons (car a) (car x)) (cdr x)))
(cleave_at (- n 1) (cdr a))))))
(define (first-half a)
(car (cleave_at (floor (/ (length a) 2)) a)))