create a list with the given number of strings - functional-programming

I am trying to create a list with a given number of strings. So, if I enter (make-row 3) it will be '("ivy" "ivy" "ivy") and if I enter (make-row 2) it will be '("ivy" "ivy).
I currently have the following code but it doesn't work:
(define (make-row a)
(cond
((= 0 a) '())
(else
(list "ivory")
(make-row (- a 1)))))
Can you please tell me how to write this code or what I doing wrong? I am learning how to program with Typed/Racket at home so don't have access to teachers or mentors :(

Just use one of the built-in procedures:
(define (make-row a)
(make-list a "ivory"))
But if you want to do it from scratch, use the standard template for building an output list by consing the results. Notice that your code won't work because of that (list "ivory") in the middle of nowhere - only the last expression of a condition is returned, and anyway that's not how we recursively build a list. Try this:
(define (make-row a)
(cond ((= 0 a) '())
(else (cons "ivory" (make-row (- a 1))))))
Either way, it works as expected:
(make-row 3)
=> '("ivory" "ivory" "ivory")

Related

Referencing variables in racket

I'm trying to write a simple procedure for finding the n:th prime but I don't think I understand how to reference variables correctly in racket.
What I want is for the inner procedure sieve-iter to add primes to the list primlst which is in the namespace of sieve but I get an infinite loop. My guess is that primlst within sieve-iter is causing issues.
(define (sieve n) ;; returns the n:th prime (n>0)
(let [(primlst '(2))
(cand 3)]
(define (sieve-iter i lst)
(cond ((null? lst) (and (cons i primlst) (sieve-iter (+ i 2) primlst))) ;;prime
((= (length primlst) n) (car primlst)) ;;end
((= (modulo i (car lst)) 0) (sieve-iter (+ i 2) primlst)) ;;non-prime
(#t (sieve-iter n (cdr lst))))) ;;unclear if prime
(sieve-iter cand primlst)))
Any help is appreciated!
First of all, you shouldn't refer to primlist at all within the sieve-iter function. Instead, you should refer to lst.
Second of all, you appear to be mistaken on the effect of this expression:
(and (cons i primlst) (sieve-iter (+ i 2) primlst))
You seem to be interpreting that as meaning "Add i to the primlist and then start the next iteration."
(cons i primlist) changes nothing. Instead, it creates a new list consisting of primlist with i in front of it and then evaluates to that value. The original primlist (which should have been lst anyway) is left untouched.
Also, and is for Boolean logic, not for stringing commands together. It evaluates each of its subexpressions separately until it finds one that evaluates to #f and then it stops.
You should replace that whole expression with this:
(sieve-iter (+ i 2) (cons i lst))
...which passes the new list created by cons to the next run of sieve-iter.
Your trying to do too much in one function, let prime-iter just worry about the iteration to build up the list of primes. Make another internal function to recurse down the existing primes to test the new candidate.
(define (sieve n) ;; returns the n:th prime (n>0)
(define (sieve-iter i lst remaining)
(cond ;((null? lst) (and (cons i primlst) (sieve-iter (+ i 2) primlst))) ;;should never be null, we are building the list up
((<= remaining 0) (car lst)) ;;checking length every time gets expensive added a variable to the function
((sieve-prime? i lst) ;;if prime add to lst and recurse on next i
(sieve-iter (+ i 2) (cons i lst) (- remaining 1)))
(else
(sieve-iter (+ i 2) lst remaining)))) ; else try next
(define (sieve-prime? i lst)
(cond ((null? lst) #t)
((= 0 (modulo i (car lst))) #f)
(else (sieve-prime? i (cdr lst)))))
(let ((primlst '(2)) ;;you generally don't modify these,
(cand 3)) ;mostly they just bind values to name for convenience or keep from having to re-calculate the same thing more than once
(sieve-iter cand primlst (- n 1))))
You could have used set! to modify primlist where it was before, but the procedure is no longer obviously a pure function.
There is another low-handing optimization possible here, when calling sieve-prime? filter the lst argument to remove values larger than the square root of i.

What is "named let" and how do I use it to implement a map function?

I'm totally new to Scheme and I am trying to implement my own map function. I've tried to find it online, however all the questions I encountered were about some complex versions of map function (such as mapping functions that take two lists as an input).
The best answer I've managed to find is here: (For-each and map in Scheme). Here is the code from this question:
(define (map func lst)
(let recur ((rest lst))
(if (null? rest)
'()
(cons (func (car rest)) (recur (cdr rest))))))
It doesn't solve my problem though because of the usage of an obscure function recur. It doesn't make sense to me.
My code looks like this:
(define (mymap f L)
(cond ((null? L) '())
(f (car L))
(else (mymap (f (cdr L))))))
I do understand the logic behind the functional approach when programming in this language, however I've been having great difficulties with coding it.
The first code snippet you posted is indeed one way to implement the map function. It uses a named let. See my comment on an URL on how it works. It basically is an abstraction over a recursive function. If you were to write a function that prints all numbers from 10 to 0 you could write it liks this
(define (printer x)
(display x)
(if (> x 0)
(printer (- x 1))))
and then call it:
(printer 10)
But, since its just a loop you could write it using a named let:
(let loop ((x 10))
(display x)
(if (> x 0)
(loop (- x 1))))
This named let is, as Alexis King pointed out, syntactic sugar for a lambda that is immediately called. The above construct is equivalent to the snippet shown below.
(letrec ((loop (lambda (x)
(display x)
(if (> x 0)
(loop (- x 1))))))
(loop 10))
In spite of being a letrec it's not really special. It allows for the expression (the lambda, in this case) to call itself. This way you can do recursion. More on letrec and let here.
Now for the map function you wrote, you are almost there. There is an issue with your two last cases. If the list is not empty you want to take the first element, apply your function to it and then apply the function to the rest of the list. I think you misunderstand what you actually have written down. Ill elaborate.
Recall that a conditional clause is formed like this:
(cond (test1? consequence)
(test2? consequence2)
(else elsebody))
You have any number of tests with an obligatory consequence. Your evaluator will execute test1? and if that evaluated to #t it will execute the consequence as the result of the entire conditional. If test1? and test2? fail it will execute elsebody.
Sidenote
Everything in Scheme is truthy except for #f (false). For example:
(if (lambda (x) x)
1
2)
This if test will evaluate to 1 because the if test will check if (lambda (x) x) is truthy, which it is. It is a lambda. Truthy values are values that will evaluate to true in an expression where truth values are expected (e.g., if and cond).
Now for your cond. The first case of your cond will test if L is null. If that is evaluated to #t, you return the empty list. That is indeed correct. Mapping something over the empty list is just the empty list.
The second case ((f (car L))) literally states "if f is true, then return the car of L".
The else case states "otherwise, return the result mymap on the rest of my list L".
What I think you really want to do is use an if test. If the list is empty, return the empty list. If it is not empty, apply the function to the first element of the list. Map the function over the rest of the list, and then add the result of applying the function the first element of the list to that result.
(define (mymap f L)
(cond ((null? L) '())
(f (car L))
(else (mymap (f (cdr L))))))
So what you want might look look this:
(define (mymap f L)
(cond ((null? L) '())
(else
(cons (f (car L))
(mymap f (cdr L))))))
Using an if:
(define (mymap f L)
(if (null? L) '()
(cons (f (car L))
(mymap f (cdr L)))))
Since you are new to Scheme this function will do just fine. Try and understand it. However, there are better and faster ways to implement this kind of functions. Read this page to understand things like accumulator functions and tail recursion. I will not go in to detail about everything here since its 1) not the question and 2) might be information overload.
If you're taking on implementing your own list procedures, you should probably make sure they're using a proper tail call, when possible
(define (map f xs)
(define (loop xs ys)
(if (empty? xs)
ys
(loop (cdr xs) (cons (f (car xs)) ys))))
(loop (reverse xs) empty))
(map (λ (x) (* x 10)) '(1 2 3 4 5))
; => '(10 20 30 40 50)
Or you can make this a little sweeter with the named let expression, as seen in your original code. This one, however, uses a proper tail call
(define (map f xs)
(let loop ([xs (reverse xs)] [ys empty])
(if (empty? xs)
ys
(loop (cdr xs) (cons (f (car xs)) ys)))))
(map (λ (x) (* x 10)) '(1 2 3 4 5))
; => '(10 20 30 40 50)

Dr. Racket Recursion count occurrences

I'm new to Racket and trying to learn it. I'm working through some problems that I'm struggling with. Here is what the problem is asking:
Write a definition for the recursive function occur that takes a data expression a and a list s and returns the number of times that the data expression a appears in the list s.
Example:
(occur '() '(1 () 2 () () 3)) =>3
(occur 1 '(1 2 1 ((3 1)) 4 1)) => 3 (note that it only looks at whole elements in the list)
(occur '((2)) '(1 ((2)) 3)) => 1
This is what I have written so far:
(define occur
(lambda (a s)
(cond
((equal? a (first s))
(else (occur a(rest s))))))
I'm not sure how to implement the count. The next problem is similar and I have no idea how to approach that. Here is what this problem says:
(This is similar to the function above, but it looks inside the sublists as well) Write a recursive function atom-occur?, which takes two inputs, an atom a and a list s, and outputs the Boolean true if and only if a appears somewhere within s, either as one of the data expressions in s, or as one of the data expression in one of the data expression in s, or…, and so on.
Example:
(atom-occur? 'a '((x y (p q (a b) r)) z)) => #t
(atom-occur? 'm '(x (y p (1 a (b 4)) z))) => #f
Any assistance would be appreciated. Thank you.
In Racket, the standard way to solve this problem would be to use built-in procedures:
(define occur
(lambda (a s)
(count (curry equal? a) s)))
But of course, you want to implement it from scratch. Don't forget the base case (empty list), and remember to add one unit whenever a new match is found. Try this:
(define occur
(lambda (a s)
(cond
((empty? s) 0)
((equal? a (first s))
(add1 (occur a (rest s))))
(else (occur a (rest s))))))
The second problem is similar, but it uses the standard template for traversing a list of lists, where we go down on the recursion on both the first and the rest of the input list, and only test for equality when we're in an atom:
(define atom-occur?
(lambda (a s)
(cond
((empty? s) #f)
((not (pair? s))
(equal? a s))
(else (or (atom-occur? a (first s))
(atom-occur? a (rest s)))))))

(Scheme) Using the map function, how do you find the sum of the sublists of a list?

So, I'm trying to add up the sublists of a list. Like, if I have something like this:
(add-pair '((1 4) (2 1)))
I want it to return this:
(5 3)
This is what I have so far:
(define pair-additions
(lambda (ls)
(map
(lambda (n)
(+ (car n) (cdr n)))ls)))
Right now, it's giving me an error saying that the input isn't a number. Can anybody help me out?
You almost got it! here is the problem:
(+ (car n) (cdr n))
For retrieving the second element of a list, you have to take the car of the cdr, not just the cdr. Change the above line for this:
(+ (car n) (car (cdr n)))
Or for this, which is a short form of the previous line:
(+ (car n) (cadr n))
Or for this, which is easier to read (if supported by your Scheme interpreter):
(+ (first n) (second n))
All the above are equivalent.

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)

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