I am defining a function binomial(n k) (aka Pascal's triangle) but am getting an error:
application: not a procedure;
expected a procedure that can be applied to arguments
given: 1
arguments...:
2
I don't understand the error because I thought this defined my function:
(define (binomial n k)
(cond ((or (= n 0) (= n k)) 1)
(else (+ (binomial(n) (- k 1))(binomial(- n 1) (- k 1))))))
In Scheme (and Lisps in general), parentheses are placed before a procedure application and after the final argument to the procedure. You've done this correctly in, e.g.,
(= n 0)
(= n k)
(- k 1)
(binomial(- n 1) (- k 1))
However, you've got an error in one of your arguments to one of your calls to binomial:
(define (binomial n k)
(cond ((or (= n 0) (= n k)) 1)
(else (+ (binomial(n) (- k 1))(binomial(- n 1) (- k 1))))))
***
Based on the syntax described above (n) is an application where n should evaluate to a procedure, and that procedure will be called with no arguments. Of course, n here actually evaluates to an integer, which is not a procedure, and can't be called (hence “application: not a procedure”). You probably want to remove the parentheses around n:
(binomial n (- k 1))
It's also worth pointing out that Dr. Racket should have highlighted the same portion of code that I did above. When I load your code and evaluate (binomial 2 1), I get the following results in which (n) is highlighted:
Your error is here:
binomial(n)
n is an integer, not a function. If you put parentheses around it like that, scheme tries to invoke an integer as a function, which naturally produces an error.
This is the correct code:
(define (binomial n k)
(cond ((or (= n 0) (= n k)) 1)
(else (+ (binomial n (- k 1))(binomial(- n 1) (- k 1))))))
Problem is at here:
(binomial (n) (- k 1))
Related
I am writing a recursive function. But the question requires you not to use the exponential function. Can anyone show me how to get larger powers by multiplying smaller powers by a?
Input a=2 n=4. Then get[2, 4, 8, 16]
Input a=3 n=4. Then get[3 9 27 81].
I was trying to multiply a by a each time, so when I input 2 and 4. I get [2 4 16 256]. So what should I do?
Here is what I have written:
(define (input a n)
(if (= n 0)
'()
(append (cdr (list [* a a] a))
(let ((a (* a a)))
(input a (- n 1))))))
You are approaching the problem wrong, you really need two recursive functions (one to build the list and one to build each element). I am assuming you are allowed to use local, but if you aren't you could move that into a helper function.
(define (build-sqr-list a n)
(local [(define (sqr-recurse a n)
(if (= n 0)
1
(* a (sqr-recurse a (sub1 n)))))]
(if (= n 0)
'()
(cons (sqr-recurse a n) (build-sqr-list a (sub1 n))))))
Define the function iota1(n, m) that takes positive integers n, m with n < m as input, and outputs the list (n,n+1,n+2,...,m)
I've tried switching the code around multiple times but cannot seem to get it to function and display a list the right way
(define (iota1 n m)
(if (eq? n 0)
'()
(append (iota1 (< n m) (+ n 1)) (list n))))
There's a few oddities to the code you provided, which I've formatted for readability:
(define (iota1 n m)
(if (eq? n 0)
'()
(append (iota (< n m) (+ n 1))
(list n))))
The first is that the expression (< n m) evaluates to a boolean value, depending on whether n is less than m or not. When you apply iota to (< n m) in the expression (iota (< n m) (+ n 1)), you are giving iota a boolean value for its first argument instead of a positive integer.
Secondly, the use of append is strange here. When constructing a list in Racket, it's much more common to use the function cons, which takes as arguments a value, and a list, and returns a new list with the value added to the front. For example,
(append '(3) (append '(4) (append '(5) '()))) ==> '(3 4 5)
(cons 3 (cons 4 (cons 5 '()))) ==> '(3 4 5)
It's a good idea to opt for using cons instead of append because it's simpler, and because it is faster, since cons does not traverse the entire list like append does.
Since this sounds a bit like a homework problem, I'll leave you with a "code template" to help you find the answer:
; n : integer
; m : integer
; return value : list of integers
(define (iota1 n m)
(if (> n m) ; base case; no need to do work when n is greater than m
... ; value that goes at the end of the list
(cons ... ; the value we want to add to the front of the list
(iota1 ... ...)))) ; the call to iota, generating the rest of the list
Welcome to the racket world, my version is here:
#lang racket
(define (iota1 n m)
(let loop ([loop_n n]
[result_list '()])
(if (<= loop_n m)
(loop
(add1 loop_n)
(cons loop_n result_list))
(reverse result_list))))
I am currently trying to solve problem 1 from projecteuler.net. Evaluation of this function only returns the name of the function. What am I doing wrong?
(defun nSum (n sum)
(if ( n = 0) ( sum) )
(cond ( (mod n 5) = 0) ( nSum ( - n 1) (+ sum n)) ( (mod n 3) = 0) (nSum(- n 1) (+ sum n)) (nSum (- n 1) (+ sum n))
)
)
(setq sum (nSum 100 0))
(write sum)
Errors
Evaluation of this function only returns the name of the function.
I cannot replicate this, how did you test your code, under which environment?
With SBCL, here is what evaluating the defun form prints:
; in: DEFUN NSUM
; (N = 0)
;
; caught WARNING:
; undefined variable: =
The = symbol is being used in a position where it is evaluated as a variable. If you want to call the function bound to =, that is (function =), which can be written also #'=, then you have to write (= ... ...).
; caught STYLE-WARNING:
; undefined function: N
Since you wrote (N = 0), i.e. with N as the first element of a form under normal evaluation rules, the code tries to call function N. In your case, you have no such function defined.
; (COND ((MOD N 5) = 0) (NSUM (- N 1) (+ SUM N)) ((MOD N 3) = 0)
; (NSUM (- N 1) (+ SUM N)) (NSUM (- N 1) (+ SUM N)))
; --> IF
; ==>
; (IF NSUM
; (PROGN (- N 1) (+ SUM N))
; (IF (MOD N 3)
; (PROGN = 0)
; (IF NSUM
; (PROGN (- N 1) (+ SUM N))
; (IF NSUM
; (PROGN # #)
; NIL))))
;
; caught WARNING:
; undefined variable: NSUM
You are writing cond clauses, and in that context, each clause is supposed to be a list matching (test . body), i.e. a test expression followed by the case body (possibly empty). You wrote:
(cond ( (mod n 5) = 0) ( nSum ( - n 1) (+ sum n)) ...)
In the above, you have two clauses, one which (tries to) tests whether N is divisible by 5, and the other which test if nSum is true.
; (SUM)
;
; caught STYLE-WARNING:
; undefined function: SUM
You added parentheses around SUM, which means you want to call function SUM (currently undefined). Parentheses matter in Lisp.
Fixing errors and formatting
Here is your code after fixing the previous errors and formatting it according to Lisp style rules:
(defun nSum (n sum)
(if (= n 0)
sum
(cond
((= 0 (mod n 5)) (nSum (- n 1) (+ sum n)))
((= 0 (mod n 3)) (nSum (- n 1) (+ sum n)))
(t (nSum (- n 1) (+ sum n))))))
Your code does not compute the desired function. Please read Gwang-Jin Kim's answer to see how to compute it a tail-recursive way, or below for a loop-based one.
Some additional remarks w.r.t. style:
You are not supposed to use snakeCase in Lisp, use instead dashes to separate words, known humbly as lisp-case (and apparently, also as kebab-case).
Your if and cond can be merged together. Also, be careful about negative N.
You can do (or test1 test2) when both tests lead to the same code being executed. This avoids code duplication.
Alternative implementation
Use LOOP:
(defun euler-1 (n)
(loop
for i below n
when (or (zerop (mod i 3))
(zerop (mod i 5)))
sum i))
(defun nsum (n)
(labels ((inner-nsum (m sum) ; using `labels` define local recursive function
(cond ((= m 0) sum)
((= (mod m 3) 0) (inner-nsum (- m 1) (+ m sum)))
((= (mod m 5) 0) (inner-nsum (- m 1) (+ m sum)))
(t (inner-nsum (- m 1) sum)))))
(inner-nsum (- n 1) 0))) ; call it with n decremented by 1
; to implement "below n"
(nsum 10) ;; 23 ; test successful!
(nsum 1000) ;; 233168
You should use eq for equality test (or perhaps equal; for integers it is the same), or = for comparing numbers. And there is no infix operator in Common Lisp. So ( n = 0) should be something like (eq n 0) or (= n 0) etc.
For class, I have to write a function that takes positive integer n and returns the sum of n’s odd digits in scheme. So far, I have my base case such that if n equals 0 then 0. But I am not sure on how to continue.
(define sumOddDigits
(lambda (n)
(if (= n 0)
0
Test cases:
(sumOddDigits 0) → 0
(sumOddDigits 4) → 0
(sumOddDigits 3) → 3
(sumOddDigits 1984) → 10
You could do it efficiently using one functional loop:
(define (sumOddDigits n)
(let loop ([n n])
(cond [(zero? n) 0]
[else
(let-values ([(q r) (quotient/remainder n 10)])
(+ (if (odd? r) r 0)
(loop q)))])))
One can get list of digits using following function which uses 'named let':
(define (getDigits n)
(let loop ((ol '()) ; start with an empty outlist
(n n))
(let-values (((q r) (quotient/remainder n 10)))
(if (= q 0) (cons r ol)
(loop (cons r ol) q)))))
Then one can apply a filter using odd? function to get all odd elements of list- and then apply 'apply' function with '+' to add all those elements:
(apply + (filter
(lambda(x)
(odd? x))
digitList))
Together following can be the full function:
(define (addOddDigits N)
(define (getDigits n)
(let loop ((ol '())
(n n))
(let-values (((q r) (quotient/remainder n 10)))
(if (= q 0) (cons r ol)
(loop (cons r ol) q)))))
(define digitList (getDigits N))
(println digitList)
(apply + (filter
(lambda(x)
(odd? x))
digitList)))
Testing:
(addOddDigits 156)
Output:
'(1 5 6)
6
Your basecase is if n < 10. Because you are then on the last digit.
You then need to check if it's odd, and if so return it. Else, return the addition qualifier(0).
If n > 10, you remainder off the first digit, then test it for odd.
If odd, then add it to a recursive call, sending in the quotient of 10(shaves off the digit you just added).
Else, you recursively call add-odds with the quotient of 10, without adding the current digit.
Here it is in a recursive form(Scheme LOVES recursion) :
(define add-odds
(lambda (n)
(if(< n 10)
(if(= (remainder n 2) 1)
n
0)
(if(= (remainder (remainder n 10) 2) 1)
(+ (remainder n 10) (add-odds (quotient n 10)))
(add-odds(quotient n 10))))))
First get a (reversed) list of digits with simple recursive implementation:
(define (list-digits n)
(if (zero? n) '()
(let-values ([(q r) (quotient/remainder n 10)])
(cons r (list-digits q)))))
then filter the odd ones and sum them:
(define (sum-of-odd-digits n)
(apply + (filter odd? (list-digits n))))
Note: (list-digits 0) returns '() but it is ok for later usage.
More accurate list-digits iterative implementation (produce list of digits in right order):
(define (list-digits n)
(define (iter n acc)
(if (zero? n) acc
(let-values ([(q r) (quotient/remainder n 10)])
(iter q (cons r acc)))))
(iter n '()))
(defun sum(n)
(cond
((= n 0) 0)
((= n 1) 1)
(T (+ n sum (- n 1)))))
If I call (sum 4) it should show 10 but it gives me an error : Variable SUM has no value
Common Lisp is a Lisp-2, which means that variables and functions are in distinct namespaces.
There is a function sum, but there is no variable sum, at the point where you're using it as a variable: (+ n sum (- n 1)).
Your intention may have been to write (+ n (sum (- n 1))) instead, calling the function sum recursively:
(defun sum (n)
(cond ((= n 0) 0)
((= n 1) 1)
(T (+ n (sum (- n 1))))))
(If you wanted to refer to the function sum as a value, e.g. to pass it to another function, you would write #'sum.)