Determine if an integer is a palindrome in a given radix (base)

Question

Write a program that reads from stdin two integers, each newline terminated, hereafter called "number" and "radix", and:

1. Prints any fixed message you want if the number is a palindrome in that radix (e.g. true, t, 1)
2. Prints any different fixed message you want if the number is not a palindrome in that radix (e.g. false, f, 0, etc.)
3. These messages must be the same per each run, but there are no rules about what they must be (whatever's best for golfing).
4. You may assume the input is valid, two positive integers. "number" will not exceed 2147483647, "radix" will not exceed 32767.
5. You may not use external resources, but you may use any math function included by default in your language.

Note: a radix is just the base of the number.

Sample runs:

16
10
false
16
3
true
16
20
true
121
10
true
5
5
false
12346
12345
true
16781313
64
true
16781313
16
true

• user10766: Note: a radix is just the base of the number.
• user10766: Looks good now. You may want to ban external resources though.
• durron597: @user2509848 hmmm, for instance?
• user10766: If a person can find a calculator on the web that converts numbers between bases, it will almost certainly be used. We have been having a rash of trolly answers lately.
• Toby Speight: Can one of the fixed messages be the empty string (assuming that the other is a non-empty string)?

Answer 1

GolfScript, 10 characters

~base.-1%=

That is an easy one for GolfScript if we do it the straightforward way. The output is 0/1 for false/true.

~ # Take input and evaluate it (stack: num rdx)
base # Fortunately the stack is in the correct order for
 # a base transformation (stack: b[])
. # Duplicate top of stack (stack: b[] b[])
-1% # Reverse array (stack: b[] brev[])
= # Compare the elements

Answer 2

J (23 char) and K (19) double feature

The two languages are very similar, both in general and in this specific golf. Here is the J:

(-:|.)#.^:_1~/".1!:1,~1

• ,~1 - Append the number 1 to itself, making the array 1 1.
• 1!:1 - Read in two strings from keyboard (1!:1 is to read, and 1 is the file handle/number for keyboard input).
• ". - Convert each string to a number.
• #.^:_1~/ - F~/ x,y means to find y F x. Our F is #.^:_1, which performs the base expansion.
• (-:|.) - Does the argument match (-:) its reverse (|.)? 1 for yes, 0 for no.

And here is the K:

a~|a:_vs/|.:'0::'``

• 0::'`` - Read in (0::) a string for each (') line from console (` is the file handle for this).
• .:' - Convert (.:) each (') string to a number.
• _vs/| - Reverse the pair of numbers, so that the radix is in front of the number, and then insert (/) the base expansion function _vs ("vector from scalar") between them.
• a~|a: - Assign this resulting expansion to a, and then check if a matches (~) its reverse (|). Again, 1 for yes, 0 for no.

• John Dvorak: @ak82 I believe it's more interesting this ways

Answer 3

APL (20)

⎕{≡∘⌽⍨⍵⊤⍨⍺/⍨⌊1+⍺⍟⍵}⎕

Outputs 0 or 1, e.g:

 ⎕{≡∘⌽⍨⍵⊤⍨⍺/⍨⌊1+⍺⍟⍵}⎕
⎕:
 5
⎕:
 5
0
 ⎕{≡∘⌽⍨⍵⊤⍨⍺/⍨⌊1+⍺⍟⍵}⎕
⎕:
 16781313
⎕:
 64
1

Explanation:

• ⎕{...}⎕: read two numbers, pass them to the function. ⍵ is the first number and ⍺ is the second number.
• ⌊1+⍺⍟⍵: floor(1+⍺ log ⍵), number of digits necessary to represent ⍵ in base ⍺.
• ⍺/⍨: the base for each digit, so ⍺ replicated by the number we just calculated.
• ⍵⊤⍨: represent ⍵ in the given base (using numbers, so it works for all values of ⍺).
• ≡∘⌽⍨: see if the result is equal to its reverse.

Answer 4

Perl, (削除) 82 (削除ここまで) (削除) 77 (削除ここまで) (削除) 73 (削除ここまで) 69 bytes

$==<>;$.=<>;push(@a,$=%$.),$=/=$.while$=;@b=reverse@a;print@a~~@b?1:0

The input numbers are expected as input lines of STDIN and the result is written as 1 or 0, the former meaning the first number is a palindrome in its representation of the given base.

Edit 1: Using $= saves some bytes, because of its internal conversion to int.

Edit 2: The smartmatch operator ~~ compares the array elements directly, thus the conversion to a string is not needed.

Edit 3: Optimization by removing of an unnecessary variable.

65 bytes: If the empty string is allowed as output for false, the last four bytes can be removed.

Ungolfed version

$= = <>;
$. = <>;
while ($=) {
 push(@a, $= % $.);
 $= /= $.; # implicit int conversion by $=
}
@b = reverse @a;
print (@a ~~ @b) ? 1 : 0

The algorithm stores the digits of the converted number in an array @a. Then the string representation of this array is compared with the array in reverse order. Spaces separates the digits.

• F. Hauri - Give Up GitHub: Sorry, my answer is really same aproach, but using $= let you whipe int step... And question stand for anything you want so nothing could be what you want ;-)
• Heiko Oberdiek: @F.Hauri: Thanks, I will update. $= is also given as tip in this answer to the question "Tips for golfing in Perl". Returning 0 costs 6 extra bytes, but it was my impression that a fixed message is not intended to be empty.
• F. Hauri - Give Up GitHub: Hem,, Return 0 cost 4 extra bytes, not 6. But I maintain: silence is anything!
• Heiko Oberdiek: @F.Hauri: Yes, 4 is correct, the extra two bytes were the parentheses of the ungolfed version.

Answer 5

Javascript 87

function f(n,b){for(a=[];n;n=(n-r)/b)a.push(r=n%b);return a.join()==a.reverse().join()}

n argument is the number, b argument is the radix.

Answer 6

Sage, 45

Runs in the interactive prompt

A=Integer(input()).digits(input())
A==A[::-1]

Prints True when it is a palindrome, prints False otherwise

Answer 7

Perl (削除) 54 56 (削除ここまで) 62

$==<>;$-=<>;while($=){$_.=$/.chr$=%$-+50;$=/=$-}say$_==reverse

To be tested:

for a in $'16\n3' $'16\n10' $'12346\n12345' $'12346\n12346' $'21\n11' $'170\n16';do
 perl -E <<<"$a" ' 
 $==<>;$-=<>;while($=){$_.=$/.chr$=%$-+50;$=/=$-}say$_==reverse
 '
 done

will give:

1
1
1

So this output 1 for true when a palindrome is found and nothing if else.

Ungolfing:

$==<>; # Stdin to `$=` (value)
$-=<>; # Stdin to `$-` (radix)
while ( $= ) {
 $_.= $/. chr ( $= % $- +50 ); # Add *separator*+ chr from next modulo to radix to `$_`
 $=/= $- # Divide value by radix
}
say $_ == reverse # Return test result

Nota:

• $_ is the current line buffer and is empty at begin.
• $= is a reserved variable, originaly used for line printing, this is a line counter. So this variable is an integer, any calcul on this would result in a truncated integer like if int() was used.
• $- was used for fun, just to not use traditional letters... (some more obfuscation)...

• durron597: to clarify, this says nothing when it's not a palindrome, and 1 when it is?
• Heiko Oberdiek: Nice tricks. However wrong positive: 21 with base 11. The digits need a separator in the string comparison.
• F. Hauri - Give Up GitHub: Aaaarg +3! @HeikoOberdiek You're right f...
• Heiko Oberdiek: @F.Hauri: Also the digits get reversed. Thus 170 with base 16 is 0xAA, a palindrome, but the result is false.
• F. Hauri - Give Up GitHub: Aaarg +6! converting to chars...

Answer 8

Mathematica (削除) 77 (削除ここまで) 43

IntegerDigits[n,b] represents n as a list of digits in base b. Each base-b digit is expressed decimally.

For example, 16781313 is not a palindrome in base 17:

IntegerDigits[16781313, 17]

{11, 13, 15, 11, 14, 1}

However, it is a palindrome in base 16:

IntegerDigits[16781313, 16]

{1, 0, 0, 1, 0, 0, 1}

---

If the ordered pairs in the above examples were entered,

(x=Input[]~IntegerDigits~Input[])==Reverse@x

would return

False (* (because {11, 13, 15, 11, 14, 1} != {1, 14, 11, 15, 13, 11} ) *)

True (* (because {1, 0, 0, 1, 0, 0, 1} is equal to {1, 0, 0, 1, 0, 0, 1} ) *)

• durron597: Weird, not necessary for the answer but I'm curious, how does it render them?
• user12205: I hate it when I lose because of a stupid typecast...
• DavidC: Kindly explain "typecast".
• user12205: My sage solution is longer than yours by 2 characters because I have to cast the input to type Integer
• DavidC: Now I understand what you mean. Thanks.

Answer 9

Haskell (80 chars)

tb 0 _=[]
tb x b=(tb(div x b)b)++[mod x b]
pali n r=(\x->(x==reverse x))(tb n r)

Call it with pali $number $radix. True, when number is a palindrome, False if not.

Answer 10

C, (削除) 140 (削除ここまで) 132

int x,r,d[32],i=0,j=0,m=1;main(){scanf("%d %d",&x,&r);for(;x;i++)d[i]=x%r,x/=r;i--;for(j=i;j;j--)if(d[j]-d[i-j])m=0;printf("%d",m);}

• radix 1 is not supported:)

• durron597: Just puts(m) would work right?
• V-X: printf("%d",m); will be by 8 characters shorter.

Answer 11

Haskell - 59

Few changes to Max Ried's answer.

0%_=[]
x%b=x`mod`b:((x`div`b)%b)
p=((reverse>>=(==)).).(%)

Answer 12

Ruby - 76 chars

f=->(n,b){n==0?[]:[n%b,*f.(n/b,b)]};d=f.(gets.to_i,gets.to_i);p d==d.reverse

Answer 13

Pyth, 4 bytes

_IjF

Try it here or check out a test suite (Takes ~10-15 seconds).

Answer 14

dc, 39 bytes

The length is a palindrome, of course (3312).

[[t]pq]sgod[O~laO*+sad0<r]dsrx+la=g[f]p

The number and radix should be on the top of the stack (in the current number base); number must be at least 0, and radix must be at least 2. Output is t if it's a palindrome and f if not. As it's not specified in the challenge, I've assumed that numbers never have leading zeros (so any number ending in 0 cannot be a palindrome).

Explanation

As a full program:

#!/usr/bin/dc
# read input
??
# success message
[[t]pq]sg
# set output radix
o
# keep a copy unmodified
d
# reverse the digits into register a
[O~ laO*+sa d0<r]dsrx
# eat the zero left on stack, and compare stored copy to a
+ la=g
# failure message
[f]p

Answer 15

LaTeX, 165 bytes

Example at desmos.com

k, the radix, is an adjustable input

b=\floor \left(\log _k\left(\floor \left(x\right)\right)\right)
f\left(x\right)=k^bx-x-\left(k^2-1\right)\sum _{n=1}^bk^{\left(b-n\right)}\floor \left(xk^{-n}\right)

If f(x)=0, x is a palindrome in base k.

Answer 16

Perl 6, 34 bytes

-4 bytes thanks to PhilH

{@(polymod $^a: $^b xx*)~~[R,] $_}

Try it online!

• Phil H: You can use $_ instead of @r to save 2
• Jo King: @PhilH Nope. (assigns a Seq, not a List)
• Phil H: Ahh, sorry didn't see the error
• Jo King: @PhilH Your second tip still helped save bytes though!
• Phil H: Always annoying that there's no shorter way to call reduce meta on $_ or @_.

Answer 17

Perl 6, 27 bytes (22 without stdin/out)

say (+get).base(get)~~.flip

Try it online!

 get() # pulls a line of stdin
 + # numerificate
( ).base(get()) # pull the radix and call base to 
 # convert to string with that base
 ~~ # alias LHS to $_ and smartmatch to
 .flip # reverse of the string in $_

Perl6, king of readable golfs (golves?) (and also some not so readable).

Perl 6 function (not stdin/stdout), 22 bytes

{$^a.base($^b)~~.flip}

Try it online!

• Jo King: The reason I didn't use base in my answer is that base only supports up to base 36, and the question asks to support radixes up to 32767
• Phil H: Ooh, did not know that. Hmm.

Answer 18

05AB1E, (削除) 4 (削除ここまで) 3 bytes

вÂQ

Try it online or verify all test cases.

Explanation:

в # The first (implicit) input converted to base second (implicit) input
 # i.e. 12345 and 12346 → [1,1]
 # i.e. 10 and 16 → [1,6]
 Â # Bifurcate the value (short for duplicate & reverse)
 # i.e. [1,1] → [1,1] and [1,1]
 # i.e. [1,6] → [1,6] and [6,1]
 Q # Check if they are still the same, and thus a palindrome
 # i.e. [1,1] and [1,1] → 1
 # i.e. [1,6] and [6,1] → 0

Answer 19

C (gcc), 79 bytes

n,r,m;main(o){for(scanf("%d %d",&n,&r),o=n;n;n/=r)m=m*r+n%r;printf("%d",m==o);}

Try it online!

Rundown

n,r,m;main(o){
for(scanf("%d %d",&n,&r), Read the number and the radix.
o=n; ...and save the number in o
n; Loop while n is non-zero
n/=r) Divide by radix to remove right-most digit.
m=m*r+n%r; Multiply m by radix to make room for a digit
 and add the digit.
printf("%d",m==o);} Print whether we have a palindrome or not.

Based on the fact that for a palindrome, the reverse of the number must equal the number itself.

Suppose you have the three-digit number ABC in some base. Multiplying it by base will always result in ABC0, and dividing it by base in AB with C as remainder. So to reverse the number we pick off the right-most digit from the original number and insert it to the right on the reversed number. To make room for that digit, we multiply the reverse by base before-hand.

Basically:

n rev
ABC 0
AB C
AB C0
A CB
A CB0
0 CBA

• durron597: This is cool, can u explain the math behind this?
• gastropner: @durron597 Sure! Added an explanation to the post.

Answer 20

Jelly, 3 bytes

bŒḂ

Try it online!

How it works

bŒḂ - Main link. Takes a number n on the left and a radix r on the right
b - Convert n to base r
 ŒḂ - Is palindrome?

Answer 21

Python 3.8 (pre-release), (削除) 167 (削除ここまで) (削除) 162 (削除ここまで) (削除) 65 (削除ここまで) 63 bytes

a,b=map(int,open(s:=0))
o=a
while a:s=s*b+a%b;a//=b
print(s==o)

Try it online!

Massive -99 thx to @Steffan

Answer 22

APL(NARS), 21 chars

{k≡⌽k←⍵⊤⍨⍺⍴⍨1+⌊⍺⍟1⌈⍵}

In the left [⍺] the base positive integer >1 in the right [⍵] one non negative integer. Return 0 for false 1 for true.

test:

 f←{k≡⌽k←⍵⊤⍨⍺⍴⍨1+⌊⍺⍟1⌈⍵}
 10 f 16
0
 3 f 16
1
 20 f 16
1
 10 f 121
1
 5 f 5
0
 12345 f 12346
1
 64 f 16781313
1
 16 f 16781313
1

Answer 23

dg - 97 bytes

Trying out dg:

n,r=map int$input!.split!
a=list!
while n=>
 a.append$chr(n%r)
 n//=r
print$a==(list$reversed a)

Explained:

n, r=map int $ input!.split! # convert to int the string from input
a = list! # ! calls a function without args
while n =>
 a.append $ chr (n % r) # append the modulus
 n //= r # integer division
print $ a == (list $ reversed a) # check for palindrome list

Answer 24

Dyalog APL, 12 bytes

Radix on the left, number on the right

(⊢≡⌽)⍤(⊥⍣ ̄1)­⁡​‎‎⁡⁠⁡‏⁠⁠⁠⁠‎⁡⁠⁢⁡‏‏​⁡⁠⁡‌⁢​‎‎⁡⁠⁢‏‏​⁡⁠⁡‌⁣​‎‎⁡⁠⁣‏‏​⁡⁠⁡‌⁤​‎‎⁡⁠⁤‏‏​⁡⁠⁡‌⁢⁡​‎‎⁡⁠⁢⁢‏‏​⁡⁠⁡‌⁢⁢​‎⁠‎⁡⁠⁢⁣‏⁠‎⁡⁠⁢⁤‏⁠‎⁡⁠⁣⁡‏⁠‎⁡⁠⁣⁢‏⁠‎⁡⁠⁣⁣‏⁠‎⁡⁠⁣⁤‏‏​⁡⁠⁡‌­
( ) # ‎⁡Train of
 ⊢ # ‎⁢ does the argument
 ≡ # ‎⁣ match
 ⌽ # ‎⁤ its reverse
 ⍤ # ‎⁢⁡Run atop
 (⊥⍣ ̄1) # ‎⁢⁢Inverse decode (which automatically makes enough digits to wholly decode the number)
💎

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