Most creative way to reverse a positive integer [closed]

Question

Provided an input as an unsigned integer:

13457

Your function/subroutine should return:

75431

Since this is a popularity contest, be creative. Creative solutions use unusual or clever techniques to accomplish given task.

Constraints:

• You cannot use arrays.
• You cannot use strings.
• No RTL Override (&#8238)

Brownie points for using creative arithmetics.

Since this is a popularity contest, I suggest not using the modulo (%) operator in your code.

About Leading zeroes:

If the input is:

12340

Then the output:

4321

would be acceptable.

Answer 1

Mathematica, no modulo!

n = 14627;
length = Ceiling[Log[10, n]];
img = Rasterize[n, RasterSize -> 400, ImageSize -> 400];
box = Rasterize[n, "BoundingBox", RasterSize -> 400, ImageSize -> 400];
width = box[[1]]; height = box[[3]];
ToExpression[
 TextRecognize[
  ImageAssemble[
   ImageTake[img, {1, height}, #] & /@ 
    NestList[# - width/length &, {width - width/length, width}, 
     length - 1]]]]

Let's break it down.

First we use some "creative arithmetics" to find out how many digits are in the number: length = Ceiling[Log[10, n]];

Next, we Rasterize the number to a nice large image:

Now we query for the bounding box of that image, and populate the width and height (actually using the baseline offset instead of the image height, because MM adds some whitespace below the baseline in the image).

Next, NestList recursively subtracts the width of the image divided by the length of the string to enable ImageTake to pluck characters from the end of the image one by one, and those are reassembled by ImageAssemble to this image:

Then we pass that on to the TextRecognize function for optical character recognition, which at this image size and rasterization quality is able to impeccably recognize the final output and give us the integer:

72641

Logarithms and OCR - It's like chocolate and peanut butter!

New and improved

This version pads out the number to deal with the obstinate behavior of TextRecognize with small numbers, and then subtracts out the pad at the end. This even works for single-digit numbers!

Though, why you would run a reverse routine on a single number is a mystery to me. But just for the sake of completeness, I even made it work for inputs of zero and one, which would normally break because the floored log doesn't return 1 for them.

n = 1;
pad = 94949;
length = If[n == 1 || n == 0, 1, Ceiling[Log[10, n]]];
img = Rasterize[n + (pad*10^length), RasterSize -> 400, 
   ImageSize -> 400];
padlength = length + 5;
box = ImageDimensions[img];
width = box[[1]]; height = box[[2]];
reversed = 
  ImageResize[
   ImageAssemble[
    ImageTake[img, {1, height}, #] & /@ 
     NestList[# - width/padlength &, {width + 1 - width/padlength, 
       width}, padlength - 1]], 200];
recognized = ToExpression[TextRecognize[reversed]];
(recognized - pad)/10^5

Answer 2

Perl/LuaTeX/Tesseract

The following Perl script reads the number as command line argument, e.g.:

    1234567890

The following Perl script prints the number via LuaTeX. A virtual font is created on the fly that mirrors the digits horizontally.

Then the whole number is again mirrored horizontally:

The final image is reread via OCR (tesseract):

    0987654321

#!/usr/bin/env perl
use strict;
$^W=1;

# Get the number as program argument or use a fixed number with all digits.
$_ = shift // 1234567890;

$\="\n"; # append EOL, when printing

# Catch negative number
exit print "NaUI (Not an Unsigned Integer)" if $_ < 0;

# Catch number with one digit.
exit ! print if ($_ = $= = $_) < 10;

undef $\;

# Write TeX file for LuaTeX
open(OUT, '>', 'temp.tex') or die "!!! Error: Cannot write: $!\n";
print OUT<<"END_PRINT";
% Catcode setting for iniTeX (a TeX format is not needed)
\\catcode`\{=1
\\catcode`\}=2
\\def\\mynumber{$_}
END_PRINT
print OUT<<'END_PRINT';
\directlua{tex.enableprimitives('',tex.extraprimitives())}
\pdfoutput=1 % PDF output
% move origin to (0,0)
\pdfhorigin=0bp
\pdfvorigin=0bp
% magnify the result by 5
\mag=5000

% Create virtual font, where the digits are mirrored
\directlua{
  callback.register('define_font',
    function (name,size)
      if name == 'cmtt10-digits' then
        f = font.read_tfm('cmtt10',size)
        f.name = 'cmtt10-digits'
        f.type = 'virtual'
        f.fonts = {{ name = 'cmtt10', size = size }}
        for i,v in pairs(f.characters) do
          if (string.char(i)):find('[1234567890]') then
            v.commands = {
               {'right',f.characters[i].width},
               {'special','pdf: q -1 0 0 1 0 0 cm'},
               {'char',i},
               {'right',-f.characters[i].width},
               {'special','pdf: Q'},
            }
          else
            v.commands = {{'char',i}}
          end
        end
      else
        f = font.read_tfm(name,size)
      end
      return f
    end
  )
}

% Activate the new font
\font\myfont=cmtt10-digits\relax
\myfont

% Put the number in a box and add a margin (for tesseract)
\dimen0=5bp % margin
\setbox0=\hbox{\kern\dimen0 \mynumber\kern\dimen0}
\ht0=\dimexpr\ht0+\dimen0\relax
\dp0=\dimexpr\dp0+\dimen0\relax
\pdfpagewidth=\wd0
\pdfpageheight=\dimexpr\ht0+\dp0\relax

% For illustration only: Print the number with the reflected digits:
\shipout\copy0 % print the number with the reflected digits

% Final version on page 2: Print the box with the number, again mirrored
\shipout\hbox{%
  \kern\wd0
  \pdfliteral{q -1 0 0 1 0 0 cm}%
  \copy0
  \pdfliteral{Q}%
}

% End job, no matter, whether iniTeX, plain TeX or LaTeX
\csname @@end\endcsname\end
END_PRINT

system "luatex --ini temp.tex >/dev/null";
system qw[convert temp.pdf temp%d.png];
system "tesseract temp1.png temp >/dev/null 2>&1";

# debug versions with output on console
#system "luatex --ini temp.tex";
#system qw[convert temp.pdf temp%d.png];
#system "tesseract temp1.png temp";

# Output the result, remove empty lines
open(IN, '<', 'temp.txt') or die "!!! Error: Cannot open: $!\n";
chomp, print while <IN>;
print "\n";
close(IN);

__END__

Answer 3

Brainfuck

Basically, it is just an input-reversing program.

,[>,]<[.<]

UPD: As Sylwester pointed out in comments, in the classical Brainfuck interpreters/compilers (without possibility to going left from zero point in the memory array) this program would not work in the absence of '>' at the beginning, so the more stable version is:

>,[>,]<[.<]

Answer 4

Haskell

reverseNumber :: Integer -> Integer
reverseNumber x = reverseNumberR x e 0
    where e = 10 ^ (floor . logBase 10 $ fromIntegral x)

reverseNumberR :: Integer -> Integer -> Integer -> Integer
reverseNumberR 0 _ _ = 0
reverseNumberR x e n = d * 10 ^ n + reverseNumberR (x - d * e) (e `div` 10) (n + 1)
    where d = x `div` e

No arrays, strings, or modulus.

Also, I know we're not supposed to use lists or strings, but I love how short it is when you do that:

reverseNumber :: Integer -> Integer
reverseNumber = read . reverse . show

Answer 5

I suppose someone has to be the partypooper.

Bash

$ rev<<<[Input]

 

$ rev<<<321
123
$ rev<<<1234567890
0987654321

Size limitations depend on your shell, but you'll be fine within reason.

Answer 6

C++

/* 
A one-liner RECUrsive reveRSE function. Observe that the reverse of a 32-bit unsigned int
can overflow the type (eg recurse (4294967295) = 5927694924 > UINT_MAX), thus the 
return type of the function should be a 64-bit int. 

Usage: recurse(n)
*/

int64_t recurse(uint32_t n, int64_t reverse=0L)
{
    return n ? recurse(n/10, n - (n/10)*10 + reverse * 10) : reverse;
}

Answer 7

Javascript

EDIT : Since there is a suggestion to not use % operator, I use a little trick now.

I know this is not a code-golf, but there is no reason to make it longer.

function r(n){v=0;while(n)v=n+10*(v-(n=~~(n/10)));return v}

r(13457) returns 75431

Moreover, it's a lot faster than string method (n.toString().split('').reverse().join('')) :

==> JSPerf report <==

Answer 8

Python

Not sure if this implementation qualifies for creative math

Also % operator was not used per se, though one might argue that divmod does the same, but then then the Question needs to be rephrased :-)

Implementation

r=lambda n:divmod(n,10)[-1]*10**int(__import__("math").log10(n))+r(n /10)if n else 0

demo

>>> r(12345)
54321
>>> r(1)
1

How does it work?

This is a recursive divmod solution *This solution determines the least significant digit and then pushes it to the end of the number.*

Yet Another Python Implementation

def reverse(n):
    def mod(n, m):
        return n - n / m * m
    _len = int(log10(n))
    return n/10**_len + mod(n, 10)*10**_len + reverse(mod(n, 10**_len)/10)*10 if n and _len else n

How does it work?

This is a recursive solution which swaps the extreme digits from the number

Reverse(n) = Swap_extreme(n) + Reverse(n % 10**int(log10(n)) / 10) 
             ; n % 10**log10(n) / n is the number without the extreme digits
             ; int(log10(n)) is the number of digits - 1
             ; n % 10**int(log10(n)) drops the most significant digit
             ; n / 10 drops the least significant digit

Swap_extreme(n) = n/10**int(log10(n)) + n%10*10**int(log10(n))
             ; n%10 is the least significant digit
             ; n/10**int(log10(n)) is the most significant digit

Example Run

reverse(123456) = 123456/10^5 + 123456 % 10 * 10^5 + reverse(123456 % 10 ^ 5 / 10)
                = 1           + 6 * 10 ^ 5 + reverse(23456/10)
                = 1           + 600000     + reverse(2345)
                = 600001 + reverse(2345)
reverse(2345)   = 2345/10^3 + 2345 % 10 * 10^3 + reverse(2345 % 10 ^ 3 / 10)
                = 2         + 5 * 10^3 + reverse(345 / 10)
                = 2         + 5000     + reverse(34)
                = 5002                 + reverse(34)
reverse(34)     = 34/10^1 + 34 % 10 * 10^1 + reverse(34 % 10 ^ 1 / 10)
                = 3       + 40             + reverse(0)
                = 43 + reverse(0)
reverse(0)      = 0

Thus

reverse(123456) = 600001 + reverse(2345)
                = 600001 + 5002 + reverse(34)
                = 600001 + 5002 + 43 + reverse(0)
                = 600001 + 5002 + 43 + 0
                = 654321

Answer 9

Just to be contrary, an overuse of the modulo operator:

unsigned int reverse(unsigned int n)
    {return n*110000%1099999999%109999990%10999900%1099000%100000;}

Note that this always reverses 5 digits, and 32 bit integers will overflow for input values more than 39045.

Answer 10

C#

Here's a way to do it without the Modulus (%) operator and just simple arithmetic.

int x = 12356;
int inv = 0;
while (x > 0)
{
    inv = inv * 10 + (x - (x / 10) * 10);
    x = x / 10;
}
return inv;

Answer 11

Bash

> fold -w1 <<<12345 | tac | tr -d '\n'
54321

Answer 12

C

#include <stdio.h>

int main(void) {
    int r = 0, x;
    scanf("%d", &x);
    while (x > 0) {
        int y = x;
        x = 0;
        while (y >= 10) { y -= 10; ++x; }
        r = r*10 + y;
    }
    printf("%d\n", r);
}

No strings, arrays, modulus or division. Instead, division by repeated subtraction.

Answer 13

Mathematica

Making an image out of number, reflecting it, partitioning it into the digits. Then there is two alternatives:

1. Compare each image of a reflected digit with prepared earlier images, replace it with the corresponding digit and construct the number out of this.

2. Reflect every digit separately, construct a new image, and pass it to the image recognition function.

I did both

reflectNumber[n_?IntegerQ] := 
 ImageCrop[
  ImageReflect[
   Image@Graphics[
     Style[Text@NumberForm[n, NumberSeparator -> {".", ""}], 
      FontFamily -> "Monospace", FontSize -> 72]], 
   Left -> Right], {Max[44 Floor[Log10[n] + 1], 44], 60}]
reflectedDigits = reflectNumber /@ Range[0, 9];
reverse[0] := 0
reverse[n_?IntegerQ /; n > 0] := 
 Module[{digits}, 
  digits = ImagePartition[reflectNumber[1000 n], {44, 60}];
  {FromDigits[
    digits[[1]] /. (d_ :> # /; d == reflectedDigits[[# + 1]] & /@ 
       Range[0, 9])],
   ToExpression@
    TextRecognize[
     ImageAssemble[
      Map[ImageReflect[#, Left -> Right] &, digits, {2}]]]}]
reverse[14257893]
> {39875241, 39875241}

EDIT: Added padding of three zeroes, because TextRecognise works correctly only with integers > 999.

Answer 14

Lua

function assemble(n,...)
    if ... then
        return 10*assemble(...)+n
    end
    return 0
end
function disassemble(n,...)
    if n>0 then
        return disassemble(math.floor(n/10),n%10,...)
    end
    return ...
end
function reverse(n)
    return assemble(disassemble(n))
end

No arrays or strings used. The number is split into digits and reassembled using the arguments list.

Answer 15

Python2

Assumes "unsigned integer" is 32-bit

import math
import sys
a=input()
p=int(math.log(a, 10))
b=a
while b%10==0:
    sys.stdout.write('0') # if 1-char string is not allowed, use chr(48) instead
    b=b/10

if p==0:
    print a
elif p==1:
    print a%10*10+a/10
elif p==2:
    print a%10*100+a%100/10*10+a/100
elif p==3:
    print a%10*1000+a%100/10*100+a%1000/100*10+a/1000
elif p==4:
    print a%10*10000+a%100/10*1000+a%1000/100*100+a%10000/1000*10+a/10000
elif p==5:
    print a%10*100000+a%100/10*10000+a%1000/100*1000+a%10000/1000*100+a%100000/10000*10+a/100000
elif p==6:
    print a%10*1000000+a%100/10*100000+a%1000/100*10000+a%10000/1000*1000+a%100000/10000*100+a%1000000/100000*10+a/1000000
elif p==7:
    print a%10*10000000+a%100/10*1000000+a%1000/100*100000+a%10000/1000*10000+a%100000/10000*1000+a%1000000/100000*100+a%10000000/1000000*10+a/10000000
elif p==8:
    print a%10*100000000+a%100/10*10000000+a%1000/100*1000000+a%10000/1000*100000+a%100000/10000*10000+a%1000000/100000*1000+a%10000000/1000000*100+a%100000000/10000000*10+a/100000000
elif p==9:
    print a%10*1000000000+a%100/10*100000000+a%1000/100*10000000+a%10000/1000*1000000+a%100000/10000*100000+a%1000000/100000*10000+a%10000000/1000000*1000+a%100000000/10000000*100+a%1000000000/100000000*10+a/1000000000

When given input 1230, it outputs 0321.

Answer 16

Postscript

/rev{0 exch{dup 10 mod 3 -1 roll 10 mul add exch 10 idiv dup 0 eq{pop exit}if}loop}def

No arrays, no strings, no variables.

gs -q -dBATCH -c '/rev{0 exch{dup 10 mod 3 -1 roll 10 mul add exch 10 idiv dup 0 eq{pop exit}if}loop}def 897251 rev ='
152798

The same without mod (which is just a shortcut, so no big difference):

/rev {
    0 exch {
        dup
        10 idiv dup
        3 1 roll 10 mul sub
        3 -1 roll 10 mul add exch 
        dup 0 eq {pop exit} if
    } loop
} def

Answer 17

C#

This uses no strings or arrays, but does use the .NET Stack<T> type (EDIT: originally used modulus operator; now removed)

public class IntegerReverser
{
    public int Reverse(int input)
    {
        var digits = new System.Collections.Generic.Stack<int>();
        int working = input;
        while (working / 10 > 0)
        {
            digits.Push(working - ((working / 10) * 10));
            working = working / 10;
        }
        digits.Push(working);
        int result = 0;
        int mult = 1;
        while (digits.Count > 0)
        {
            result += digits.Pop() * mult;
            mult *= 10;
        }
        return result;
    }
}

Answer 18

C

In that the obvious solution is represented in a couple other languages, might as well post it in C.

Golfed:

r;main(n){scanf("%d",&n);for(;n;n/=10)r=r*10+n%10;printf("%d",r);}

Ungolfed:

#include <stdio.h>

int main()
{
     int n, r = 0;
     scanf("%d", &n);
     for(;n;n/=10)
     { 
          r = r * 10 + n % 10;
     }
     printf("%d", r);
}

EDIT: Just saw the modulus edit.

Golfed (no modulus):

r;main(n){scanf("%d",&n);for(;n;n/=10)r=r*10+(n-10*(n/10));printf("%d",r);}

Ungolfed (no modulus):

#include <stdio.h>

int main()
{
     int n, r, m = 0;
     scanf("%d", &n);
     for(;n;n/=10)
     { 
          r=r*10+(n-10*(n/10));
     }
     printf("%d", r);
}

Answer 19

python (easily done in assembly)

Reverses the bits of a byte. Points for not doing the exact same thing everyone else did?

x = int(input("byte: "), 2)
x = ((x * 8623620610) & 1136090292240) % 1023
print("{0:b}".format(x).zfill(8))

example

byte: 10101010
01010101

Answer 20

Java

This is the this i've come up with, no strings, no arrays... not even variables (in Java I mind you):

public static int reverse(int n) {
    return n/10>0?(int)(modulo(n,10)*Math.pow(10, count(n)))+reverse(n/10):(int)(modulo(n,10)*Math.pow(10,count(n)));
}

public static int count(int i) {
    return (i = i/10)>0?count(i)+1:0;
}

public static int modulo(int i,int j) {
    return (i-j)>=0?modulo(i-j, j):i;
}

EDIT A more readable version

/** Method to reverse an integer, without the use of String, Array (List), and %-operator */
public static int reverse(int n) {
    // Find first int to display
    int newInt = modulo(n,10);
    // Find it's position
    int intPos = (int) Math.pow(10, count(n));
    // The actual value
    newInt = newInt*intPos;
    // Either add newInt to the recursive call (next integer), or return the found
    return (n/10>0) ? newInt+reverse(n/10) : newInt;
}

/** Use the stack, with a recursive call, to count the integer position */
public static int count(int i) {
    return (i = i/10)>0?count(i)+1:0;
}

/** A replacement for the modulo operator */
public static int modulo(int i,int j) {
    return (i-j)>=0?modulo(i-j, j):i;
}

Answer 21

PowerShell

A quick solution in PowerShell. No arrays or strings used, either implicitly or explicitly.

function rev([int]$n) {
    $x = 0
    while ($n -gt 0) {
        $x = $x * 10
        $x += $n % 10
        $n = [int][math]::Floor($n / 10)
    }
    $x
}

Testing:

PS > rev(13457)
75431

PS > rev(rev(13457))
13457

Answer 22

C++

#include<iostream>
#include<conio.h>
#include<fstream>
using namespace std;
int main()
{
    int i,size;
    float num;
    char ch;
    cout<<"enter the number \t: ";
    cin>>num;
    ofstream outf("tmp.tmp");
    outf<<num;
    outf.close();
    ifstream inf("tmp.tmp");
    inf.seekg(0,ios::end);
    size=inf.tellg();
    inf.seekg(-1,ios::cur);
    cout<<"Reverse of it\t\t: ";
    for(i=0;i<size;i++)
    {
        inf>>ch;
        if(ch!='0'||i!=0)
        cout<<ch;
        inf.seekg(-2,ios::cur);
    }
    inf.close();
            remove("tmp.tmp");
    getch();
    return 0;
}  

OUTPUT

Three sample runs

Test with zeros

It too reverses floating numbers!!!

If you want to run this code then run it on your computer because it creates a temporary file during its run-time and I am not sure if online compilers would make a temporary file on your computer

Answer 23

ECMAScript 6

reverse=x=>{
    var k=-(l=(Math.log10(x)|0)),
        p=x=>Math.pow(10,x),
        s=x*p(l);
    for(;k;k++) s-=99*(x*p(k)|0)*p(l+k);
    return s
}

Then:

• reverse(12345) outputs 54321
• reverse(3240) outputs 423
• reverse(6342975) outputs 5792436

Answer 24

Fission

$SX/
\S?L
K\O

This program reverses the input.

$ echo -n '12345' | fsn tac.fsn
54321

Answer 25

FORTH

I think this is the opposite of popular... but using Forth is always creative...

Let's create a new word

: REV 
  BEGIN
    S->D 10 U/
    SWAP 1 .R
  DUP 0= UNTIL 
CR ;

Here, it uses word U/ that returns remainder and quotient, remainder is sent to output as number within a field 1 character long, until dividend is zero. No string is used, at least until something is sent to video. I do not use a modulo operator, instead I use integer division with remainder and quotient. Let's try

12345 REV 54321
ok

Answer 26

Turing Machine Code

Using the syntax from here.

0 * * l 0
0 _ # r 2
2 # # r 2
2 0 # l A
2 1 # l B
2 2 # l C
2 3 # l D
2 4 # l E
2 5 # l F
2 6 # l G
2 7 # l H
2 8 # l I
2 9 # l J
2 _ _ l Z
A * * l A
A _ 0 l Q 
B * * l B
B _ 1 l Q 
C * * l C
C _ 2 l Q
D * * l D
D _ 3 l Q
E * * l E
E _ 4 l Q
F * * l F
F _ 5 l Q
G * * l G
G _ 6 l Q
H * * l H
H _ 7 l Q
I * * l I
I _ 8 l Q
J * * l J
J _ 9 l Q
Q # # r 2
Q * * r Q
Z # _ l Z
Z * * l ZZ
ZZ _ * r ZZZ
ZZ * * l ZZ
ZZZ 0 _ r ZZZ
ZZZ * * * halt

Try it online!

Answer 27

Python

import itertools

def rev(n):
    l = next(m for m in itertools.count() if n/10**m == 0)
    return sum((n-n/10**(i+1)*10**(i+1))/10**i*10**(l-i-1) for i in range(l))

Answer 28

C

#include <stdio.h>

int c(int n) {
    return !n ? 0 : 1+c(n/10);
}

int p(int n) {
    return !n ? 1 : 10*p(n-1);
}

int r(int n) {
    return !n ? 0 : n%10*p(c(n/10))+r(n/10);
}

int main() {
    printf("%d\n", r(13457));

    return 0;
}

Answer 29

Batch

Missed the part about not using strings - oh well.

@echo off
setLocal enableDelayedExpansion enableExtensions
for /f %%a in ('copy /Z "%~dpf0" nul') do set "ASCII_13=%%a"
set num=%~1
set cnum=%num%
set len=0
:c
if defined num set num=%num:~1%&set /a len+=1&goto :c
set /a len-=1
for /L %%a in (%len%,-1,0) do set /p "=!ASCII_13!!cnum:~%%a,1!"<nul

Answer 30

Python 2

import math

def reverseNumber(num):
    length = int(math.ceil(math.log10(num)))
    reversed = 0

    for i in range(0, length):
        temp = num // math.pow(10, length - i - 1)
        num -= temp * math.pow(10, length - i - 1)
        reversed += int(temp * math.pow(10, i))

    return reversed

print reverseNumber(12345)