Print all integers

Question

Write a program or function which will provably print all integers exactly once given infinite time and memory.

Possible outputs could be:

0, 1, -1, 2, -2, 3, -3, 4, -4, …

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1, -2, -3, -4, -5, -6, -7, -8, -9, 10, 11, …

This is not a valid output, as this would never enumerate negative numbers:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, …

• The output must be in decimal, unless your language does not support decimal integer (in that case use the natural representation of integers your language uses).

• Your program has to work up to the numbers with the biggest magnitude of the standard integer type of your language.

• Each integer must be separated from the next using any separator (a space, a comma, a linebreak, etc.) that is not a digit nor the negative sign of your language.

• The separator must not change at any point.

• The separator can consist of multiple characters, as long as none of them is a digit nor the negative sign (e.g. ,  is as valid as just ,).

• Any supported integer must eventually be printed after a finite amount of time.

Scoring

This is code-golf, so the shortest answer in bytes wins

Leaderboard

var QUESTION_ID=93441,OVERRIDE_USER=41723;function answersUrl(e){return"https://api.stackexchange.com/2.2/questions/"+QUESTION_ID+"/answers?page="+e+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+ANSWER_FILTER}function commentUrl(e,s){return"https://api.stackexchange.com/2.2/answers/"+s.join(";")+"/comments?page="+e+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+COMMENT_FILTER}function getAnswers(){jQuery.ajax({url:answersUrl(answer_page++),method:"get",dataType:"jsonp",crossDomain:!0,success:function(e){answers.push.apply(answers,e.items),answers_hash=[],answer_ids=[],e.items.forEach(function(e){e.comments=[];var s=+e.share_link.match(/\d+/);answer_ids.push(s),answers_hash[s]=e}),e.has_more||(more_answers=!1),comment_page=1,getComments()}})}function getComments(){jQuery.ajax({url:commentUrl(comment_page++,answer_ids),method:"get",dataType:"jsonp",crossDomain:!0,success:function(e){e.items.forEach(function(e){e.owner.user_id===OVERRIDE_USER&&answers_hash[e.post_id].comments.push(e)}),e.has_more?getComments():more_answers?getAnswers():process()}})}function getAuthorName(e){return e.owner.display_name}function process(){var e=[];answers.forEach(function(s){var r=s.body;s.comments.forEach(function(e){OVERRIDE_REG.test(e.body)&&(r="<h1>"+e.body.replace(OVERRIDE_REG,"")+"</h1>")});var a=r.match(SCORE_REG);a&&e.push({user:getAuthorName(s),size:+a[2],language:a[1],link:s.share_link})}),e.sort(function(e,s){var r=e.size,a=s.size;return r-a});var s={},r=1,a=null,n=1;e.forEach(function(e){e.size!=a&&(n=r),a=e.size,++r;var t=jQuery("#answer-template").html();t=t.replace("{{PLACE}}",n+".").replace("{{NAME}}",e.user).replace("{{LANGUAGE}}",e.language).replace("{{SIZE}}",e.size).replace("{{LINK}}",e.link),t=jQuery(t),jQuery("#answers").append(t);var o=e.language;/<a/.test(o)&&(o=jQuery(o).text()),s[o]=s[o]||{lang:e.language,user:e.user,size:e.size,link:e.link}});var t=[];for(var o in s)s.hasOwnProperty(o)&&t.push(s[o]);t.sort(function(e,s){return e.lang>s.lang?1:e.lang<s.lang?-1:0});for(var c=0;c<t.length;++c){var i=jQuery("#language-template").html(),o=t[c];i=i.replace("{{LANGUAGE}}",o.lang).replace("{{NAME}}",o.user).replace("{{SIZE}}",o.size).replace("{{LINK}}",o.link),i=jQuery(i),jQuery("#languages").append(i)}}var ANSWER_FILTER="!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe",COMMENT_FILTER="!)Q2B_A2kjfAiU78X(md6BoYk",answers=[],answers_hash,answer_ids,answer_page=1,more_answers=!0,comment_page;getAnswers();var SCORE_REG=/<h\d>\s*([^\n,]*[^\s,]),.*?(\d+)(?=[^\n\d<>]*(?:<(?:s>[^\n<>]*<\/s>|[^\n<>]+>)[^\n\d<>]*)*<\/h\d>)/,OVERRIDE_REG=/^Override\s*header:\s*/i;

body{text-align:left!important}#answer-list,#language-list{padding:10px;width:290px;float:left}table thead{font-weight:700}table td{padding:5px}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> <link rel="stylesheet" type="text/css" href="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b"> <div id="answer-list"> <h2>Leaderboard</h2> <table class="answer-list"> <thead> <tr><td></td><td>Author</td><td>Language</td><td>Size</td></tr></thead> <tbody id="answers"> </tbody> </table> </div><div id="language-list"> <h2>Winners by Language</h2> <table class="language-list"> <thead> <tr><td>Language</td><td>User</td><td>Score</td></tr></thead> <tbody id="languages"> </tbody> </table> </div><table style="display: none"> <tbody id="answer-template"> <tr><td>{{PLACE}}</td><td>{{NAME}}</td><td>{{LANGUAGE}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr></tbody> </table> <table style="display: none"> <tbody id="language-template"> <tr><td>{{LANGUAGE}}</td><td>{{NAME}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr></tbody> </table>

Answer 1

QBasic, 23 bytes

Script that takes no input and outputs to the console. Values are newline delimited and increment in the order of \$0, -1, 1, -2, 2, \cdots\$.

?0
Do
i=i+1
?-i
?i
Loop

Answer 2

Python 3, 44 bytes

i=0;print(i)
while 1:i+=1;print(i);print(-i)

Try it online!

Answer 3

Keg, -pn, 15 9 bytes

0.1{:④±.⑨

Try it online!

Answer History

15 bytes

0. ,1{④± ,④ ,±⑨

Try it online!

Really messy I know, but it works. Integers are space seperated

Answer 4

cQuents, 7 bytes

=0:k,-k

Try it online!

Do you really need an explanation?

Answer 5

Red, 37 bytes

n: 1 forever[print[n 0 - n]n: n + 1]0

Answer 6

Symja, 38 37 bytes

i=0;While(0<1,Print(i);i++;Print(-i))

Try It Online!

To see that this will work for all integers, view this demonstration for numbers up to 100.

Answer 7

C, 55 Bytes

i=1;f(){putc('0');while(i>0){printf(",%d,%d",-i,i++);}}

Explanation

/*int*/ i = 1;
int f()
{
    putc('0');/*Print out 0 because -0 isn't a number*/
    while(i>0) /*i>0 handles overflow, ensuring all valid *
                 * integers are printed once and only once  */ {
        printf(",%d,%d",-i,i++);
        /* Unpacking the above line:
        the 1st %d prints out -i
        the 2nd %d prints out i
        i++ adds 1 to i(after it's passed to the printf)*/
    }
}

I put the comma at the beginning of the printf statement so that I didn't have to put it at the end of the puts and at the end of the printf.

Output: 0,-1,1,-2,2...

Edit: full C program version

@cleblanc made an answer that is a full C program, rather than a function, so I decided to do that too(Our answers are otherwise completely separate).

C, 58 Bytes

i=1;main(){putc('0');while(i>0){printf(",%d,%d",-i,i++);}}

Explanation

More or less the same as the original answer, but changing the function's name to main makes it a standalone program, rather than a function.

Answer 8

Julia, 24 bytes

f(n=0)=f(~n+(0>@show n))

Try it online!

Answer 9

Vyxal 5, 8 bytes

∞›(n,n⌐,

Explanation:

∞›(n,n⌐, # main program
∞›       # creates an infinite generator starting at 1
  (      # iterates over it
   n,    # prints the numbers [1, ∞)
     n⌐, # prints the numbers (-∞, 0]

Mapping would be better, but currently mapping generator output is not optimal.

Try it Online!

Answer 10

BRASCA, 20 18 bytes

-2 bytes thanks to RezNesX

nEo1[:nEo:0$-nEo}]

Try it online!

Explanation (old)

<implicit>           - The stack has infinite zeroes at the bottom
nEo                  - Print "0" and a space
   1[a            A] - Infinite loop:
      }:nEo          -   Print next positive integer and a space
           $         -   Swap to the negative number on the stack
            {:nEo    -   Print next negative integer and a space
                 $   -   Swap back to the positive number on the stack

Answer 11

AWK, 33 32 bytes

This code prints all integers in one line:

BEGIN{for(ORS=FS;;)print -i++,i}

An alternative 33-byte answer, which prints one integer per line:

BEGIN{for(;;)print n+=i++*(-1)^i}

Try it online!

Answer 12

GolfScript, 12 bytes

0{.p.~p).}do

0            # push 0 to the stack
 {           # this block will execute at least once, even though the TOS is 0
  .p         # print the current number
    .~p      # print the bitwise NOT of the current number
       )     # increments the current number
        .}do # creates an infinite loop

Because the bitwise NOT of x = (-x - 1), as the number increments, the inverse decrements. The bitwise NOT of 0 is -1, therefore it can be trivially proven that all integers are counted exactly once.

I know there's already a (longer) GolfScript solution here, I apologise if this is breaking any rules.

Answer 13

Commodore C64 BASIC, 29 BASIC Bytes (does not end gracefully), 24 PETSCII characters with keyword abbreviations

0?i%,nO(i%),;:i%=i%+1:gO

By declaring a variable with a % identifier, you are telling Commodore BASIC to produce only integer representations of any floating point number, and this is within the range of -32768 to +32767 inclusive. The nO command, or NOT is a bitwise operator which may only be used with the same range previously mentioned (PRINT NOT (32768) for instance produces an ?ILLEGAL QUANTITY ERROR. Further reading about this is detailed here.

Because we are using line 0, we don't need to specify a line number with the GOTO command (at least not in BASIC 2.0 on the C64 and VIC-20; this may not be the same for all versions of Commodore BASIC).

The output is produced like:

0 -1 1 -2

and will continue until the maximum range is met, and produce an error.

With a graceful ending, 39 BASIC Bytes, 35 PETSCII characters with keyword abbreviations

0?i%,nO(i%),;:i%=i%+1:ifi%<32768then0

The same as above, but an IF condition is added. We can just use THEN0 rather than THEN GOTO 0 to save some typing.

Answer 14

Fortran (GFortran), 34 bytes

i=0
1 i=i+1;print*,1-i,i;goto1;end

Boringly had to waste 4 bytes setting i=0 otherwise Fortran just initialises the variable to anything

Try it online!

Answer 15

Commodore Basic, 18 bytes

1N=N+1:?N,1-N,:G┌1

PETSCII substitution: ┌ = SHIFT+O

Prints the sequence "1, 0, 2, -1, 3, -2...", with characters separated by tabs.

• Work up to the numbers with the biggest magnitude of the standard integer type? Yes. Commodore Basic integers have a range of -32768 to +32767; this program uses 40-bit floats with a 32-bit mantissa, and can print any number between -999999999 and 999999999.
• Output in decimal? Yes. Integers stored in a floating-point number are printed as integers as long as they are nine digits or less.
• Each integer separated from the next using any separator? Yes. There is always a tab character between two integers.
• The separator must not change? Yes. The separator is always exactly one tab character.
• The separator can consist of multiple characters, as long as none of them is a digit nor the negative sign? Yes. A tab character is neither a digit nor a negative sign.
• Any supported integer must eventually be printed after a finite amount of time? Yes. After about 25 minutes, it'll print the sequence 32767 -32766 32768 -32767 32769 -32768, finishing out the set of Commodore Basic-supported integers.

Answer 16

C, 64 58 Bytes

Thanks to @12431234123412341234123

f(n){printf(",%d,-%d",n,n);f(++n);}main(){f(printf("0"));}

Try it online!

A full program that terminates after printing all the integers it can represent.

Output

0,1,-1,2,-2,3,-3,4,-4,5,-5,6,-6,7,-7,8,-8,9,-9,10,...

Answer 17

Uiua, 18 bytes

⍥(+⟜⊃±∵&s)∞¯1_1&s0

Explanation:

  ⍥(+⟜⊃±∵&s)∞¯1_1&s0             
# ^ ^ ^^^   ^^   ^
# | | |||   ||   └- print 0
# | | |||   |└----- [-1 1]
# | | |||   └------ do infinitely
# | | ||└---------- print each
# | | |└----------- sign of elements
# | | └------------ fork both functions
# | └-------------- increment by sign
# └---------------- repeat until

Answer 18

Swift 5.9, 32 bytes

(0...).map{print($0)
print(~$0)}

I tried desperately to merge the two calls to print(_:separator:terminator:) into one, but the fact that terminator is a newline by default seriously complicates things.

Answer 19

Uiua, 14 characters

⍢(¯-<0±..).1 0

Explanation

⍢(¯-<0±..).1 0
           1 0 starting values
          .    condition for while (Uiua has no booleans, so 1 is true)
⍢(       )     infinite loop
       ..      creates 2 copies of the current value
     <0±       determines if the number is negative
   ¯-          negate the number, but additionally add one to it if the condition was true

Answer 20

Setanta, 42 40 bytes

i:=0nuair-a 1{scriobh(i)i+=1scriobh(-i)}

Try on try-setanta.ie

Answer 21

Rattle, 12 bytes

p[+[p*_1]2]0

Try it Online! [NOTE: this code will time out because of the infinite loop, if you want to see any output then change the 0 for a finite value (e.g. 100). There is no output with the infinite loop because of how the online interpreter is set up, if run offline there would be infinite output.]

Explanation

p               print 0
 [         ]0   infinite loop
  +             increment
   [    ]2      loop twice
    p           print value
     *_1        multiply by -1

Answer 22

Oracle SQL 11.2, 77 73 72 68 bytes

SELECT CEIL((LEVEL-1)/2)*(MOD(LEVEL,2)*2-1)FROM DUAL CONNECT BY 1=1;

Answer 23

Non-wrapping Brain****, 9 bytes

Thanks to Scepheo for saving one byte!

+[.+<.->] 

Answer 24

Bash, 33 55 bytes

for((;;)){ echo -n $[-i++],$i,;((i==LLONG_MAX))&&exit;}

Unfortunately bash won't give an integer overflow error when $i exceeds the maximum size of the type used to store it. Therefore, I updated the code to include a termination criteria, that requires $LLONG_MAX to be defined in the environment or passed on the command line.

Run example: on my system bash uses signed 64-bit integers

LLONG_MAX=$[2**63-1] ./all_integers.sh

The following code is a 32 byte version (1 less) of my original post, that assumed undefined printing behavior after the integer overflow.

for((;;)){ echo -n $[-i++],$i,;}

Answer 25

C++ with Boost, 143 bytes

#include <boost/multiprecision/cpp_int.hpp>
#include <iostream>
boost::multiprecision::cpp_int i;main(){while(++i)std::cout<<1-i<<','<<i<<',';}

Not very short, but it does use an arbitrary-precision type. To test that, I tried replacing ++i with i=2*i+1, and very soon there were numbers several hundred digits long being printed correctly. This should work until the number takes up all your stack memory.

Answer 26

Swift 3 (34 bytes)

(Int.min...Int.max).map{print($0)}

Really, we should be able to get this down to 30 bytes like so:

(Int.min...Int.max).map(print)

But the compiler doesn't allow this yet.

Answer 27

k (20 bytes)

The function between curly braces is repeatedly iterated on it's result, starting at zero, until the result converges at 0W (k infinity).

{-1@'$?-1 1*x;x+1}/0

The function prints the argument and its negation and then returns incremented argument.

Answer 28

C# function 53 bytes

int j;void X(){for(;;)Console.Write($"{j++},-{j},");}

Explanation:

Create a variable "j" in class scope. This will default to have a value of zero. Write and increment value and then write the negative of that value. This will output "0,-1," on the first loop and "1,-2," on the 2nd loop.

Answer 29

Python, 40 bytes

p=print
p(0)
i=1
while 1:p(i);p(-i);i+=1

Answer 30

QBIC, 14 bytes

{?1-q ?q q=q+1

qis 1 by default in QBIC, so this prints (1-1=) 0, 1, -1, 2, -2... separated by line breaks.