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Sudoku Solver in 140bytes

Sudoku Solver in 140 bytes

Solve a Sudoku grid only using magic, recursion, and 140bytes of brute force.

function R
a, // the array representing the sudoko grid
// placeholder arguments
i, // index of the last empty cell
j, // index to check the candidates for the cell 'i'
m, // candidate number for the the cell 'i'
g // flag whether 'm' is a already used in the same row|col|node as 'i'
// phase 1: look for an empty cell
a[i]; // keep going if the cell isn't empty
i--||+a // decrease the index and call 'a.toString()' if we went through the whole grid
// phase 2: check all candidate numbers for the cell 'i'
g=a[i]=--m; // put the candidate in the cell 'i' already and set 'g' to something truthy
// at the end of phase 2, the cell 'i' is reset to 0 for "higher" branches of the recursion
g&&R(a) // recurse if 'm' isn't already used in the same row|col|node as 'i'
// phase 3: check if the candidate number is used already
for(j in a) // loop through the whole grid again
g*= // turn 'g' falsy if
a[j^i==j] // we are not on the cell 'i'
^m // and the cell 'j' is set to 'm'
|| // and we are in the same row|col|node as 'i'
function R(a,i,j,m,g){for(i=80;a[i];i--||+a);for(m=10;g=a[i]=--m;g&&R(a))for(j in a)g*=a[j^i==j]^m||i/9^j/9&&i%9^j%9&&i/27^j/27|i%9/3^j%9/3}
Version 2, December 2004
Copyright (C) 2011 Mathieu 'p01' Henri <>
Everyone is permitted to copy and distribute verbatim or modified
copies of this license document, and changing it is allowed as long
as the name is changed.
"name": "sudokuSolver",
"description": "Brute force sudoku solver.",
"keywords": [
"brute force"
<!doctype html>
<title>Sudoku Solver in 140bytes</title>
<div>Expected value: <b>4,2,8,1,5,9,6,7,3,1,9,6,3,7,4,8,2,5,3,7,5,8,6,2,9,4,1,9,8,1,4,2,3,5,6,7,5,6,4,7,1,8,3,9,2,7,3,2,5,9,6,1,8,4,2,4,3,6,8,1,7,5,9,6,1,7,9,4,5,2,3,8,8,5,9,2,3,7,4,1,6</b></div>
<div>Actual value: <b id="ret"></b></div>
var testGrid = [0,0,0,1,5,0,0,7,0,1,0,6,0,0,0,8,2,0,3,0,0,8,6,0,0,4,0,9,0,0,4,0,0,5,6,7,0,0,4,7,0,8,3,0,0,7,3,2,0,0,6,0,0,4,0,4,0,0,8,1,0,0,9,0,1,7,0,0,0,2,0,8,0,5,0,0,3,7,0,0,0];
var myFunction = function R(a,i,j,m,g){for(i=80;a[i];i--||+a);for(m=10;g=a[i]=--m;g&&R(a))for(j in a)g*=a[j^i==j]^m||i/9^j/9&&i%9^j%9&&i/27^j/27|i%9/3^j%9/3};
var original=Array.prototype.toString;
Array.prototype.toString=function sudokuToString()
if( (sudokuToString.caller||arguments.caller)==f )
document.getElementById( "ret" ).textContent=;
})( myFunction );
myFunction( testGrid );

evert commented Sep 20, 2011

you're my hero

qfox commented Sep 20, 2011

Haha cool :)

I think you can rewrite ~--i to i-- and be fine.

Also, why would you return the original grid in the callback? Isn't it safe to assume that the original calling code would have some reference to that array under closure? Or was this a requirement for your specific need? In fact, why have the callback there at all? There's nothing async to this code, why introduce it that way..? Cut it out and you'll have your 7 bytes. In fact, you could then just get rid of the first for loop completely. So there's probably something to that callback that I'm missing :)


p01 commented Sep 21, 2011

@evert: :)

@qfox: :p doh! Thanks for the i--instead of ~--i

The callback costs 7 bytes in total, but it saves the expensive hassle of having to return ( 6 byte for the statement alone ) with fall through for the recursions that don't lead to a solution.

Also, f isn't called with original grid, but with a grid that has been modified through several recursions testing all possible candidates for each empty cell ;)

qfox commented Sep 21, 2011

@p01 f is called with a by reference... so it is passing on the same array, albeit changed. Nowhere in the code are you creating a new array. So if the callback has a closure over the original array, it will now have a closure over a modified array since you're changing the array in place.


p01 commented Sep 21, 2011

I see. Another byte bites the dust! 145 bytes

An option I am not too fond of would be to push some logic into f and change:
thus saving 2 bytes ( down to 143 bytes )

We could save a whooping 6 bytes ( down to 139 bytes ) by requiring ES5 ( thus loosing IE8 support ) and use

qfox commented Sep 21, 2011

Ok, so unless you were explicitly trying to make this async, I still don't see the point of the callback.

Aside from that, I would not call the callback <=80 times for every recursion. It would kind of defy the point of the callback anyways.

What exactly is the callback supposed to do?

In your test, if myFunction would not have a callback at all, it would become:

myFunction( testGrid);
document.getElementById( "ret" ).textContent=testGrid;

Same code. So I don't see a reason for the callback unless you had something else in mind :)

qfox commented Sep 21, 2011

So basically it would be something like this:
function R(a,i,j,m,g){for(i=80;a[i--];);for(m=10;g=a[i]=--m;g&&R(a))for(j in a)g*=a[j^i==j]^m||i/9^j/9&&i%9^j%9&&i/27^j/27|i%9/3^j%9/3} (135 bytes). Only stripped the callback part.


p01 commented Sep 21, 2011

You are missing the very important fact that the loop in phase 2 keeps changing the array and eventually resets the cell to 0 in order to test next subtree of the recursion in case the current one only leads to invalid grids.


p01 commented Sep 21, 2011

Indeed calling f all the time would be stupid.

The callback ( which costs 9 bytes ) is called once a solution is found AND allows us to not care about the following recursions.

Without the callback we would have to shortcut the loop in phase 2 to prevent the next recursions from changing the array. Doubt it's possible in less than 9 bytes :\

qfox commented Sep 21, 2011

Yeah I see now, ok let's see about that :)

jed commented Sep 21, 2011

this is just incredible.

You people amaze me... +100 for the commented code!

Very nice.

atk commented Sep 22, 2011

ES5 indexOf could save us 1 byte:
function R(a,f,i,j,m,g){for(i=a.indexOf(0),~i||f(),m=10;g=a[i]=--m;g&&R(a,f))for(j in a)g*=a[j^i==j]^m||i/9^j/9&&i%9^j%9&&i/27^j/27|i%9/3^j%9/3}

@p01 Out of curiosity (related to a side project I'm working on) - what would happen if the grid provided had no solution?

ie: If it fell out-with of the 6,670,903,752,021,072,936,960 possible permutations

Would it be easy enough to return false, or something to that effect?

atk commented Sep 23, 2011

The number of actual calculated permutations is already reduced by the number of zeros in the input array; anyway, can a solution not be found, it would enter an infinite loop as at least one zero in the field cannot be cleared up.


p01 commented Sep 27, 2011

I must say I find the closure thing wonky. Calling myFunction(a,f); which in turn calls f with no arguments just feel strange to me.


p01 commented Sep 27, 2011

So I was thinking why not simply use the .toString method of the array to output the grid, and ... Boom! We have a winner!

140 bytes

function R(a,i,j,m,g){for(i=80;a[i];i--||+a);for(m=10;g=a[i]=--m;g&&R(a))for(j in a)g*=a[j^i==j]^m||i/9^j/9&&i%9^j%9&&i/27^j/27|i%9/3^j%9/3}

qfox commented Sep 27, 2011

Sleepy again? Why +a? Without checking further, either you meant ++a or the ||+a is completely useless...

@qfox +a is just invoking a.toString(), not intended as an increment.

jed commented Sep 27, 2011

the example doesn't work anymore, unfortunately.

qfox commented Sep 27, 2011

@cjcliffe I understand, but it's in the third part of the for statement, who's return-value is discarded. Hence, useless, because the toString has no notable side effects. At least none in this code.

atk commented Sep 27, 2011

Please provide a working example.

@qfox ah, how I was reading I assumed it would just set a to a.toString() when i reached 0 (when the || condition would trigger it)


p01 commented Sep 28, 2011

Sorry for the broken example guys. Fixed now.

Yes +a does invoke .toString() here when i is equal to 0 and the cell #0 was not empty.

jed commented Sep 28, 2011

hey @p01, can you figure out why it works in firefox and not in chrome? if indeed you golfed it down to a reliably working 140, that would be HUGE.


p01 commented Sep 28, 2011

It does work in Opera and Firefox.

I'll try to figure what is going with the other browsers... if my baby girl "let" me, Priorities.
Meanwhile any help is appreciated.

atk commented Sep 28, 2011

Chrome/V8 is somewhat critical on having his prototypes overwritten. Perhaps we can do with an object looking like an array and having a toString property? like in

for(var sudoku={toString:function(){ document.getElementById( "ret" ).textContent=... }},s=0,t=testSudoku.length;s<t;s++)sudoku[s]=testSudoku[s];

fgnass commented Sep 28, 2011

Here's another (maybe a little less dirty) approach that raises an error in order to stop the recursion. Hence the invocation has to be wrapped inside a try/catch block:


p01 commented Sep 28, 2011

Nice moves!

@fgnass: Clever (ab)use of a ReferenceError. Before even using a callback method I tried a similar but more expensive approach with throw a

Bravo sir, bravo.

sprjr commented Sep 28, 2011

I want to be like you when I grow up.

lrvick commented Sep 28, 2011

You make me happy.

This is awesome.

Just a notification: as I wrote on on Reddit the current version of the code is buggy. (See the linked post for details and a solution.)


p01 commented Sep 29, 2011

Finally someone managed to reproduce this glitch. I tried the exact fix you suggested a few days ago: It works, unfortunately it is one byte bigger ( not smaller ), which bring us back to 141 bytes. One byte too many for

But I'm sure we can golf a valid version down to 140 bytes.

qfox commented Sep 29, 2011

Oh, I only see now that you're adding sugar for the toString "callback" in the test. I hadn't seen that before, just read the comments. That's why I was confused by the ||+a part. If you modify toString, the rules obviously change.

So I can see what you mean, but do you think this would be possible or acceptable in a js1k? I'd think the (temporary) toString modification is boiler plate, but still required for the solution. Guess what I'm asking is, do you really think this is a proper 140b entry, or should the toString modification actually kind of be part of it. Especially when golfing, I think it matters. And I think it does. Just my two cents... :)


p01 commented Sep 29, 2011

The toString sugar would definitely count in a JS1K: Every thing counts in JS1K.

However things seem a more lax at See the base64 entries for instance where the whole list of characters is passed as argument ( a whooping 64+ bytes for free ).

That being said, if people are OK with encapsulating the call in a try/catch, then we can settle this at 140 bytes with a mix of fgnass ReferenceError trick and maksverver decomposition of the test i!=j && a[j]!=m

qfox commented Sep 29, 2011

However things seem a more lax at See the base64 entries for instance

Fair enough :)

atk commented Sep 30, 2011

I agree, though I'd rather find a way to shorten up the calculation for 1 bit...

My head just explo***BOOOOOOM***

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