Implement the shortest Sudoku solver using guessing. Since I have received a few request I have added this as an alternative question for those wishing to implement a brute force sudoku solver.
Sudoku Puzzle:
| 1 2 3 | 4 5 6 | 7 8 9
-+-----------------------
A| 3 | 1 |
B| 6 | | 5
C| 5 | | 9 8 3
-+-----------------------
D| 8 | 6 | 3 2
E| | 5 |
F| 9 3 | 8 | 6
-+-----------------------
G| 7 1 4 | | 9
H| 2 | | 8
I| | 4 | 3
Answer:
| 1 2 3 | 4 5 6 | 7 8 9
-+-----------------------
A| 8 3 2 | 5 9 1 | 6 7 4
B| 4 9 6 | 3 8 7 | 2 5 1
C| 5 7 1 | 2 6 4 | 9 8 3
-+-----------------------
D| 1 8 5 | 7 4 6 | 3 9 2
E| 2 6 7 | 9 5 3 | 4 1 8
F| 9 4 3 | 8 1 2 | 7 6 5
-+-----------------------
G| 7 1 4 | 6 3 8 | 5 2 9
H| 3 2 9 | 1 7 5 | 8 4 6
I| 6 5 8 | 4 2 9 | 1 3 7
Rules:
- Assume all mazes are solvable by logic only.
- All input will be 81 characters long. Missing characters will be 0.
- Output the solution as a single string.
- The "grid" may be stored internally however you wish.
- The solution must be using a brute force guessing solution.
- Solutions should solve within a reasonable time limit.
Example I/O:
>sudoku.py "030001000006000050500000983080006302000050000903800060714000009020000800000400030"
832591674496387251571264983185746392267953418943812765714638529329175846658429137
-
\$\begingroup\$ How can the input be 27 characters long? It needs to be 81 characters long - 9 rows x 9 columns. That's what your example does too. Also, I assume that "missing characters will be 0" means that if the number of characters is less than 81, then the zeroes go on the end? \$\endgroup\$Jonathan M Davis– Jonathan M Davis2011年02月03日 05:15:44 +00:00Commented Feb 3, 2011 at 5:15
-
\$\begingroup\$ Oh, wait. I get the missing characters will be 0 bit. Duh. Those are the ones that need to be guessed. In any case, the number of characters does need to be 81, not 27. \$\endgroup\$Jonathan M Davis– Jonathan M Davis2011年02月03日 05:22:38 +00:00Commented Feb 3, 2011 at 5:22
-
16\$\begingroup\$ it seems rules 5 and 6 kinda conflict.... \$\endgroup\$pseudonym117– pseudonym1172014年07月11日 13:36:40 +00:00Commented Jul 11, 2014 at 13:36
14 Answers 14
k (72 bytes)
Credit for this goes to Arthur Whitney, creator of the k language.
p,:3/:_(p:9\:!81)%3
s:{*(,x)(,/{@[x;y;:;]'&21=x[&|/p[;y]=p]?!10}')/&~x}
Python, 188 bytes
This is a further shortened version of my winning submission for CodeSprint Sudoku, modified for command line input instead of stdin (as per the OP):
def f(s):
x=s.find('0')
if x<0:print s;exit()
[c in[(x-y)%9*(x/9^y/9)*(x/27^y/27|x%9/3^y%9/3)or s[y]for y in range(81)]or f(s[:x]+c+s[x+1:])for c in'%d'%5**18]
import sys
f(sys.argv[1])
If you're using Python 2, '%d'%5**18
can be replaced with `5**18`
to save 3 bytes.
To make it run faster, you can replace '%d'%5**18
with any permutation of '123456789'
at a cost of 1 byte.
If you want it to accept the input on stdin instead, you can replace import sys;f(sys.argv[1])
with f(raw_input())
, bringing it down to 177 bytes.
def f(s):
x=s.find('0')
if x<0:print s;exit()
[c in[(x-y)%9*(x/9^y/9)*(x/27^y/27|x%9/3^y%9/3)or s[y]for y in range(81)]or f(s[:x]+c+s[x+1:])for c in'%d'%5**18]
f(raw_input())
Python, 197 characters
def S(s):
i=s.find('0')
if i<0:print s;return
for v in'123456789':
if sum(v==s[j]and(i/9==j/9or i%9==j%9or(i%9/3==j%9/3and i/27==j/27))for j in range(81))==0:S(s[:i]+v+s[i+1:])
S(raw_input())
Perl, 120 bytes
Oh, I remember golfing that back in 2008... And it in fact stopped working in perl 5.12 since implicit setting of @_ by split was removed then. So only try this on a sufficiently old perl.
Run with the input on STDIN:
sudoku.pl <<< "030001000006000050500000983080006302000050000903800060714000009020000800000400030"
sudoku.pl
:
${/[@_[map{$i-($i="@-")%9+$_,9*$_+$i%9,9*$_%26+$i-$i%3+$i%9-$i%27}0..8%split""]]/o||do0ドル}for$_=$`.$_.$'.<>,/0/||print..9
-
2\$\begingroup\$ It's Clarke's third law, but in reverse! \$\endgroup\$Conor O'Brien– Conor O'Brien2016年03月17日 12:36:14 +00:00Commented Mar 17, 2016 at 12:36
Answer in D:
import std.algorithm;
import std.conv;
import std.ascii;
import std.exception;
import std.stdio;
void main(string[] args)
{
enforce(args.length == 2, new Exception("Missing argument."));
enforce(args[1].length == 81, new Exception("Invalid argument."));
enforce(!canFind!((a){return !isDigit(to!dchar(a));})
(args[1]),
new Exception("Entire argument must be digits."));
auto sudoku = new Sudoku(args[1]);
sudoku.fillIn();
writeln(sudoku);
}
class Sudoku
{
public:
this(string str) nothrow
{
normal = new int[][](9, 9);
for(size_t i = 0, k =0; i < 9; ++i)
{
for(size_t j = 0; j < 9; ++j)
normal[i][j] = to!int(str[k++]) - '0';
}
reversed = new int*[][](9, 9);
for(size_t i = 0; i < 9; ++i)
{
for(size_t j = 0; j < 9; ++j)
reversed[j][i] = &normal[i][j];
}
boxes = new int*[][](9, 9);
indexedBoxes = new int*[][][](9, 9);
for(size_t boxRow = 0, boxNum = 0; boxRow < 3; ++boxRow)
{
for(size_t boxCol = 0; boxCol < 3; ++boxCol, ++boxNum)
{
for(size_t i = 3 * boxRow, square = 0; i < 3 * (boxRow + 1); ++i)
{
for(size_t j = 3 * boxCol; j < 3 * (boxCol + 1); ++j)
{
boxes[boxNum][square++] = &normal[i][j];
indexedBoxes[i][j] = boxes[boxNum];
}
}
}
}
}
void fillIn()
{
fillIn(0, 0);
}
@property bool valid()
{
assert(full);
for(size_t i = 0; i < 9; ++i)
{
for(int n = 1; n < 10; ++n)
{
if(!canFind(normal[i], n) ||
!canFind!"*a == b"(reversed[i], n) ||
!canFind!"*a == b"(boxes[i], n))
{
return false;
}
}
}
return true;
}
override string toString() const
{
char[81] retval;
for(size_t i = 0, k =0; i < 9; ++i)
{
for(size_t j = 0; j < 9; ++j)
retval[k++] = to!char(normal[i][j] + '0');
}
return to!string(retval);
}
private:
@property bool full()
{
for(size_t i = 0; i < 9; ++i)
{
if(canFind(normal[i], 0))
return false;
}
return true;
}
bool fillIn(size_t row, size_t col)
{
if(row == 9)
return valid;
size_t nextRow = row;
size_t nextCol = col + 1;
if(nextCol == 9)
{
nextRow = row + 1;
nextCol = 0;
}
if(normal[row][col] == 0)
{
for(int n = 1; n < 10; ++n)
{
if(canFind(normal[row], n) ||
canFind!"*a == b"(reversed[col], n) ||
canFind!"*a == b"(indexedBoxes[row][col], n))
{
continue;
}
normal[row][col] = n;
if(fillIn(nextRow, nextCol))
return true;
}
normal[row][col] = 0;
return false;
}
else
return fillIn(nextRow, nextCol);
}
int[][] normal;
int*[][] reversed;
int*[][] boxes;
int*[][][] indexedBoxes;
}
With the sample input, it takes .033s on my Phenom II X6 1090T when compiled with dmd -w
(i.e. without optimizations), and it takes .011s when compiled with dmd -w -O -inline -release
(i.e. with optimizations).
J, 103
'p n'=:(;#)I.0=a=:("."0)Y
((a p}~3 :'>:?n#9')^:([:(27~:[:+/[:(9=#@~.)"1[:,/(2 23ドル),;.3],|:,])9 9$])^:_)a
expected run time: O(gazillion billion years)
-
1\$\begingroup\$ And why is the expected run time "O(gazillion billion years)"? (shouldn't that be just "gazillion billion years" without the O? \$\endgroup\$Justin– Justin2014年02月13日 05:21:07 +00:00Commented Feb 13, 2014 at 5:21
-
1\$\begingroup\$ When I saw this question I immediatly knew that J is going to crush this one. There has to be a way to make this shorter than K. \$\endgroup\$koko– koko2014年02月13日 10:18:06 +00:00Commented Feb 13, 2014 at 10:18
-
1\$\begingroup\$ @Quincunx, strictly speaking, it's a wrong use of big-O; the "joke" was supposed to read "constant run time, asymptotically gazillion billion years". \$\endgroup\$Eelvex– Eelvex2014年02月13日 14:51:32 +00:00Commented Feb 13, 2014 at 14:51
-
\$\begingroup\$ @koko, I couldn't find something better but I'm still working on it. \$\endgroup\$Eelvex– Eelvex2014年02月13日 14:52:55 +00:00Commented Feb 13, 2014 at 14:52
Perl, 235 chars
$_=$s=<>;$r=join$/,map{$n=$_;'.*(?!'.(join'|',map+($_%9==$n%9||int($_/9)==int($n/9)||int($_/27)==int($n/27)&&int($_/3%3)==int($n/3%3)and$_<$n?'\\'.($_+1):$_>$n&&substr$s,$_,1)||X,@a).')(.).*'}@a=0..80;s!.!($&||123456789).$/!eg;say/^$r/
This is a golfed version of something I posted many years ago to the Fun With Perl mailing list: a sudoku-solving regexp.
Basically, it mangles the input into 81 lines, each containing all the numbers that could occur in the corresponding square. It then constructs a regexp to match one number from each line, using backreferences and negative lookahead assertions to reject solutions that violate the row, column or region constraints. Then it matches the string against the regexp, letting Perl's regexp engine do the hard work of trial and backtracking.
Astonishingly, it's possible to create a single regexp that works for any input, like my original program does. Unfortunately, it's quite slow, so I based the golfed code here on the hardcoded-givens version (found later in the FWP thread), which tweaks the regexp to reject early any solutions that it knows will later violate a constraint. This makes it reasonably fast for easy to moderate level sudokus, although particularly hard ones can still take a rather long time to solve.
Run the code with perl -M5.010
to enable the Perl 5.10+ say
feature. The input should be given on standard input, and the solution will be printed to standard output; example:
$ perl -M5.010 golf/sudoku.pl
030001000006000050500000983080006302000050000903800060714000009020000800000400030
832591674496387251571264983185746392267953418943812765714638529329175846658429137
1-liner coffee-script
solve = (s, c = 0) -> if c is 81 then s else if s[x = c/9|0][y = c%9] isnt 0 then solve s, c+1 else (([1..9].filter (g) -> ![0...9].some (i) -> g in [s[x][i], s[i][y], s[3*(x/3|0) + i/3|0][3*(y/3|0) + i%3]]).some (g) -> s[x][y] = g; solve s, c+1) or s[x][y] = 0
Here is the bigger version with sample usage:
solve = (sudoku, cell = 0) ->
if cell is 9*9 then return sudoku
x = cell%9
y = (cell - x)/9
if sudoku[x][y] isnt 0 then return solve sudoku, cell+1
row = (i) -> sudoku[x][i]
col = (i) -> sudoku[i][y]
box = (i) -> sudoku[x - x%3 + (i - i%3)/3][y - y%3 + i%3]
good = (guess) -> [0...9].every (i) -> guess not in [row(i), col(i), box(i)]
guesses = [1..9].filter good
solves = (guess) -> sudoku[x][y] = guess; solve sudoku, cell+1
(guesses.some solves) or sudoku[x][y] = 0
sudoku = [
[1,0,0,0,0,7,0,9,0],
[0,3,0,0,2,0,0,0,8],
[0,0,9,6,0,0,5,0,0],
[0,0,5,3,0,0,9,0,0],
[0,1,0,0,8,0,0,0,2],
[6,0,0,0,0,4,0,0,0],
[3,0,0,0,0,0,0,1,0],
[0,4,0,0,0,0,0,0,7],
[0,0,7,0,0,0,3,0,0]
]
console.log if solve sudoku then sudoku else 'could not solve'
-
1\$\begingroup\$ Could be shortened by shortening
solve
, removing lots of whitespace (I know it's significant, but in many places it could be removed), using symbols instead of words (like!=
instead ofisnt
), using indentation instead ofthen
keyword, replacing[0...9]
with[0..8]
. \$\endgroup\$null– null2013年01月04日 11:56:50 +00:00Commented Jan 4, 2013 at 11:56
Microsoft Excel Formula (383 Characters)
Receives 81 character string and outputs the same. Replace variable "i" in the last part of the formula "WRAPROWS(MID(i,SEQUENCE(1,81,1),1),9)" with the 81 character puzzle string.
=LET(S,LAMBDA(S,p,LET(n,SEQUENCE(9,9,0),z,XMATCH(0,TOCOL(--p))-1,g,UNIQUE(VSTACK(SEQUENCE(9),TOCOL(INDEX(p,FLOOR(INT(z/9),3)+{1;2;3},FLOOR(MOD(z,9),3)+{1,2,3})),TOCOL(INDEX(p,INT(z/9)+1,)),INDEX(p,,MOD(z,9)+1)),,1),c,LAMBDA(c,L,x,IF(x>ROWS(L),FALSE,LET(s,S(S,IF(n=z,INDEX(L,x),p)),IF(AND(s),s,c(c,L,x+1))))),IFERROR(c(c,g,1),p))),CONCAT(S(S,--WRAPROWS(MID(i,SEQUENCE(1,81,1),1),9))))
If the condition to read and output an 81 character string is omitted, you could reference an inputted puzzle in the spreadsheet as a range "A1:I9" and solve it in 341 characters
=LET(S,LAMBDA(S,p,LET(n,SEQUENCE(9,9,0),z,XMATCH(0,TOCOL(--p))-1,g,UNIQUE(VSTACK(SEQUENCE(9),TOCOL(INDEX(p,FLOOR(INT(z/9),3)+{1;2;3},FLOOR(MOD(z,9),3)+{1,2,3})),TOCOL(INDEX(p,INT(z/9)+1,)),INDEX(p,,MOD(z,9)+1)),,1),c,LAMBDA(c,L,x,IF(x>ROWS(L),FALSE,LET(s,S(S,IF(n=z,INDEX(L,x),p)),IF(AND(s),s,c(c,L,x+1))))),IFERROR(c(c,g,1),p))),S(S,A1:I9))
Unpacked and with comments:
=LET(
S, LAMBDA(S, p,
LET(
n, SEQUENCE(9, 9, 0), // Creates a 9x9 grid initialized with zeros
z, XMATCH(0, TOCOL(--p))-1, // Finds the first empty cell (value 0)
g, UNIQUE(
VSTACK(
SEQUENCE(9), // Numbers 1-9 for possible candidates
TOCOL(INDEX(p, FLOOR(INT(z/9),3) + {1;2;3}, FLOOR(MOD(z,9),3) + {1,2,3})), // Values from 3x3 box
TOCOL(INDEX(p, INT(z/9) + 1, )), // Values from the same row
INDEX(p,, MOD(z,9) + 1) // Values from the same column
), ,1
), // Filters unique numbers to determine valid possibilities
c, LAMBDA(c, L, x,
IF(
x > ROWS(L), FALSE, // Terminates recursion if out of range
LET(
s, S(S, IF(n = z, INDEX(L, x), p)), // Recursively updates the Sudoku grid
IF(AND(s), s, c(c, L, x + 1)) // Continues recursion or returns solution
)
)
), // Recursive function to fill in Sudoku grid
IFERROR(c(c, g, 1), p) // Handles errors and returns the completed puzzle
)
),
S(S, A1:I9) // Initiates the solving function with the given puzzle range
)
D (322 chars)
For each unsolved square it builds an array of available options and then loops over it.
import std.algorithm,std.range,std.stdio;void main(char[][]args){T s(T)(T p){foreach(i,ref c;p)if(c<49){foreach(o;"123456789".setDifference(chain(p[i/9*9..i/9*9+9],p[i%9..$].stride(9),p[i/27*27+i%9/3*3..$][0..21].chunks(3).stride(3).joiner).array.sort)){c=o&63;if(s(p))return p;}c=48;return[];}return p;}s(args[1]).write;}
with whitespace:
import std.algorithm, std.range, std.stdio;
void main(char[][] args) {
T s(T)(T p) {
foreach (i, ref c; p) if (c < 49) {
foreach (o; "123456789".setDifference(chain(
p[i/9*9..i/9*9+9],
p[i%9..$].stride(9),
p[i/27*27+i%9/3*3..$][0..21].chunks(3).stride(3).joiner
).array.sort))
{
c = o&63;
if (s(p)) return p;
}
c=48;
return [];
}
return p;
}
s(args[1]).write;
}
Clojure - 480 bytes
The size exploded, but atleast it's a pretty number. I think it could be improved a lot by using just 1D-vector. Anyways, the test case takes a little under four seconds on my laptop. I thought it would be fitting to define a function, as it is a functional language after all.
(defn f[o &[x y]](if x(if(> y 8)(apply str(map #(apply str %)o))(first(for[q[(o y)]v(if(=(q x)0)(range 1 10)[(q x)])d[(assoc o y(assoc(o y)x v))]s[(and(every? true?(concat(for[i(range 9)](and(or(not=((d y)i)v)(= i x))(or(not=((d i)x)v)(= i y))))(for[m[#(+ %2(- %(mod % 3)))]r[(range 3)]a r b r c[(m y b)]e[(m x a)]](or(and(= e x)(= c y))(not=((d y)x)((d c)e))))))(f d(mod(+ x 1)9)(if(= x 8)(+ 1 y)y)))]:when s]s)))(f(vec(for[a(partition 9 o)](vec(map #(Integer.(str %))a))))0 0)))
Examples:
(f "030001000006000050500000983080006302000050000903800060714000009020000800000400030")
=> "832591674496387251571264983185746392267953418943812765714638529329175846658429137"
(f "004720900039008005001506004040010520028050170016030090400901300100300840007085600")
=> "654723981239148765871596234743819526928654173516237498482961357165372849397485612"
A slightly ungolfed (and prettier) version:
(defn check-place [o x y v]
(and (every? true? (for [i (range 9)]
(and (or (not= ((o y) i) v) (= i x))
(or (not= ((o i) x) v) (= i y)))))
(every? true?
(for [r [(range 3)]
a r
b r
c [(+ b (- y (mod y 3)))]
d [(+ a (- x (mod x 3)))]]
(or (and (= d x) (= c y)) (not= ((o y) x) ((o c) d)))))))
(defn solve-sudoku [board & [x y]]
(if x
(if (> y 8)
(apply str (map #(apply str %) board))
(first
(for [v (if (= ((board y) x) 0) (range 1 10) [((board y) x)])
:let [a (mod (+ x 1) 9)
b (if (= x 8) (+ 1 y) y)
d (assoc board y (assoc (board y) x v))
s (and (check-place d x y v) (solve-sudoku d a b))]
:when s]
s)))
(solve-sudoku (vec (for [a (partition 9 board)]
(vec (map #(Integer. (str %)) a)))) 0 0)))
J, 94 bytes
Works in exactly the same way as the K version, namely with a BFS (so it shall output all solutions). It prints spaces between output digits, but so does the K program. I’m not counting "s=:" as this is just naming the function (just like I wouldn’t count the filename in another language).
s=: [:<@((]i.0:)}"0 _~(>:i.9)-.{&((+./ .=|:)3(],.[,@#.<.@%~)9 9#:i.81)@i.&0#])"1^:(0 e.,)@;^:_"."0
s'030001000006000050500000983080006302000050000903800060714000009020000800000400030'
8 3 2 5 9 1 6 7 4 4 9 6 3 8 7 2 5 1 5 7 1 2 6 4 9 8 3 1 8 5 7 4 6 3 9 2 2 6 7 9 5 3 4 1 8 9 4 3 8 1 2 7 6 5 7 1 4 6 3 8 5 2 9 3 2 9 1 7 5 8 4 6 6 5 8 4 2 9 1 3 7
PowerShell, (削除) 244 (削除ここまで) (削除) 242 (削除ここまで) (削除) 218 (削除ここまで) 215 bytes
$a=(24,24,6)*3|%{,(0..8|%{($r++)});,(0..8|%{$c%81;$c+=9});$c++;,((1,1,7)*3|%{+$q;$q+=$_});$q-=$_}
$f={param($s)$l,$r=$s-split0,2;if($p=$a|?{$l.length-in$_}){1..9|?{"$_"-notin($p|%{$s[$_]})}|%{&$f "$l$_$r"}}else{$s}}
The script finds all solutions for a sudoku.
Unrolled:
$a=(24,24,6)*3|%{ # array of indexes for a sudoku...
,(0..8|%{($r++)}) # rows
,(0..8|%{$c%81;$c+=9});$c++ # columns
,((1,1,7)*3|%{+$q;$q+=$_});$q-=$_ # and squares
}
$f = {
param($s)
# optional log. remove this statement in a release version.
if($script:iter++ -lt 100 -or ($script:iter%100)-eq0){
Write-Information ('{0}: {1,6}: {2}'-f (get-Date), $script:iter, ($s-replace0,' ')) -InformationAction Continue
}
$left,$right=$s-split0,2 # split by a first 0; $left.length is a position of this 0 if $s contains the 0
if( $parts=$a|?{$left.length-in$_} ){ # get sudoku parts (rows, columns, squares) contain the position
1..9|?{ # try a digit
"$_"-notin($parts|%{$s[$_]}) # all digits in these parts will be unique if parts do not contain the digit
}|%{
&$f "$left$_$right" # recursive call with the digit
} #|select -f 1 # uncomment this to get a first result only
}
else{
$s
}
}
Test cases:
@(
# 5 iterations, my notebook: 00:00:00, all
# 5 iterations, my notebook: 00:00:00, first only
, ( "832591674496387251571264983185746392267953418943812765714638529329175846658400030",
"832591674496387251571264983185746392267953418943812765714638529329175846658429137" )
# ~29600 iterations, my notebook: 00:01:27, all
# ~2100 iterations, my notebook: 00:00:10, first only
# , ( "830001000006000050500000983080006302000050000903800060714000009020000800000400030",
# "832591674496387251571264983185746392267953418943812765714638529329175846658429137" )
# ~49900 iterations, my notebook: 00:02:39, all
# ~22400 iterations, my notebook: 00:01:20, first only
# , ( "030001000006000050500000983080006302000050000903800060714000009020000800000400030",
# "832591674496387251571264983185746392267953418943812765714638529329175846658429137" )
) | % {
$sudoku, $expected = $_
$time = Measure-Command {
$result = &$f $sudoku
}
"$($result-contains$expected): $time"
$result
}
Perl (195 chars)
use integer;@A=split//,<>;sub R{for$i(0..80){next if$A[$i];my%t=map{$_/9==$/9||$_%9==$i%9||$_/27==$i/27&&$_%9/3==$i%9/3?$A[$_]:0=>1}0..80;R($A[$i]=$_)for grep{!$t{$_}}1..9;return$A[$i]=0}die@A}R
All credit goes to the creator here, and the explanation can be found there as well.
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1\$\begingroup\$ If you didn't write it yourself, then you should check the "Community Wiki" button. \$\endgroup\$Kyle Kanos– Kyle Kanos2014年07月11日 14:04:06 +00:00Commented Jul 11, 2014 at 14:04
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\$\begingroup\$ Hmm, wasn't aware of that requirement. \$\endgroup\$Kyle Kanos– Kyle Kanos2014年07月11日 20:28:58 +00:00Commented Jul 11, 2014 at 20:28
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