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{{task|Games}}
;Task:
Solve a partially filled-in normal 9x9 [[wp:Sudoku|Sudoku]] grid and display the result in a human-readable format.
;references:
* [[wp:Algorithmics_of_sudoku|Algorithmics of Sudoku]] may help implement this.
* [https://www.youtube.com/watch?v=G_UYXzGuqvM Python Sudoku Solver] Computerphile video.
<br><br>
=={{header|11l}}==
{{trans|Kotlin}}
<syntaxhighlight lang="11l">T Sudoku
solved = 0B
grid = [0] * 81
F (rows)
assert(rows.len == 9 & all(rows.map(row -> row.len == 9)), ‘Grid must be 9 x 9’)
L(i) 9
L(j) 9
.grid[9 * i + j] = Int(rows[i][j])
F solve()
print("Starting grid:\n\n"(.))
.placeNumber(0)
print(I .solved {"Solution:\n\n"(.)} E ‘Unsolvable!’)
F placeNumber(pos)
I .solved
R
I pos == 81
.solved = 1B
R
I .grid[pos] > 0
.placeNumber(pos + 1)
R
L(n) 1..9
I .checkValidity(n, pos % 9, pos I/ 9)
.grid[pos] = n
.placeNumber(pos + 1)
I .solved
R
.grid[pos] = 0
F checkValidity(v, x, y)
L(i) 9
I .grid[y * 9 + i] == v |
.grid[i * 9 + x] == v
R 0B
V startX = (x I/ 3) * 3
V startY = (y I/ 3) * 3
L(i) startY .< startY + 3
L(j) startX .< startX + 3
I .grid[i * 9 + j] == v
R 0B
R 1B
F String()
V s = ‘’
L(i) 9
L(j) 9
s ‘’= .grid[i * 9 + j]‘ ’
I j C (2, 5)
s ‘’= ‘| ’
s ‘’= "\n"
I i C (2, 5)
s ‘’= "------+-------+------\n"
R s
V rows = [‘850002400’,
‘720000009’,
‘004000000’,
‘000107002’,
‘305000900’,
‘040000000’,
‘000080070’,
‘017000000’,
‘000036040’]
Sudoku(rows).solve()</syntaxhighlight>
{{out}}
<pre>
Starting grid:
8 5 0 | 0 0 2 | 4 0 0
7 2 0 | 0 0 0 | 0 0 9
0 0 4 | 0 0 0 | 0 0 0
------+-------+------
0 0 0 | 1 0 7 | 0 0 2
3 0 5 | 0 0 0 | 9 0 0
0 4 0 | 0 0 0 | 0 0 0
------+-------+------
0 0 0 | 0 8 0 | 0 7 0
0 1 7 | 0 0 0 | 0 0 0
0 0 0 | 0 3 6 | 0 4 0
Solution:
8 5 9 | 6 1 2 | 4 3 7
7 2 3 | 8 5 4 | 1 6 9
1 6 4 | 3 7 9 | 5 2 8
------+-------+------
9 8 6 | 1 4 7 | 3 5 2
3 7 5 | 2 6 8 | 9 1 4
2 4 1 | 5 9 3 | 7 8 6
------+-------+------
4 3 2 | 9 8 1 | 6 7 5
6 1 7 | 4 2 5 | 8 9 3
5 9 8 | 7 3 6 | 2 4 1
</pre>
=={{header|8th}}==
<syntaxhighlight lang="8th">
\
\ Simple iterative backtracking Sudoku solver for 8th
\
needs array/each-slice
[ 00, 00, 00, 03, 03, 03, 06, 06, 06,
00, 00, 00, 03, 03, 03, 06, 06, 06,
00, 00, 00, 03, 03, 03, 06, 06, 06,
27, 27, 27, 30, 30, 30, 33, 33, 33,
27, 27, 27, 30, 30, 30, 33, 33, 33,
27, 27, 27, 30, 30, 30, 33, 33, 33,
54, 54, 54, 57, 57, 57, 60, 60, 60,
54, 54, 54, 57, 57, 57, 60, 60, 60,
54, 54, 54, 57, 57, 57, 60, 60, 60 ] constant top-left-cell
\ Bit number presentations
a:new 2 b:new b:clear a:push ( 2 b:new b:clear swap 1 b:bit! a:push ) 0 8 loop constant posbit
: posbit? \ n -- s
posbit swap a:@ nip ;
: search \ b -- n
null swap
( dup -rot b:bit@ if rot drop break else nip then ) 0 8 loop
swap ;
: b-or \ b b -- b
' n:bor b:op ;
: b-and \ b b -- b
' n:band b:op ;
: b-xor \ b b -- b
b:xor
[ xff, x01 ] b:new
b-and ;
: b-not \ b -- b
xff b:xor
[ xff, x01 ] b:new
b-and ;
: b-any \ a -- b
' b-or 0 posbit? a:reduce ;
: row \ a row -- a
9 n:* 9 a:slice ;
: col \ a col -- a
-1 9 a:slice+ ;
\ For testing sub boards
: sub \ a n -- a
top-left-cell swap a:@ nip over over 3 a:slice
-rot 9 n:+ 2dup 3 a:slice
-rot 9 n:+ 3 a:slice
a:+ a:+ ;
a:new 0 args "Give Sudoku text file as param" thrownull
f:slurp "Cannot read file" thrownull >s "" s:/
' >n a:map ( posbit? a:push ) a:each! drop constant board
: display-board
board ( search nip -1 ?: n:1+ ) a:map
"+-----+-----+-----+\n"
"|%d %d %d|%d %d %d|%d %d %d|\n" s:+
"|%d %d %d|%d %d %d|%d %d %d|\n" s:+
"|%d %d %d|%d %d %d|%d %d %d|\n" s:+
"+-----+-----+-----+\n" s:+
"|%d %d %d|%d %d %d|%d %d %d|\n" s:+
"|%d %d %d|%d %d %d|%d %d %d|\n" s:+
"|%d %d %d|%d %d %d|%d %d %d|\n" s:+
"+-----+-----+-----+\n" s:+
"|%d %d %d|%d %d %d|%d %d %d|\n" s:+
"|%d %d %d|%d %d %d|%d %d %d|\n" s:+
"|%d %d %d|%d %d %d|%d %d %d|\n" s:+
"+-----+-----+-----+\n" s:+
s:strfmt . ;
\ Store move history
a:new constant history
\ Possible numbers for a cell
: candidates? \ n -- s
dup dup 9 n:/ n:int swap 9 n:mod \ row col
board swap col b-any
board rot row b-any
b-or
board rot sub b-any
b-or
b-not ;
\ If found: -- n T
\ If not found: -- T
: find-free-cell
false
board ( 0 posbit? b:= if nip true break else drop then ) a:each drop ;
: validate
true
board
( dup -rot a:@ swap 2 pick 0 posbit? a:! 2 pick candidates? 2 pick b:= if
-rot a:!
else
2drop drop
false swap
break
then ) 0 80 loop drop ;
: solve
repeat
find-free-cell if
dup candidates?
repeat
search null? if
drop board -rot a:! drop
history a:len 0 n:= if
drop false ;;
then
a:pop nip
a:open
else
n:1+ posbit?
dup
board 4 pick rot a:! drop
b-xor
2 a:close
history swap a:push drop
break
then
again
else
validate
break
then
again ;
: app:main
"Sudoku puzzle:\n" .
display-board cr
solve if
"Sudoku solved:\n" .
display-board
else
"No solution!\n" .
then ;
</syntaxhighlight>
=={{header|Ada}}==
{{trans|C++}}
<syntaxhighlight lang="ada">
with Ada.Text_IO;
procedure Sudoku is
type sudoku_ar_t is array ( integer range 0..80 ) of integer range 0..9;
FINISH_EXCEPTION : exception;
procedure prettyprint(sudoku_ar: sudoku_ar_t);
function checkValidity( val : integer; x : integer; y : integer; sudoku_ar: in sudoku_ar_t) return Boolean;
procedure placeNumber(pos: Integer; sudoku_ar: in out sudoku_ar_t);
procedure solve(sudoku_ar: in out sudoku_ar_t);
function checkValidity( val : integer; x : integer; y : integer; sudoku_ar: in sudoku_ar_t) return Boolean
is
begin
for i in 0..8 loop
if ( sudoku_ar( y * 9 + i ) = val or sudoku_ar( i * 9 + x ) = val ) then
return False;
end if;
end loop;
declare
startX : constant integer := ( x / 3 ) * 3;
startY : constant integer := ( y / 3 ) * 3;
begin
for i in startY..startY+2 loop
for j in startX..startX+2 loop
if ( sudoku_ar( i * 9 +j ) = val ) then
return False;
end if;
end loop;
end loop;
return True;
end;
end checkValidity;
procedure placeNumber(pos: Integer; sudoku_ar: in out sudoku_ar_t)
is
begin
if ( pos = 81 ) then
raise FINISH_EXCEPTION;
end if;
if ( sudoku_ar(pos) > 0 ) then
placeNumber(pos+1, sudoku_ar);
return;
end if;
for n in 1..9 loop
if( checkValidity( n, pos mod 9, pos / 9 , sudoku_ar ) ) then
sudoku_ar(pos) := n;
placeNumber(pos + 1, sudoku_ar );
sudoku_ar(pos) := 0;
end if;
end loop;
end placeNumber;
procedure solve(sudoku_ar: in out sudoku_ar_t)
is
begin
placeNumber( 0, sudoku_ar );
Ada.Text_IO.Put_Line("Unresolvable !");
exception
when FINISH_EXCEPTION =>
Ada.Text_IO.Put_Line("Finished !");
prettyprint(sudoku_ar);
end solve;
procedure prettyprint(sudoku_ar: sudoku_ar_t)
is
line_sep : constant String := "------+------+------";
begin
for i in sudoku_ar'Range loop
Ada.Text_IO.Put(sudoku_ar(i)'Image);
if (i+1) mod 3 = 0 and not((i+1) mod 9 = 0) then
Ada.Text_IO.Put("|");
end if;
if (i+1) mod 9 = 0 then
Ada.Text_IO.Put_Line("");
end if;
if (i+1) mod 27 = 0 then
Ada.Text_IO.Put_Line(line_sep);
end if;
end loop;
end prettyprint;
sudoku_ar : sudoku_ar_t :=
(
8,5,0,0,0,2,4,0,0,
7,2,0,0,0,0,0,0,9,
0,0,4,0,0,0,0,0,0,
0,0,0,1,0,7,0,0,2,
3,0,5,0,0,0,9,0,0,
0,4,0,0,0,0,0,0,0,
0,0,0,0,8,0,0,7,0,
0,1,7,0,0,0,0,0,0,
0,0,0,0,3,6,0,4,0
);
begin
solve( sudoku_ar );
end Sudoku;
</syntaxhighlight>
{{out}}
<pre>
Finished !
8 5 9| 6 1 2| 4 3 7
7 2 3| 8 5 4| 1 6 9
1 6 4| 3 7 9| 5 2 8
------+------+------
9 8 6| 1 4 7| 3 5 2
3 7 5| 2 6 8| 9 1 4
2 4 1| 5 9 3| 7 8 6
------+------+------
4 3 2| 9 8 1| 6 7 5
6 1 7| 4 2 5| 8 9 3
5 9 8| 7 3 6| 2 4 1
</pre>
=={{header|ALGOL 68}}==
Line 11 ⟶ 401:
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny].}}
{{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of '''format'''[ted] ''transput''.}}
<
MODE BOX = [3, 3]CHAR;
Line 105 ⟶ 495:
"__1__6__9"))
END CO
)</
{{out}}
<pre>
Line 125 ⟶ 515:
=={{header|AutoHotkey}}==
<
SetBatchLines, -1
SetTitleMatchMode, 3
Line 268 ⟶ 658:
r .= SubStr(p, A_Index, 1) . "|"
return r
}</
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f SUDOKU_RC.AWK
BEGIN {
# row1 row2 row3 row4 row5 row6 row7 row8 row9
# puzzle = "111111111 111111111 111111111 111111111 111111111 111111111 111111111 111111111 111111111" # NG duplicate hints
# puzzle = "1........ ..274.... ...5....4 .3....... 75....... .....96.. .4...6... .......71 .....1.30" # NG can't use zero
# puzzle = "1........ ..274.... ...5....4 .3....... 75....... .....96.. .4...6... .......71 .....1.39" # no solution
# puzzle = "1........ ..274.... ...5....4 .3....... 75....... .....96.. .4...6... .......71 .....1.3." # OK
puzzle = "123456789 456789123 789123456 ......... ......... ......... ......... ......... ........." # OK
gsub(/ /,"",puzzle)
if (length(puzzle) != 81) { error("length of puzzle is not 81") }
if (puzzle !~ /^[1-9\.]+$/) { error("only 1-9 and . are valid") }
if (gsub(/[1-9]/,"&",puzzle) < 17) { error("too few hints") }
if (errors > 0) {
exit(1)
}
plot(puzzle,"unsolved")
if (dup_hints_check(puzzle) == 1) {
if (solve(puzzle) == 1) {
dup_hints_check(sos)
plot(sos,"solved")
printf("\nbef: %s\naft: %s\n",puzzle,sos)
exit(0)
}
else {
error("no solution")
}
}
exit(1)
}
function dup_hints_check(ss, esf,msg,Rarr,Carr,Barr,i,r_row,r_col,r_pos,r_hint,c_row,c_col,c_pos,c_hint,box) {
esf = errors # errors so far
for (i=0; i<81; i++) {
# row
r_row = int(i/9) + 1 # determine row: 1..9
r_col = i%9 + 1 # determine column: 1..9
r_pos = i + 1 # determine hint position: 1..81
r_hint = substr(ss,r_pos,1) # extract 1 character; the hint
Rarr[r_row,r_hint]++ # save row
# column
c_row = i%9 + 1 # determine row: 1..9
c_col = int(i/9) + 1 # determine column: 1..9
c_pos = (c_row-1) * 9 + c_col # determine hint position: 1..81
c_hint = substr(ss,c_pos,1) # extract 1 character; the hint
Carr[c_col,c_hint]++ # save column
# box (there has to be a better way)
if ((r_row r_col) ~ /[123][123]/) { box = 1 }
else if ((r_row r_col) ~ /[123][456]/) { box = 2 }
else if ((r_row r_col) ~ /[123][789]/) { box = 3 }
else if ((r_row r_col) ~ /[456][123]/) { box = 4 }
else if ((r_row r_col) ~ /[456][456]/) { box = 5 }
else if ((r_row r_col) ~ /[456][789]/) { box = 6 }
else if ((r_row r_col) ~ /[789][123]/) { box = 7 }
else if ((r_row r_col) ~ /[789][456]/) { box = 8 }
else if ((r_row r_col) ~ /[789][789]/) { box = 9 }
else { box = 0 }
Barr[box,r_hint]++ # save box
}
dup_hints_print(Rarr,"row")
dup_hints_print(Carr,"column")
dup_hints_print(Barr,"box")
return((errors == esf) ? 1 : 0)
}
function dup_hints_print(arr,rcb, hint,i) {
# rcb - Row Column Box
for (i=1; i<=9; i++) { # "i" is either the row, column, or box
for (hint=1; hint<=9; hint++) { # 1..9 only; don't care about "." place holder
if (arr[i,hint]+0 > 1) { # was a digit specified more than once
error(sprintf("duplicate hint in %s %d",rcb,i))
}
}
}
}
function plot(ss,text1,text2, a,b,c,d,ou) {
# 1st call prints the unsolved puzzle.
# 2nd call prints the solved puzzle
printf("| - - - + - - - + - - - | %s\n",text1)
for (a=0; a<3; a++) {
for (b=0; b<3; b++) {
ou = "|"
for (c=0; c<3; c++) {
for (d=0; d<3; d++) {
ou = sprintf("%s %1s",ou,substr(ss,1+d+3*c+9*b+27*a,1))
}
ou = ou " |"
}
print(ou)
}
printf("| - - - + - - - + - - - | %s\n",(a==2)?text2:"")
}
}
function solve(ss, a,b,c,d,e,r,co,ro,bi,bl,nss) {
i = 0
# first, use some simple logic to fill grid as much as possible
do {
i++
didit = 0
delete nr
delete nc
delete nb
delete ca
for (a=0; a<81; a++) {
b = substr(ss,a+1,1)
if (b == ".") { # construct row, column and block at cell
c = a % 9
r = int(a/9)
ro = substr(ss,r*9+1,9)
co = ""
for (d=0; d<9; d++) { co = co substr(ss,d*9+c+1,1) }
bi = int(c/3)*3+(int(r/3)*3)*9+1
bl = ""
for (d=0; d<3; d++) { bl = bl substr(ss,bi+d*9,3) }
e = 0
# count non-occurrences of digits 1-9 in combined row, column and block, per row, column and block, and flag cell/digit as candidate
for (d=1; d<10; d++) {
if (index(ro co bl, d) == 0) {
e++
nr[r,d]++
nc[c,d]++
nb[bi,d]++
ca[c,r,d] = bi
}
}
if (e == 0) { # in case no candidate is available, give up
return(0)
}
}
}
# go through all cell/digit candidates
# hidden singles
for (crd in ca) {
# a candidate may have been deleted after the loop started
if (ca[crd] != "") {
split(crd,spl,SUBSEP)
c = spl[1]
r = spl[2]
d = spl[3]
bi = ca[crd]
a = c + r * 9
# unique solution if at least one non-occurrence counter is exactly 1
if ((nr[r,d] == 1) || (nc[c,d] == 1) || (nb[bi,d] == 1)) {
ss = substr(ss,1,a) d substr(ss,a+2,length(ss))
didit = 1
# remove candidates from current row, column, block
for (e=0; e<9; e++) {
delete ca[c,e,d]
delete ca[e,r,d]
}
for (e=0; e<3; e++) {
for (b=0; b<3; b++) {
delete ca[int(c/3)*3+b,int(r/3)*3+e,d]
}
}
}
}
}
} while (didit == 1)
# second, pick a viable solution for the next empty cell and see if it leads to a solution
a = index(ss,".")-1
if (a == -1) { # no more empty cells, done
sos = ss
return(1)
}
else {
c = a % 9
r = int(a/9)
# concatenate current row, column and block
# row
co = substr(ss,r*9+1,9)
# column
for (d=0; d<9; d++) { co = co substr(ss,d*9+c+1,1) }
# block
c = int(c/3)*3+(int(r/3)*3)*9+1
for (d=0; d<3; d++) { co = co substr(ss,c+d*9,3) }
for (b=1; b<10; b++) { # get a viable digit
if (index(co,b) == 0) { # check if candidate digit already exists
# is viable, put in cell
nss = substr(ss,1,a) b substr(ss,a+2,length(ss))
d = solve(nss) # try to solve
if (d == 1) { # if successful, return
return(1)
}
}
}
}
return(0) # no digits viable, no solution
}
function error(message) { printf("error: %s\n",message) ; errors++ }
</syntaxhighlight>
{{out}}
<pre>
| - - - + - - - + - - - | unsolved
| 1 2 3 | 4 5 6 | 7 8 9 |
| 4 5 6 | 7 8 9 | 1 2 3 |
| 7 8 9 | 1 2 3 | 4 5 6 |
| - - - + - - - + - - - |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| - - - + - - - + - - - |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| - - - + - - - + - - - |
| - - - + - - - + - - - | solved
| 1 2 3 | 4 5 6 | 7 8 9 |
| 4 5 6 | 7 8 9 | 1 2 3 |
| 7 8 9 | 1 2 3 | 4 5 6 |
| - - - + - - - + - - - |
| 2 1 4 | 3 6 5 | 8 9 7 |
| 3 6 5 | 8 9 7 | 2 1 4 |
| 8 9 7 | 2 1 4 | 3 6 5 |
| - - - + - - - + - - - |
| 5 3 1 | 6 4 2 | 9 7 8 |
| 6 4 2 | 9 7 8 | 5 3 1 |
| 9 7 8 | 5 3 1 | 6 4 2 |
| - - - + - - - + - - - |
bef: 123456789456789123789123456......................................................
aft: 123456789456789123789123456214365897365897214897214365531642978642978531978531642
</pre>
=={{header|BBC BASIC}}==
{{works with|BBC BASIC for Windows}}
[[Image:sudoku_bbc.gif|right]]
<
*FONT Arial,28
Line 377 ⟶ 990:
ENDIF
NEXT
= D%</
=={{header|BCPL}}==
<
// Implemented by Martin Richards.
// If you have cintcode BCPL installed on a Linux system you can compile and run this program
// execute the following sequence of commands.
// cd $BCPLROOT
// cintsys
// c bc sudoku
// sudoku
// This is a really naive program to solve SuDoku problems. Even so it is usually quite fast.
Line 767 ⟶ 1,388:
{ count := count + 1
prboard()
}</
=={{header|Befunge}}==
Input should be provided as a sequence of 81 digits (optionally separated by whitespace), with zero representing an unknown value.
<syntaxhighlight lang="befunge">99*>1-:0>:#$"0"\# #~`#$_"0"-\::9%:9+00p3/\9/:99++10p3vv%2g\g01<
2%v|:p+9/9\%9:\p\g02\1p\g01\1:p\g00\1:+8:\p02+*93+*3/<>\20g\g#:
v<+>:0\`>v >\::9%:9+00p3/\9/:99++10p3/3*+39*+20p\:8+::00g\g2%\^
v^+^pppp$_:|v<::<_>1-::9%\9/9+g.::9%!\3%+>>#v_>" "v..v,<<<+55<<
03!$v9:_>1v$>9%\v^|:<_v#<%<9<:<<_v#+%*93\!::<,,"|"<\/>:#^_>>>v^
p|<$0.0^!g+:#9/9<^@ ^,>#+5<5_>#!<>#$0"------+-------+-----":#<^
<>v$v1:::0<>"P"`!^>0g#0v#p+9/9\%9:p04:\pg03g021pg03g011pg03g001
::>^_:#<0#!:p#-\#1:#g0<>30g010g30g020g30g040g:9%\:9/9+\01-\1+0:</syntaxhighlight>
{{in}}
<pre>8 5 0 0 0 2 4 0 0
7 2 0 0 0 0 0 0 9
0 0 4 0 0 0 0 0 0
0 0 0 1 0 7 0 0 2
3 0 5 0 0 0 9 0 0
0 4 0 0 0 0 0 0 0
0 0 0 0 8 0 0 7 0
0 1 7 0 0 0 0 0 0
0 0 0 0 3 6 0 4 0</pre>
{{out}}
<pre>8 5 9 | 6 1 2 | 4 3 7
7 2 3 | 8 5 4 | 1 6 9
1 6 4 | 3 7 9 | 5 2 8
------+-------+------
9 8 6 | 1 4 7 | 3 5 2
3 7 5 | 2 6 8 | 9 1 4
2 4 1 | 5 9 3 | 7 8 6
------+-------+------
4 3 2 | 9 8 1 | 6 7 5
6 1 7 | 4 2 5 | 8 9 3
5 9 8 | 7 3 6 | 2 4 1</pre>
=={{header|Bracmat}}==
The program:
<
Solves any 9x9 sudoku, using backtracking.
Line 959 ⟶ 1,619:
. new$((its.sudoku),!arg):?puzzle
& (puzzle..Display)$
);</
Solve a sudoku that is hard for a brute force solver:
<
, (.- - - - - - - - -)
(.- - - - - 3 - 8 5)
Line 971 ⟶ 1,631:
(.- - 2 - 1 - - - -)
(.- - - - 4 - - - 9)
);</
Solution:
<pre>|~~~|~~~|~~~|
Line 991 ⟶ 1,651:
The following code is really only good for size 3 puzzles. A longer, even less readable version [[Sudoku/C|here]] could handle size 4s.
<
void show(int *x)
Line 1,057 ⟶ 1,717:
return 0;
}</
=={{header|
===
{{trans|Java}}
<
class SudokuSolver
Line 1,164 ⟶ 1,824:
Console.Read();
}
}</
=== Best First Search===
<!-- By Martin Freedman, 20/11/2021 -->
<syntaxhighlight lang="csharp">using System.Linq;
using static System.Linq.Enumerable;
using System.Collections.Generic;
using System;
using System.Runtime.CompilerServices;
namespace SodukoFastMemoBFS {
internal readonly record struct Square (int Row, int Col);
internal record Constraints (IEnumerable<int> ConstrainedRange, Square Square);
internal class Cache : Dictionary<Square, Constraints> { };
internal record CacheGrid (int[][] Grid, Cache Cache);
internal static class SudokuFastMemoBFS {
internal static U Fwd<T, U>(this T data, Func<T, U> f) => f(data);
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static int RowCol(int rc) => rc <= 2 ? 0 : rc <= 5 ? 3 : 6;
private static bool Solve(this CacheGrid cg, Constraints constraints, int finished) {
var (row, col) = constraints.Square;
foreach (var i in constraints.ConstrainedRange) {
cg.Grid[row][col] = i;
if (cg.Cache.Count == finished || cg.Solve(cg.Next(constraints.Square), finished))
return true;
}
cg.Grid[row][col] = 0;
return false;
}
private static readonly int[] domain = Range(0, 9).ToArray();
private static readonly int[] range = Range(1, 9).ToArray();
private static bool Valid(this int[][] grid, int row, int col, int val) {
for (var i = 0; i < 9; i++)
if (grid[row][i] == val || grid[i][col] == val)
return false;
for (var r = RowCol(row); r < RowCol(row) + 3; r++)
for (var c = RowCol(col); c < RowCol(col) + 3; c++)
if (grid[r][c] == val)
return false;
return true;
}
private static IEnumerable<int> Constraints(this int[][] grid, int row, int col) =>
range.Where(val => grid.Valid(row, col, val));
private static Constraints Next(this CacheGrid cg, Square square) =>
cg.Cache.ContainsKey(square)
? cg.Cache[square]
: cg.Cache[square]=cg.Grid.SortedCells();
private static Constraints SortedCells(this int[][] grid) =>
(from row in domain
from col in domain
where grid[row][col] == 0
let cell = new Constraints(grid.Constraints(row, col), new Square(row, col))
orderby cell.ConstrainedRange.Count() ascending
select cell).First();
private static CacheGrid Parse(string input) =>
input
.Select((c, i) => (index: i, val: int.Parse(c.ToString())))
.GroupBy(id => id.index / 9)
.Select(grp => grp.Select(id => id.val).ToArray())
.ToArray()
.Fwd(grid => new CacheGrid(grid, new Cache()));
public static string AsString(this int[][] grid) =>
string.Join('\n', grid.Select(row => string.Concat(row)));
public static int[][] Run(string input) {
var cg = Parse(input);
var marked = cg.Grid.SelectMany(row => row.Where(c => c > 0)).Count();
return cg.Solve(cg.Grid.SortedCells(), 80 - marked) ? cg.Grid : new int[][] { Array.Empty<int>() };
}
}
}</syntaxhighlight>
Usage
<syntaxhighlight lang="csharp">using System.Linq;
using static System.Linq.Enumerable;
using static System.Console;
using System.IO;
namespace SodukoFastMemoBFS {
static class Program {
static void Main(string[] args) {
var num = int.Parse(args[0]);
var puzzles = File.ReadLines(@"sudoku17.txt").Take(num);
var single = puzzles.First();
var watch = new System.Diagnostics.Stopwatch();
watch.Start();
WriteLine(SudokuFastMemoBFS.Run(single).AsString());
watch.Stop();
WriteLine($"{single}: {watch.ElapsedMilliseconds} ms");
WriteLine($"Doing {num} puzzles");
var total = 0.0;
watch.Start();
foreach (var puzzle in puzzles) {
watch.Reset();
watch.Start();
SudokuFastMemoBFS.Run(puzzle);
watch.Stop();
total += watch.ElapsedMilliseconds;
Write(".");
}
watch.Stop();
WriteLine($"\nPuzzles:{num}, Total:{total} ms, Average:{total / num:0.00} ms");
ReadKey();
}
}
}</syntaxhighlight>
Output
<pre>693784512
487512936
125963874
932651487
568247391
741398625
319475268
856129743
274836159
000000010400000000020000000000050407008000300001090000300400200050100000000806000: 336 ms
Doing 100 puzzles
....................................................................................................
Puzzles:100, Total:5316 ms, Average:53.16 ms</pre>
===Solver===
{{libheader|Microsoft Solver Foundation}}
<!-- By Nigel Galloway, Jan 29, 2012 -->
<
namespace Sudoku
Line 1,240 ⟶ 2,032:
}
}
}</
Produces:
<pre>
Line 1,255 ⟶ 2,047:
146 897 325
</pre>
==="Dancing Links"/Algorithm X===
<syntaxhighlight lang="csharp">using System;
using System.Collections.Generic;
using System.Text;
using static System.Linq.Enumerable;
public class Sudoku
{
public static void Main2() {
string puzzle = "....7.94.....9...53....5.7...74..1..463...........7.8.8........7......28.5.26....";
string solution = new Sudoku().Solutions(puzzle).FirstOrDefault() ?? puzzle;
Print(puzzle, solution);
}
private DLX dlx;
public void Build() {
const int rows = 9 * 9 * 9, columns = 4 * 9 * 9;
dlx = new DLX(rows, columns);
for (int i = 0; i < columns; i++) dlx.AddHeader();
for (int cell = 0, row = 0; row < 9; row++) {
for (int column = 0; column < 9; column++) {
int box = row / 3 * 3 + column / 3;
for (int digit = 0; digit < 9; digit++) {
dlx.AddRow(cell, 81 + row * 9 + digit, 2 * 81 + column * 9 + digit, 3 * 81 + box * 9 + digit);
}
cell++;
}
}
}
public IEnumerable<string> Solutions(string puzzle) {
if (puzzle == null) throw new ArgumentNullException(nameof(puzzle));
if (puzzle.Length != 81) throw new ArgumentException("The input is not of the correct length.");
if (dlx == null) Build();
for (int i = 0; i < puzzle.Length; i++) {
if (puzzle[i] == '0' || puzzle[i] == '.') continue;
if (puzzle[i] < '1' && puzzle[i] > '9') throw new ArgumentException($"Input contains an invalid character: ({puzzle[i]})");
int digit = puzzle[i] - '0' - 1;
dlx.Give(i * 9 + digit);
}
return Iterator();
IEnumerable<string> Iterator() {
var sb = new StringBuilder(new string('.', 81));
foreach (int[] rows in dlx.Solutions()) {
foreach (int r in rows) {
sb[r / 81 * 9 + r / 9 % 9] = (char)(r % 9 + '1');
}
yield return sb.ToString();
}
}
}
static void Print(string left, string right) {
foreach (string line in GetPrintLines(left).Zip(GetPrintLines(right), (l, r) => l + "\t" + r)) {
Console.WriteLine(line);
}
IEnumerable<string> GetPrintLines(string s) {
int r = 0;
foreach (string row in s.Cut(9)) {
yield return r == 0
? "╔═══╤═══╤═══╦═══╤═══╤═══╦═══╤═══╤═══╗"
: r % 3 == 0
? "╠═══╪═══╪═══╬═══╪═══╪═══╬═══╪═══╪═══╣"
: "╟───┼───┼───╫───┼───┼───╫───┼───┼───╢";
yield return "║ " + row.Cut(3).Select(segment => segment.DelimitWith(" │ ")).DelimitWith(" ║ ") + " ║";
r++;
}
yield return "╚═══╧═══╧═══╩═══╧═══╧═══╩═══╧═══╧═══╝";
}
}
}
public class DLX //Some functionality elided
{
private readonly Header root = new Header(null, null) { Size = int.MaxValue };
private readonly List<Header> columns;
private readonly List<Node> rows;
private readonly Stack<Node> solutionNodes = new Stack<Node>();
private int initial = 0;
public DLX(int rowCapacity, int columnCapacity) {
columns = new List<Header>(columnCapacity);
rows = new List<Node>(rowCapacity);
}
public void AddHeader() {
Header h = new Header(root.Left, root);
h.AttachLeftRight();
columns.Add(h);
}
public void AddRow(params int[] newRow) {
Node first = null;
if (newRow != null) {
for (int i = 0; i < newRow.Length; i++) {
if (newRow[i] < 0) continue;
if (first == null) first = AddNode(rows.Count, newRow[i]);
else AddNode(first, newRow[i]);
}
}
rows.Add(first);
}
private Node AddNode(int row, int column) {
Node n = new Node(null, null, columns[column].Up, columns[column], columns[column], row);
n.AttachUpDown();
n.Head.Size++;
return n;
}
private void AddNode(Node firstNode, int column) {
Node n = new Node(firstNode.Left, firstNode, columns[column].Up, columns[column], columns[column], firstNode.Row);
n.AttachLeftRight();
n.AttachUpDown();
n.Head.Size++;
}
public void Give(int row) {
solutionNodes.Push(rows[row]);
CoverMatrix(rows[row]);
initial++;
}
public IEnumerable<int[]> Solutions() {
try {
Node node = ChooseSmallestColumn().Down;
do {
if (node == node.Head) {
if (node == root) {
yield return solutionNodes.Select(n => n.Row).ToArray();
}
if (solutionNodes.Count > initial) {
node = solutionNodes.Pop();
UncoverMatrix(node);
node = node.Down;
}
} else {
solutionNodes.Push(node);
CoverMatrix(node);
node = ChooseSmallestColumn().Down;
}
} while(solutionNodes.Count > initial || node != node.Head);
} finally {
Restore();
}
}
private void Restore() {
while (solutionNodes.Count > 0) UncoverMatrix(solutionNodes.Pop());
initial = 0;
}
private Header ChooseSmallestColumn() {
Header traveller = root, choice = root;
do {
traveller = (Header)traveller.Right;
if (traveller.Size < choice.Size) choice = traveller;
} while (traveller != root && choice.Size > 0);
return choice;
}
private void CoverRow(Node row) {
Node traveller = row.Right;
while (traveller != row) {
traveller.DetachUpDown();
traveller.Head.Size--;
traveller = traveller.Right;
}
}
private void UncoverRow(Node row) {
Node traveller = row.Left;
while (traveller != row) {
traveller.AttachUpDown();
traveller.Head.Size++;
traveller = traveller.Left;
}
}
private void CoverColumn(Header column) {
column.DetachLeftRight();
Node traveller = column.Down;
while (traveller != column) {
CoverRow(traveller);
traveller = traveller.Down;
}
}
private void UncoverColumn(Header column) {
Node traveller = column.Up;
while (traveller != column) {
UncoverRow(traveller);
traveller = traveller.Up;
}
column.AttachLeftRight();
}
private void CoverMatrix(Node node) {
Node traveller = node;
do {
CoverColumn(traveller.Head);
traveller = traveller.Right;
} while (traveller != node);
}
private void UncoverMatrix(Node node) {
Node traveller = node;
do {
traveller = traveller.Left;
UncoverColumn(traveller.Head);
} while (traveller != node);
}
private class Node
{
public Node(Node left, Node right, Node up, Node down, Header head, int row) {
Left = left ?? this;
Right = right ?? this;
Up = up ?? this;
Down = down ?? this;
Head = head ?? this as Header;
Row = row;
}
public Node Left { get; set; }
public Node Right { get; set; }
public Node Up { get; set; }
public Node Down { get; set; }
public Header Head { get; }
public int Row { get; }
public void AttachLeftRight() {
this.Left.Right = this;
this.Right.Left = this;
}
public void AttachUpDown() {
this.Up.Down = this;
this.Down.Up = this;
}
public void DetachLeftRight() {
this.Left.Right = this.Right;
this.Right.Left = this.Left;
}
public void DetachUpDown() {
this.Up.Down = this.Down;
this.Down.Up = this.Up;
}
}
private class Header : Node
{
public Header(Node left, Node right) : base(left, right, null, null, null, -1) { }
public int Size { get; set; }
}
}
static class Extensions
{
public static IEnumerable<string> Cut(this string input, int length)
{
for (int cursor = 0; cursor < input.Length; cursor += length) {
if (cursor + length > input.Length) yield return input.Substring(cursor);
else yield return input.Substring(cursor, length);
}
}
public static string DelimitWith<T>(this IEnumerable<T> source, string separator) => string.Join(separator, source);
}</syntaxhighlight>
{{out}}
<pre>
╔═══╤═══╤═══╦═══╤═══╤═══╦═══╤═══╤═══╗ ╔═══╤═══╤═══╦═══╤═══╤═══╦═══╤═══╤═══╗
║ . │ . │ . ║ . │ 7 │ . ║ 9 │ 4 │ . ║ ║ 2 │ 1 │ 5 ║ 8 │ 7 │ 6 ║ 9 │ 4 │ 3 ║
╟───┼───┼───╫───┼───┼───╫───┼───┼───╢ ╟───┼───┼───╫───┼───┼───╫───┼───┼───╢
║ . │ . │ . ║ . │ 9 │ . ║ . │ . │ 5 ║ ║ 6 │ 7 │ 8 ║ 3 │ 9 │ 4 ║ 2 │ 1 │ 5 ║
╟───┼───┼───╫───┼───┼───╫───┼───┼───╢ ╟───┼───┼───╫───┼───┼───╫───┼───┼───╢
║ 3 │ . │ . ║ . │ . │ 5 ║ . │ 7 │ . ║ ║ 3 │ 4 │ 9 ║ 1 │ 2 │ 5 ║ 8 │ 7 │ 6 ║
╠═══╪═══╪═══╬═══╪═══╪═══╬═══╪═══╪═══╣ ╠═══╪═══╪═══╬═══╪═══╪═══╬═══╪═══╪═══╣
║ . │ . │ 7 ║ 4 │ . │ . ║ 1 │ . │ . ║ ║ 5 │ 8 │ 7 ║ 4 │ 3 │ 2 ║ 1 │ 6 │ 9 ║
╟───┼───┼───╫───┼───┼───╫───┼───┼───╢ ╟───┼───┼───╫───┼───┼───╫───┼───┼───╢
║ 4 │ 6 │ 3 ║ . │ . │ . ║ . │ . │ . ║ ║ 4 │ 6 │ 3 ║ 9 │ 8 │ 1 ║ 7 │ 5 │ 2 ║
╟───┼───┼───╫───┼───┼───╫───┼───┼───╢ ╟───┼───┼───╫───┼───┼───╫───┼───┼───╢
║ . │ . │ . ║ . │ . │ 7 ║ . │ 8 │ . ║ ║ 1 │ 9 │ 2 ║ 6 │ 5 │ 7 ║ 3 │ 8 │ 4 ║
╠═══╪═══╪═══╬═══╪═══╪═══╬═══╪═══╪═══╣ ╠═══╪═══╪═══╬═══╪═══╪═══╬═══╪═══╪═══╣
║ 8 │ . │ . ║ . │ . │ . ║ . │ . │ . ║ ║ 8 │ 2 │ 6 ║ 7 │ 4 │ 3 ║ 5 │ 9 │ 1 ║
╟───┼───┼───╫───┼───┼───╫───┼───┼───╢ ╟───┼───┼───╫───┼───┼───╫───┼───┼───╢
║ 7 │ . │ . ║ . │ . │ . ║ . │ 2 │ 8 ║ ║ 7 │ 3 │ 4 ║ 5 │ 1 │ 9 ║ 6 │ 2 │ 8 ║
╟───┼───┼───╫───┼───┼───╫───┼───┼───╢ ╟───┼───┼───╫───┼───┼───╫───┼───┼───╢
║ . │ 5 │ . ║ 2 │ 6 │ . ║ . │ . │ . ║ ║ 9 │ 5 │ 1 ║ 2 │ 6 │ 8 ║ 4 │ 3 │ 7 ║
╚═══╧═══╧═══╩═══╧═══╧═══╩═══╧═══╧═══╝ ╚═══╧═══╧═══╩═══╧═══╧═══╩═══╧═══╧═══╝</pre>
=={{header|C++}}==
{{trans|Java}}
<
using namespace std;
Line 1,338 ⟶ 2,432:
int main() {
SudokuSolver ss("850002400"
ss.solve();
return EXIT_SUCCESS;
}</syntaxhighlight>
=={{header|Clojure}}==
<
(:use [clojure.pprint :only (cl-format)]))
Line 1,376 ⟶ 2,469:
(if (= x (dec c))
(recur ng 0 (inc y))
(recur ng (inc x) y)))))))</
<
(solve [[3 9 4 0 0 2 6 7 0]
[0 0 0 3 0 0 4 0 0]
Line 1,398 ⟶ 2,491:
8 2 6 4 1 9 7 3 5
nil</
=={{header|Common Lisp}}==
A simple solver without optimizations (except for pre-computing the possible entries of a cell).
<
(dotimes (i 9 neighbors)
(let ((x (aref grid row i)))
Line 1,441 ⟶ 2,534:
(setf (aref grid row column) choice)
(when (eq grid (solve grid row (1+ column)))
(return grid))))))</
Example:
<pre>> (defparameter *puzzle*
Line 1,468 ⟶ 2,561:
(7 5 9 2 3 8 1 4 6)
(8 2 6 4 1 9 7 3 5))</pre>
=={{header|Crystal}}==
Based on the Java implementation presented in the video "[https://www.youtube.com/watch?v=mcXc8Mva2bA Create a Sudoku Solver In Java...]".
<syntaxhighlight lang="ruby">GRID_SIZE = 9
def isNumberInRow(board, number, row)
board[row].includes?(number)
end
def isNumberInColumn(board, number, column)
board.any?{|row| row[column] == number }
end
def isNumberInBox(board, number, row, column)
localBoxRow = row - row % 3
localBoxColumn = column - column % 3
(localBoxRow...(localBoxRow+3)).each do |i|
(localBoxColumn...(localBoxColumn+3)).each do |j|
return true if board[i][j] == number
end
end
false
end
def isValidPlacement(board, number, row, column)
return !isNumberInRow(board, number, row) &&
!isNumberInColumn(board, number, column) &&
!isNumberInBox(board, number, row, column)
end
def solveBoard(board)
board.each_with_index do |row, i|
row.each_with_index do |cell, j|
if(cell == 0)
(1..GRID_SIZE).each do |n|
if(isValidPlacement(board,n,i,j))
board[i][j]=n
if(solveBoard(board))
return true
else
board[i][j]=0
end
end
end
return false
end
end
end
return true
end
def printBoard(board)
board.each_with_index do |row, i|
row.each_with_index do |cell, j|
print cell
print '|' if j == 2 || j == 5
print '\n' if j == 8
end
print "-"*11 + '\n' if i == 2 || i == 5
end
print '\n'
end
board = [
[7, 0, 2, 0, 5, 0, 6, 0, 0],
[0, 0, 0, 0, 0, 3, 0, 0, 0],
[1, 0, 0, 0, 0, 9, 5, 0, 0],
[8, 0, 0, 0, 0, 0, 0, 9, 0],
[0, 4, 3, 0, 0, 0, 7, 5, 0],
[0, 9, 0, 0, 0, 0, 0, 0, 8],
[0, 0, 9, 7, 0, 0, 0, 0, 5],
[0, 0, 0, 2, 0, 0, 0, 0, 0],
[0, 0, 7, 0, 4, 0, 2, 0, 3]]
printBoard(board)
if(solveBoard(board))
printBoard(board)
end
</syntaxhighlight>
{{out}}
<pre>
702|050|600
000|003|000
100|009|500
-----------
800|000|090
043|000|750
090|000|008
-----------
009|700|005
000|200|000
007|040|203
732|458|619
956|173|824
184|629|537
-----------
871|564|392
643|892|751
295|317|468
-----------
329|786|145
418|235|976
567|941|283
</pre>
=={{header|Curry}}==
Copied from [http://www.informatik.uni-kiel.de/~curry/examples/ Curry: Example Programs].
<
--- Solving Su Doku puzzles in Curry with FD constraints
---
Line 1,533 ⟶ 2,728:
" 5 7 921 ",
" 64 9 ",
" 2 438"]</
Line 1,539 ⟶ 2,734:
{{Works with|PAKCS}}
Minimal w/o read or show utilities.
<
import Constraint (allC)
import List (transpose)
Line 1,572 ⟶ 2,767:
, [7,_,_,6,_,_,5,_,_]
]
main | sudoku xs = xs where xs = test</
{{Out}}
<pre>Execution time: 0 msec. / elapsed: 10 msec.
Line 1,580 ⟶ 2,775:
{{trans|C++}}
A little over-engineered solution, that shows some strong static typing useful in larger programs.
<
std.ascii, std.typecons;
Line 1,706 ⟶ 2,901:
else
solution.get.representSudoku.writeln;
}</
{{out}}
<pre>8 5 . | . . 2 | 4 . .
Line 1,734 ⟶ 2,929:
===Short Version===
Adapted from: http://code.activestate.com/recipes/576725-brute-force-sudoku-solver/
<
const(int)[] solve(immutable int[] s) pure nothrow @safe {
Line 1,767 ⟶ 2,962:
0, 0, 0, 0, 3, 6, 0, 4, 0];
writefln("%(%s\n%)", problem.solve.chunks(9));
}</
{{out}}
<pre>[8, 5, 9, 6, 1, 2, 4, 3, 7]
Line 1,781 ⟶ 2,976:
===No-Heap Version===
This version is similar to the precedent one, but it shows idioms to avoid memory allocations on the heap. This is enforced by the use of the @nogc attribute.
<
Nullable!(const ubyte[81]) solve(in ubyte[81] s) pure nothrow @safe @nogc {
Line 1,822 ⟶ 3,017:
0, 0, 0, 0, 3, 6, 0, 4, 0];
writefln("%(%s\n%)", problem.solve.get[].chunks(9));
}</
Same output.
=={{header|Delphi}}==
Example taken from C++
<
TIntArray = array of Integer;
Line 1,951 ⟶ 3,146:
ShowMessage('Solved!');
end;
end;</
Usage:
<
SudokuSolver: TSudokuSolver;
begin
Line 1,970 ⟶ 3,165:
FreeAndNil(SudokuSolver);
end;
end;</
=={{header|EasyLang}}==
<syntaxhighlight lang="text">
len row[] 90
len col[] 90
len box[] 90
len grid[] 82
#
proc init . .
for pos = 1 to 81
if pos mod 9 = 1
s$ = input
if s$ = ""
s$ = input
.
len inp[] 0
for i = 1 to len s$
if substr s$ i 1 <> " "
inp[] &= number substr s$ i 1
.
.
.
dig = number inp[(pos - 1) mod 9 + 1]
if dig > 0
grid[pos] = dig
r = (pos - 1) div 9
c = (pos - 1) mod 9
b = r div 3 * 3 + c div 3
row[r * 10 + dig] = 1
col[c * 10 + dig] = 1
box[b * 10 + dig] = 1
.
.
.
init
#
proc display . .
for i = 1 to 81
write grid[i] & " "
if i mod 3 = 0
write " "
.
if i mod 9 = 0
print ""
.
if i mod 27 = 0
print ""
.
.
.
#
proc solve pos . .
while grid[pos] <> 0
pos += 1
.
if pos > 81
# solved
display
return
.
r = (pos - 1) div 9
c = (pos - 1) mod 9
b = r div 3 * 3 + c div 3
r *= 10
c *= 10
b *= 10
for d = 1 to 9
if row[r + d] = 0 and col[c + d] = 0 and box[b + d] = 0
grid[pos] = d
row[r + d] = 1
col[c + d] = 1
box[b + d] = 1
solve pos + 1
row[r + d] = 0
col[c + d] = 0
box[b + d] = 0
.
.
grid[pos] = 0
.
solve 1
#
input_data
5 3 0 0 2 4 7 0 0
0 0 2 0 0 0 8 0 0
1 0 0 7 0 3 9 0 2
0 0 8 0 7 2 0 4 9
0 2 0 9 8 0 0 7 0
7 9 0 0 0 0 0 8 0
0 0 0 0 3 0 5 0 6
9 6 0 0 1 0 3 0 0
0 5 0 6 9 0 0 1 0
</syntaxhighlight>
=={{header|Elixir}}==
{{trans|Erlang}}
<
def display( grid ), do: ( for y <- 1..9, do: display_row(y, grid) )
Line 2,130 ⟶ 3,421:
{{3, 8}, 2}, {{5, 8}, 1},
{{5, 9}, 4}, {{9, 9}, 9}]
Sudoku.task( difficult )</
{{out}}
Line 2,190 ⟶ 3,481:
=={{header|Erlang}}==
I first try to solve the Sudoku grid without guessing. For the guessing part I eschew spawning a process for each guess, instead opting for backtracking. It is fun trying new things.
<syntaxhighlight lang="erlang">
-module( sudoku ).
Line 2,353 ⟶ 3,644:
display( Solved ),
io:nl().
</syntaxhighlight>
{{out}}
<pre>
Line 2,437 ⟶ 3,728:
0 is the empty cell.
<syntaxhighlight lang="erre">
!--------------------------------------------------------------------
! risolve Sudoku: in input il file SUDOKU.TXT
Line 2,844 ⟶ 4,135:
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
===Backtracking===
<!-- By Martin Freedman, 26/11/2021 -->
<syntaxhighlight lang="fsharp">module SudokuBacktrack
//Helpers
let tuple2 a b = a,b
let flip f a b = f b a
let (>>=) f g = Option.bind g f
/// "A1" to "I9" squares as key in values dictionary
let key a b = $"{a}{b}"
/// Cross product of elements in ax and elements in bx
let cross ax bx = [| for a in ax do for b in bx do key a b |]
// constants
let valid = "1234567890.,"
let rows = "ABCDEFGHI"
let cols = "123456789"
let squares = cross rows cols
// List of all row, cols and boxes: aka units
let unitList =
[for c in cols do cross rows (string c) ]@ // row units
[for r in rows do cross (string r) cols ]@ // col units
[for rs in ["ABC";"DEF";"GHI"] do for cs in ["123";"456";"789"] do cross rs cs ] // box units
/// Dictionary of units for each square
let units =
[for s in squares do s, [| for u in unitList do if u |> Array.contains s then u |] ] |> Map.ofSeq
/// Dictionary of all peer squares in the relevant units wrt square in question
let peers =
[for s in squares do units[s] |> Array.concat |> Array.distinct |> Array.except [s] |> tuple2 s] |> Map.ofSeq
/// Should parse grid in many input formats or return None
let parseGrid grid =
let ints = [for c in grid do if valid |> Seq.contains c then if ",." |> Seq.contains c then 0 else (c |> string |> int)]
if Seq.length ints = 81 then ints |> Seq.zip squares |> Map.ofSeq |> Some else None
/// Outputs single line puzzle with 0 as empty squares
let asString = function
| Some values -> values |> Map.toSeq |> Seq.map (snd>>string) |> String.concat ""
| _ -> "No solution or Parse Failure"
/// Outputs puzzle in 2D format with 0 as empty squares
let prettyPrint = function
| Some (values:Map<_,_>) ->
[for r in rows do [for c in cols do (values[key r c] |> string) ] |> String.concat " " ] |> String.concat "\n"
| _ -> "No solution or Parse Failure"
/// Is digit allowed in the square in question? !!! hot path !!!!
/// Array/Array2D no faster and they need explicit copy since not immutable
let constraints (values:Map<_,_>) s d = peers[s] |> Seq.map (fun p -> values[p]) |> Seq.exists ((=) d) |> not
/// Move to next square or None if out of bounds
let next s = squares |> Array.tryFindIndex ((=)s) |> function Some i when i + 1 < 81 -> Some squares[i + 1] | _ -> None
/// Backtrack recursively and immutably from index
let rec backtracker (values:Map<_,_>) = function
| None -> Some values // solved!
| Some s when values[s] > 0 -> backtracker values (next s) // square not empty
| Some s ->
let rec tracker = function
| [] -> None
| d::dx ->
values
|> Map.change s (Option.map (fun _ -> d))
|> flip backtracker (next s)
|> function
| None -> tracker dx
| success -> success
[for d in 1..9 do if constraints values s d then d] |> tracker
/// solve sudoku using simple backtracking
let solve grid = grid |> parseGrid >>= flip backtracker (Some "A1")</syntaxhighlight>
'''Usage:'''
<syntaxhighlight lang="fsharp">open System
open SudokuBacktrack
[<EntryPoint>]
let main argv =
let puzzle = "000028000800010000000000700000600403200004000100700000030400500000000010060000000"
puzzle |> printfn "Puzzle:\n%s"
puzzle |> parseGrid |> prettyPrint |> printfn "Formatted:\n%s"
puzzle |> solve |> prettyPrint |> printfn "Solution:\n%s"
printfn "Press any key to exit"
Console.ReadKey() |> ignore
0</syntaxhighlight>
{{Output}}<pre>
Puzzle:
000028000800010000000000700000600403200004000100700000030400500000000010060000000
Formatted:
0 0 0 0 2 8 0 0 0
8 0 0 0 1 0 0 0 0
0 0 0 0 0 0 7 0 0
0 0 0 6 0 0 4 0 3
2 0 0 0 0 4 0 0 0
1 0 0 7 0 0 0 0 0
0 3 0 4 0 0 5 0 0
0 0 0 0 0 0 0 1 0
0 6 0 0 0 0 0 0 0
Solution:
6 1 7 3 2 8 9 4 5
8 9 4 5 1 7 2 3 6
3 2 5 9 4 6 7 8 1
9 7 8 6 5 1 4 2 3
2 5 6 8 3 4 1 7 9
1 4 3 7 9 2 6 5 8
7 3 1 4 8 9 5 6 2
4 8 9 2 6 5 3 1 7
5 6 2 1 7 3 8 9 4
Press any key to exit
</pre>
===Constraint Satisfaction (Norvig)===
<!-- By Martin Freedman, 27/11/2021 -->
<syntaxhighlight lang="fsharp">// https://norvig.com/sudoku.html
// using array O(1) lookup & mutable instead of map O(logn) immutable - now 6 times faster
module SudokuCPSArray
open System
/// from 11 to 99 as squares key maps to 0 to 80 in arrays
let key a b = (9*a + b) - 10
/// Keys generator
let cross ax bx = [| for a in ax do for b in bx do key a b |]
let digits = [|1..9|]
let rows = digits
let cols = digits
let empty = "0,."
let valid = "123456789"+empty
let boxi = [for b in 1..3..9 -> [|b..b+2|]]
let squares = cross rows cols
/// List of all row, cols and boxes: aka units
let unitlist =
[for c in cols -> cross rows [|c|] ]@
[for r in rows -> cross [|r|] cols ]@
[for rs in boxi do for cs in boxi do cross rs cs ]
/// Dictionary of units for each square
let units =
[|for s in squares do [| for u in unitlist do if u |> Array.contains s then u |] |]
/// Dictionary of all peer squares in the relevant units wrt square in question
let peers =
[| for s in squares do units[s] |> Array.concat |> Array.distinct |> Array.except [s] |]
/// folds folder returning Some on completion or returns None if not
let rec all folder state source =
match state, source with
| None, _ -> None
| Some st, [] -> Some st
| Some st , hd::rest -> folder st hd |> (fun st1 -> all folder st1 rest)
/// Assign digit d to values[s] and propagate (via eliminate)
/// Return Some values, except None if a contradiction is detected.
let rec assign (values:int[][]) (s) d =
values[s]
|> Array.filter ((<>)d)
|> List.ofArray |> all (fun vx d1 -> eliminate vx s d1) (Some values)
/// Eliminate digit d from values[s] and propagate when values[s] size is 1.
/// Return Some values, except return None if a contradiction is detected.
and eliminate (values:int[][]) s d =
let peerElim (values1:int[][]) = // If a square s is reduced to one value d, then *eliminate* d from the peers.
match Seq.length values1[s] with
| 0 -> None // contradiction - removed last value
| 1 -> peers[s] |> List.ofArray |> all (fun vx1 s1 -> eliminate vx1 s1 (values1[s] |> Seq.head) ) (Some values1)
| _ -> Some values1
let unitsElim values1 = // If a unit u is reduced to only one place for a value d, then *assign* it there.
units[s]
|> List.ofArray
|> all (fun (vx1:int[][]) u ->
let sx = [for s in u do if vx1[s] |> Seq.contains d then s]
match Seq.length sx with
| 0 -> None
| 1 -> assign vx1 (Seq.head sx) d
| _ -> Some vx1) (Some values1)
match values[s] |> Seq.contains d with
| false -> Some values // Already eliminated, nothing to do
| true ->
values[s] <- values[s]|> Array.filter ((<>)d)
values
|> peerElim
|> Option.bind unitsElim
/// Convert grid into a Map of {square: char} with "0","."or"," for empties.
let parseGrid grid =
let cells = [for c in grid do if valid |> Seq.contains c then if empty |> Seq.contains c then 0 else ((string>>int)c)]
if Seq.length cells = 81 then cells |> Seq.zip squares |> Map.ofSeq |> Some else None
/// Convert grid to a Map of constraint propagated possible values, or return None if a contradiction is detected.
let applyCPS (parsedGrid:Map<_,_>) =
let values = [| for s in squares do digits |]
parsedGrid
|> Seq.filter (fun (KeyValue(_,d)) -> digits |> Seq.contains d)
|> List.ofSeq
|> all (fun vx (KeyValue(s,d)) -> assign vx s d) (Some values)
/// Calculate string centre for each square - which can contain more than 1 digit when debugging
let centre s width =
let n = width - (Seq.length s)
if n <= 0 then s
else
let half = n/2 + (if (n%2>0 && width%2>0) then 1 else 0)
sprintf "%s%s%s" (String(' ',half)) s (String(' ', n - half))
/// Display these values as a 2-D grid. Used for debugging
let prettyPrint (values:int[][]) =
let asString = Seq.map string >> String.concat ""
let width = 1 + ([for s in squares do Seq.length values[s]] |> List.max)
let line = sprintf "%s\n" ((String('-',width*3) |> Seq.replicate 3) |> String.concat "+")
[for r in rows do
for c in cols do
sprintf "%s%s" (centre (asString values[key r c]) width) (if List.contains c [3;6] then "|" else "")
sprintf "\n%s"(if List.contains r [3;6] then line else "") ]
|> String.concat ""
/// Outputs single line puzzle with 0 as empty squares
let asString values = values |> Map.toSeq |> Seq.map (snd>>string) |> String.concat ""
let copy values = values |> Array.map Array.copy
/// Using depth-first search and propagation, try all possible values.
let rec search (values:int[][])=
[for s in squares do if Seq.length values[s] > 1 then Seq.length values[s] ,s]
|> function
| [] -> Some values // Solved!
| list -> // tryPick ~ Norvig's `some`
list |> List.minBy fst
|> fun (_,s) -> values[s] |> Seq.tryPick (fun d -> assign (copy values) s d |> (Option.bind search))
let run n g f = parseGrid >> function None -> n | Some m -> f m |> g
let solver = run "Parse Error" (Option.fold (fun _ t -> t |> prettyPrint) "No Solution")
let solveNoSearch: string -> string = solver applyCPS
let solveWithSearch: string -> string = solver (applyCPS >> (Option.bind search))
let solveWithSearchToMapOnly:string -> int[][] option = run None id (applyCPS >> (Option.bind search)) </syntaxhighlight>
'''Usage'''<syntaxhighlight lang="fsharp">open System
open SudokuCPSArray
open System.Diagnostics
open System.IO
[<EntryPoint>]
let main argv =
printfn "Easy board solution automatic with constraint propagation"
let easy = "..3.2.6..9..3.5..1..18.64....81.29..7.......8..67.82....26.95..8..2.3..9..5.1.3.."
easy |> solveNoSearch |> printfn "%s"
printfn "Simple elimination not possible"
let simple = "4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......"
simple |> run "Parse Error" asString id |> printfn "%s"
simple |> solveNoSearch |> printfn "%s"
printfn "Try again with search:"
simple |> solveWithSearch |> printfn "%s"
let watch = Stopwatch()
let hard = "85...24..72......9..4.........1.7..23.5...9...4...........8..7..17..........36.4."
printfn "Hard"
watch.Start()
hard |> solveWithSearch |> printfn "%s"
watch.Stop()
printfn $"Elapsed milliseconds = {watch.ElapsedMilliseconds } ms"
watch.Reset()
let puzzles =
if Seq.length argv = 1 then
let num = argv[0] |> int
printfn $"First {num} puzzles in sudoku17 (http://staffhome.ecm.uwa.edu.au/~00013890/sudoku17)"
File.ReadLines(@"sudoku17.txt") |> Seq.take num |>Array.ofSeq
else
printfn $"All puzzles in sudoku17 (http://staffhome.ecm.uwa.edu.au/~00013890/sudoku17)"
File.ReadLines(@"sudoku17.txt") |>Array.ofSeq
watch.Start()
let result = puzzles |> Array.map solveWithSearchToMapOnly
watch.Stop()
if result |> Seq.forall Option.isSome then
let total = watch.ElapsedMilliseconds
let avg = (float total) /(float result.Length)
printfn $"\nPuzzles:{result.Length}, Total:%.2f{((float)total)/1000.0} s, Average:%.2f{avg} ms"
else
printfn "Some sudoku17 puzzles failed"
Console.ReadKey() |> ignore
0</syntaxhighlight>
{{Output}}Timings run on i7500U @2.75Ghz CPU, 16GB RAM<pre>Easy board solution automatic with constraint propagation
4 8 3 |9 2 1 |6 5 7
9 6 7 |3 4 5 |8 2 1
2 5 1 |8 7 6 |4 9 3
------+------+------
5 4 8 |1 3 2 |9 7 6
7 2 9 |5 6 4 |1 3 8
1 3 6 |7 9 8 |2 4 5
------+------+------
3 7 2 |6 8 9 |5 1 4
8 1 4 |2 5 3 |7 6 9
6 9 5 |4 1 7 |3 8 2
Simple elimination not possible
400000805030000000000700000020000060000080400000010000000603070500200000104000000
4 1679 12679 | 139 2369 269 | 8 1239 5
26789 3 1256789 | 14589 24569 245689 | 12679 1249 124679
2689 15689 125689 | 7 234569 245689 | 12369 12349 123469
------------------------+------------------------+------------------------
3789 2 15789 | 3459 34579 4579 | 13579 6 13789
3679 15679 15679 | 359 8 25679 | 4 12359 12379
36789 4 56789 | 359 1 25679 | 23579 23589 23789
------------------------+------------------------+------------------------
289 89 289 | 6 459 3 | 1259 7 12489
5 6789 3 | 2 479 1 | 69 489 4689
1 6789 4 | 589 579 5789 | 23569 23589 23689
Try again with search:
4 1 7 |3 6 9 |8 2 5
6 3 2 |1 5 8 |9 4 7
9 5 8 |7 2 4 |3 1 6
------+------+------
8 2 5 |4 3 7 |1 6 9
7 9 1 |5 8 6 |4 3 2
3 4 6 |9 1 2 |7 5 8
------+------+------
2 8 9 |6 4 3 |5 7 1
5 7 3 |2 9 1 |6 8 4
1 6 4 |8 7 5 |2 9 3
Hard
8 5 9 |6 1 2 |4 3 7
7 2 3 |8 5 4 |1 6 9
1 6 4 |3 7 9 |5 2 8
------+------+------
9 8 6 |1 4 7 |3 5 2
3 7 5 |2 6 8 |9 1 4
2 4 1 |5 9 3 |7 8 6
------+------+------
4 3 2 |9 8 1 |6 7 5
6 1 7 |4 2 5 |8 9 3
5 9 8 |7 3 6 |2 4 1
Elapsed milliseconds = 8 ms
All puzzles in sudoku17 (http://staffhome.ecm.uwa.edu.au/~00013890/sudoku17)
Puzzles:49151, Total:80.99 s, Average:1.65 ms</pre>
===SLPsolve===
<syntaxhighlight lang="fsharp">
// Solve Sudoku Like Puzzles. Nigel Galloway: September 6th., 2018
let fN y n g=let _q n' g'=[for n in n*n'..n*n'+n-1 do for g in g*g'..g*g'+g-1 do yield (n,g)]
let N=[|for n in 0..(y/n)-1 do for g in 0..(y/g)-1 do yield _q n g|]
(fun n' g'->N.[((n'/n)*n+g'/g)])
let fI n=let _q g=[for n in 0..n-1 do yield (g,n)]
let N=[|for n in 0..n-1 do yield _q n|]
(fun g (_:int)->N.[g])
let fG n=let _q g=[for n in 0..n-1 do yield (n,g)]
let N=[|for n in 0..n-1 do yield _q n|]
(fun (_:int) n->N.[n])
let fE v z n g fn=let N,G,B,fn=fI z,fG z,fN z n g,readCSV ',' fn|>List.ofSeq
let fG n g mask=List.except (N n g@G n g@B n g) mask
let b=List.except(List.map(fun n->(n.row,n.col))fn)[for n in 0..z-1 do for g in 0..z-1 do yield (n,g)]
let q=Map.ofList[for v' in v do yield ((v'),List.choose(fun n->if n.value=v' then Some(n.row,n.col) else None)fn|>List.fold(fun z (n,g)->(n,g)::fG n g z)b)]
(fG,(fun n->Map.find n q),z,v)
let SLPsolve (N,G,z,l)=
let rec nQueens col mask res=[
if col=z then yield res else
yield! List.filter(fun(n,_)->n=col)mask|>List.collect(fun(n,g)->nQueens (col+1) (N n g mask) ((n,g)::res))]
let rec sudoku l res=seq{
match l with
|h::t->let n=nQueens 0 (List.except (List.concat res) (G h)) []
yield! n|>Seq.collect(fun n->sudoku t (n::res))
|_->yield res}
sudoku l []
let printSLP n g=
List.map2(fun n g->List.map(fun(n',g')->((n',g'),n))g) (List.rev n) g|>List.concat|>List.sortBy (fun ((_,n),_)->n)|>List.groupBy(fun ((n,_),_)->n)|>List.sortBy(fun(n,_)->n)
|>List.iter(fun (_,n)->n|>Seq.fold(fun z ((_,g),v)->[z..g-1]|>Seq.iter(fun _->printf " |");printf "%s|" v; g+1 ) 0 |>ignore;printfn "")
</syntaxhighlight>
'''Usage:'''
Given sud1.csv:
<pre>
7,1,,4,,6,,2
,,,,7,,,,3
4,,,,,1,,8
,,,,1,3,,,9
,,1,,,,7
2,,,8,6
,2,,1,,,,,4
9,,,,8
,7,,6,,4,,5,2
</pre>
then
<syntaxhighlight lang="fsharp">
let n=SLPsolve (fE ([1..9]|>List.map(string)) 9 3 3 "sud1.csv")
printSLP ([1..9]|>List.map(string)) (Seq.item 0 n)
</syntaxhighlight>
{{out}}
<pre>
7|1|8|4|3|6|9|2|5|
5|6|2|9|7|8|4|1|3|
4|3|9|5|2|1|6|8|7|
6|8|5|7|1|3|2|4|9|
3|9|1|2|4|5|7|6|8|
2|4|7|8|6|9|5|3|1|
8|2|6|1|5|7|3|9|4|
9|5|4|3|8|2|1|7|6|
1|7|3|6|9|4|8|5|2|
</pre>
=={{header|Forth}}==
{{works with|4tH|3.60.0}}
<
include lib/istype.4th
include lib/argopen.4th
Line 3,211 ⟶ 4,914:
;
sudoku</
=={{header|Fortran}}==
{{works with|Fortran|90 and later}}
This implementation uses a brute force method. The subroutine <code>solve</code> recursively checks valid entries using the rules defined in the function <code>is_safe</code>. When <code>solve</code> is called beyond the end of the sudoku, we know that all the currently entered values are valid. Then the result is displayed.
<
implicit none
Line 3,313 ⟶ 5,016:
end subroutine pretty_print
end program sudoku</
{{out}}<pre>
+-----+-----+-----+
Line 3,342 ⟶ 5,045:
|6 9 5|4 1 7|3 8 2|
+-----+-----+-----+</pre>
=={{header|FreeBASIC}}==
{{trans|VBA}}
<syntaxhighlight lang="freebasic">Dim Shared As Integer cuadricula(9, 9), cuadriculaResuelta(9, 9)
Function isSafe(i As Integer, j As Integer, n As Integer) As Boolean
Dim As Integer iMin, jMin, f, c
If cuadricula(i, j) <> 0 Then Return (cuadricula(i, j) = n)
'cuadricula(i, j) es una celda vacía. Compruebe si n está OK
'primero revisa la fila i
For f = 1 To 9
If cuadricula(i, f) = n Then Return False
Next f
'ahora comprueba la columna j
For c = 1 To 9
If cuadricula(c, j) = n Then Return False
Next c
'finalmente, compruebe el subcuadrado de 3x3 que contiene cuadricula(i,j)
iMin = 1 + 3 * Int((i - 1) / 3)
jMin = 1 + 3 * Int((j - 1) / 3)
For c = iMin To iMin + 2
For f = jMin To jMin + 2
If cuadricula(c, f) = n Then Return False
Next f
Next c
'todas las pruebas estuvieron OK
Return True
End Function
Sub Resolver(i As Integer, j As Integer)
Dim As Integer f, c, n, temp
If i > 9 Then
'salir con cuadriculaResuelta = cuadricula
For c = 1 To 9
For f = 1 To 9
cuadriculaResuelta(c, f) = cuadricula(c, f)
Next f
Next c
Exit Sub
End If
For n = 1 To 9
If isSafe(i, j, n) Then
temp = cuadricula(i, j)
cuadricula(i, j) = n
If j = 9 Then
Resolver i + 1, 1
Else
Resolver i, j + 1
End If
cuadricula(i, j) = temp
End If
Next n
End Sub
Dim As String s(9)
'inicializar la cuadrícula usando 9 cadenas, una por fila
s(1) = "001005070"
s(2) = "920600000"
s(3) = "008000600"
s(4) = "090020401"
s(5) = "000000000"
s(6) = "304080090"
s(7) = "007000300"
s(8) = "000007069"
s(9) = "010800700"
Dim As Integer i, j
For i = 1 To 9
For j = 1 To 9
cuadricula(i, j) = Int(Val(Mid(s(i), j, 1)))
Next j
Next i
Resolver 1, 1
Print "Solucion:"
Color 12: Print "---------+---------+---------"
For i = 1 To 9
For j = 1 To 9
Color 7: Print cuadriculaResuelta(i, j); " ";
Color 12
If (j Mod 3 = 0) And (j <> 9) Then Color 12: Print "|";
Next j
If (i Mod 3 = 0) Then Print !"\n---------+---------+---------" Else Print
Next i
Sleep</syntaxhighlight>
{{out}}
<pre>
Solucion:
---------+---------+---------
6 3 1 | 2 4 5 | 9 7 8
9 2 5 | 6 7 8 | 1 4 3
4 7 8 | 3 1 9 | 6 5 2
---------+---------+---------
7 9 6 | 5 2 3 | 4 8 1
1 8 2 | 9 6 4 | 5 3 7
3 5 4 | 7 8 1 | 2 9 6
---------+---------+---------
8 6 7 | 4 9 2 | 3 1 5
2 4 3 | 1 5 7 | 8 6 9
5 1 9 | 8 3 6 | 7 2 4
---------+---------+---------
</pre>
=={{header|FutureBasic}}==
First is a short version:
<syntaxhighlight lang="futurebasic">
include "Util_Containers.incl"
begin globals
container gC
end globals
BeginCDeclaration
short solve_sudoku(short i);
short check_sudoku(short r, short c);
CFMutableStringRef print_sudoku();
EndC
BeginCFunction
short sudoku[9][9] = {
{3,0,0,0,0,1,4,0,9},
{7,0,0,0,0,4,2,0,0},
{0,5,0,2,0,0,0,1,0},
{5,7,0,0,4,3,0,6,0},
{0,9,0,0,0,0,0,3,0},
{0,6,0,7,9,0,0,8,5},
{0,8,0,0,0,5,0,4,0},
{0,0,6,4,0,0,0,0,7},
{9,0,5,6,0,0,0,0,3},
};
short check_sudoku( short r, short c )
{
short i;
short rr, cc;
for (i = 0; i < 9; i++)
{
if (i != c && sudoku[r][i] == sudoku[r][c]) return 0;
if (i != r && sudoku[i][c] == sudoku[r][c]) return 0;
rr = r/3 * 3 + i/3;
cc = c/3 * 3 + i%3;
if ((rr != r || cc != c) && sudoku[rr][cc] == sudoku[r][c]) return 0;
}
return -1;
}
short solve_sudoku( short i )
{
short r, c;
if (i < 0) return 0;
else if (i >= 81) return -1;
r = i / 9;
c = i % 9;
if (sudoku[r][c])
return check_sudoku(r, c) && solve_sudoku(i + 1);
else
for (sudoku[r][c] = 9; sudoku[r][c] > 0; sudoku[r][c]--)
{
if ( solve_sudoku(i) ) return -1;
}
return 0;
}
CFMutableStringRef print_sudoku()
{
short i, j;
CFMutableStringRef mutStr;
mutStr = CFStringCreateMutable( kCFAllocatorDefault, 0 );
for (i = 0; i < 9; i++)
{
for (j = 0; j < 9; j++)
{
CFStringAppendFormat( mutStr, NULL, (CFStringRef)@" %d", sudoku[i][j] );
}
CFStringAppendFormat( mutStr, NULL, (CFStringRef)@"\r" );
}
return( mutStr );
}
EndC
toolbox fn solve_sudoku( short i ) = short
toolbox fn check_sudoku( short r, short c ) = short
toolbox fn print_sudoku() = CFMutableStringRef
short solution
CFMutableStringRef cfRef
gC = " "
cfRef = fn print_sudoku()
fn ContainerCreateWithCFString( cfRef, gC )
print : print "Sudoku challenge:" : print : print gC
solution = fn solve_sudoku(0)
print : print "Sudoku solved:" : print
if ( solution )
gC = " "
cfRef = fn print_sudoku()
fn ContainerCreateWithCFString( cfRef, gC )
print gC
else
print "No solution found"
end if
HandleEvents
</syntaxhighlight>
Output:
<pre>
Sudoku challenge:
3 0 0 0 0 1 4 0 9
7 0 0 0 0 4 2 0 0
0 5 0 2 0 0 0 1 0
5 7 0 0 4 3 0 6 0
0 9 0 0 0 0 0 3 0
0 6 0 7 9 0 0 8 5
0 8 0 0 0 5 0 4 0
0 0 6 4 0 0 0 0 7
9 0 5 6 0 0 0 0 3
Sudoku solved:
3 2 8 5 6 1 4 7 9
7 1 9 3 8 4 2 5 6
6 5 4 2 7 9 3 1 8
5 7 1 8 4 3 9 6 2
8 9 2 1 5 6 7 3 4
4 6 3 7 9 2 1 8 5
2 8 7 9 3 5 6 4 1
1 3 6 4 2 8 5 9 7
9 4 5 6 1 7 8 2 3
</pre>
More code in this one, but faster execution:
<pre>
begin globals
_digits = 9
_setH = 3
_setV = 3
_nSetH = 3
_nSetV = 3
begin record Board
Boolean f(_digits,_digits,_digits)
char match(_digits,_digits)
pointer previousBoard // singly-linked list used to discover repetitions
dim &&
end record
Board quiz
CFTimeInterval t
end globals
local mode
local fn CopyBoard( source as ^Board, dest as ^Board )
BlockMoveData( source, dest, sizeof( Board ) )
dest.previousBoard = source // linked list
end fn
local fn prepare( b as ^Board )
short i, j, n
for i = 1 to _digits
for j = 1 to _digits
for n = 1 to _digits
b.match[i, j] = 0
b.f[i, j, n] = _true
next n
next j
next i
end fn
local fn printBoard( b as ^Board )
short i, j
for i = 1 to _digits
for j = 1 to _digits
Print b.match[i, j];
next j
print
next i
end fn
local fn verifica( b as ^Board )
short i, j, n, first, x, y, ii
Boolean check
check = _true
for i = 1 to _digits
for j = 1 to _digits
if ( b.match[i, j] == 0 )
check = _false
for n = 1 to _digits
if ( b.f[i, j, n] != _false )
check = _true
end if
next n
if ( check == _false ) then exit fn
end if
next j
next i
check = _true
for j = 1 to _digits
for n = 1 to _digits
first = 0
for i = 1 to _digits
if ( b.match[i, j] == n )
if ( first == 0 )
first = i
else
check = _false
exit fn
end if
end if
next i
next n
next j
for i = 1 to _digits
for n = 1 to _digits
first = 0
for j = 1 to _digits
if ( b.match[i, j] == n )
if ( first == 0 )
first = j
else
check = _false
exit fn
end if
end if
next j
next n
next i
for x = 0 to ( _nSetH - 1 )
for y = 0 to ( _nSetV - 1 )
first = 0
for ii = 0 to ( _digits - 1 )
i = x * _setH + ii mod _setH + 1
j = y * _setV + ii / _setH + 1
if ( b.match[i, j] == n )
if ( first == 0 )
first = j
else
check = _false
exit fn
end if
end if
next ii
next y
next x
end fn = check
local fn setCell( b as ^Board, x as short, y as short, n as short) as boolean
short i, j, rx, ry
Boolean check
b.match[x, y] = n
for i = 1 to _digits
b.f[x, i, n] = _false
b.f[i, y, n] = _false
next i
rx = (x - 1) / _setH
ry = (y - 1) / _setV
for i = 1 to _setH
for j = 1 to _setV
b.f[ rx * _setH + i, ry * _setV + j, n ] = _false
next j
next i
check = fn verifica( #b )
if ( check == _false ) then exit fn
end fn = check
local fn solve( b as ^Board )
short i, j, n, first, x, y, ii, ppi, ppj
Boolean check
check = _true
for i = 1 to _digits
for j = 1 to _digits
if ( b.match[i, j] == 0 )
first = 0
for n = 1 to _digits
if ( b.f[i, j, n] != _false )
if ( first == 0 )
first = n
else
first = -1
exit for
end if
end if
next n
if ( first > 0 )
check = fn setCell( #b, i, j, first )
if ( check == _false ) then exit fn
check = fn solve(#b)
if ( check == _false ) then exit fn
end if
end if
next j
next i
for i = 1 to _digits
for n = 1 to _digits
first = 0
for j = 1 to _digits
if ( b.match[i, j] == n ) then exit for
if ( b.f[i, j, n] != _false ) and ( b.match[i, j] == 0 )
if ( first == 0 )
first = j
else
first = -1
exit for
end if
end if
next j
if ( first > 0 )
check = fn setCell( #b, i, first, n )
if ( check == _false ) then exit fn
check = fn solve(#b)
if ( check == _false ) then exit fn
end if
next n
next i
for j = 1 to _digits
for n = 1 to _digits
first = 0
for i = 1 to _digits
if ( b.match[i, j] == n ) then exit for
if ( b.f[i, j, n] != _false ) and ( b.match[i, j] == 0 )
if ( first == 0 )
first = i
else
first = -1
exit for
end if
end if
next i
if ( first > 0 )
check = fn setCell( #b, first, j, n )
if ( check == _false ) then exit fn
check = fn solve(#b)
if ( check == _false ) then exit fn
end if
next n
next j
for x = 0 to ( _nSetH - 1 )
for y = 0 to ( _nSetV - 1 )
for n = 1 to _digits
first = 0
for ii = 0 to ( _digits - 1 )
i = x * _setH + ii mod _setH + 1
j = y * _setV + ii / _setH + 1
if ( b.match[i, j] == n ) then exit for
if ( b.f[i, j, n] != _false ) and ( b.match[i, j] == 0 )
if ( first == 0 )
first = n
ppi = i
ppj = j
else
first = -1
exit for
end if
end if
next ii
if ( first > 0 )
check = fn setCell( #b, ppi, ppj, n )
if ( check == _false ) then exit fn
check = fn solve(#b)
if ( check == _false ) then exit fn
end if
next n
next y
next x
end fn = check
local fn resolve( b as ^Board )
Boolean check, daFinire
long i, j, n
Board localBoard
check = fn solve(b)
if ( check == _false )
exit fn
end if
daFinire = _false
for i = 1 to _digits
for j = 1 to _digits
if ( b.match[i, j] == 0 )
daFinire = _true
for n = 1 to _digits
if ( b.f[i, j, n] != _false )
fn CopyBoard( b, @localBoard )
check = fn setCell(@localBoard, i, j, n)
if ( check != _false )
check = fn resolve( @localBoard )
if ( check == -1 )
fn CopyBoard( @localBoard, b )
exit fn
end if
end if
end if
next n
end if
next j
next i
if daFinire
else
check = -1
end if
end fn = check
fn prepare( @quiz )
DATA 0,0,0,0,2,9,0,8,7
DATA 0,9,7,3,0,0,0,0,0
DATA 0,0,2,0,0,0,4,0,9
DATA 0,0,3,9,0,1,0,0,6
DATA 0,4,0,0,0,0,0,9,0
DATA 9,0,0,7,0,3,1,0,0
DATA 0,0,9,0,0,0,6,0,0
DATA 0,0,0,0,0,5,8,2,0
DATA 2,8,0,1,3,0,0,0,0
short i, j, d
for i = 1 to _digits
for j = 1 to _digits
read d
fn setCell(@quiz, j, i, d)
next j
next i
Print : print "quiz:"
fn printBoard( @quiz )
print : print "-------------------" : print
Boolean check
t = fn CACurrentMediaTime
check = fn resolve(@quiz)
t = (fn CACurrentMediaTime - t) * 1000
if ( check )
print "solution:"; str$( t ) + " ms"
else
print "No solution found"
end if
fn printBoard( @quiz )
HandleEvents
</pre>
Output:
<pre>
quiz:
0 0 0 0 0 9 0 0 2
0 9 0 0 4 0 0 0 8
0 7 2 3 0 0 9 0 0
0 3 0 9 0 7 0 0 1
2 0 0 0 0 0 0 0 3
9 0 0 1 0 3 0 5 0
0 0 4 0 0 1 6 8 0
8 0 0 0 9 0 0 2 0
7 0 9 6 0 0 0 0 0
-------------------
solution: 6.956 ms
3 8 6 5 7 9 4 1 2
1 9 5 2 4 6 3 7 8
4 7 2 3 1 8 9 6 5
6 3 8 9 5 7 2 4 1
2 5 1 8 6 4 7 9 3
9 4 7 1 2 3 8 5 6
5 2 4 7 3 1 6 8 9
8 6 3 4 9 5 1 2 7
7 1 9 6 8 2 5 3 4
</pre>
=={{header|Go}}==
Line 3,348 ⟶ 5,701:
Input to function solve is an 81 character string.
This seems to be a conventional computer representation for Sudoku puzzles.
<
import "fmt"
Line 3,549 ⟶ 5,902:
}
c.r.l, c.l.r = &c.x, &c.x
}</
{{out}}
<pre>
Line 3,577 ⟶ 5,930:
8 2 6 | 4 1 9 | 7 3 5
</pre>
=={{header|Golfscript}}==
Código sacado de http://www.golfscript.com/
Imprime todas las soluciones posibles, sale con un error, pero funciona.
<syntaxhighlight lang="golfscript">
'Solution:'
;'2 8 4 3 7 5 1 6 9
0 0 9 2 0 0 0 0 7
0 0 1 0 0 4 0 0 2
0 5 0 0 0 0 8 0 0
0 0 8 0 0 0 9 0 0
0 0 6 0 0 0 0 4 0
9 0 0 1 0 0 5 0 0
8 0 0 0 0 7 6 0 4
4 2 5 6 8 9 7 3 1'
{9/[n]*puts}:p; #optional formatting
~]{:@0?:^~!{@p}*10,@9/^9/=-@^9%>9%-@3/^9%3/>3%3/^27/={+}*-{@^<\+@1^+>+}/1}do
</syntaxhighlight>
=={{header|Groovy}}==
Line 3,582 ⟶ 5,955:
Non-guessing part is iterative. Guessing part is recursive. Implementation uses exception handling to back out of bad guesses.
I consider this a "brute force" solution of sorts, in that it is the same method I use when solving Sudokus manually.
<syntaxhighlight lang="groovy">final CELL_VALUES = ('1'..'9')
class GridException extends Exception {
Line 3,649 ⟶ 6,024:
}
grid
}</
'''Test/Benchmark Cases'''
Mentions of ''"exceptionally difficult" example in Wikipedia'' refer to this (former) page: [[https://en.wikipedia.org/w/index.php?title=Sudoku_solving_algorithms&oldid=410240496#Exceptionally_difficult_Sudokus_.28hardest_Sudokus.29 Exceptionally difficult Sudokus]]
<
//Used in Curry solution: ~ 0.1 seconds
'819..5.....2...75..371.4.6.4..59.1..7..3.8..2..3.62..7.5.7.921..64...9.....2..438',
Line 3,716 ⟶ 6,091:
solution.each { println it }
println "\nELAPSED: ${elapsed} seconds"
}</
{{out}} (last only):
Line 3,750 ⟶ 6,125:
=={{header|Java}}==
<
{
private int mBoard[][];
Line 3,758 ⟶ 6,133:
private boolean mColSubset[][];
private boolean mBoxSubset[][];
public Sudoku(int board[][]) {
mBoard = board;
mBoardSize = mBoard.length;
mBoxSize = (int)Math.sqrt(mBoardSize);
initSubsets();
}
public void initSubsets() {
mRowSubset = new boolean[mBoardSize][mBoardSize];
Line 3,778 ⟶ 6,154:
}
}
private void setSubsetValue(int i, int j, int value, boolean present) {
mRowSubset[i][value - 1] = present;
Line 3,784 ⟶ 6,160:
mBoxSubset[computeBoxNo(i, j)][value - 1] = present;
}
public boolean solve() {
return solve(0, 0);
}
public boolean solve(int i, int j) {
if(i == mBoardSize) {
Line 3,809 ⟶ 6,185:
}
}
mBoard[i][j] = 0;
return false;
}
private boolean isValid(int i, int j, int val) {
val--;
Line 3,819 ⟶ 6,195:
return !isPresent;
}
private int computeBoxNo(int i, int j) {
int boxRow = i / mBoxSize;
Line 3,825 ⟶ 6,201:
return boxRow * mBoxSize + boxCol;
}
public void print() {
for(int i = 0; i < mBoardSize; i++) {
Line 3,835 ⟶ 6,211:
System.out.print("| ");
}
System.out.print(mBoard[i][j] != 0 ? ((Object) (Integer.valueOf(mBoard[i][j]))) : "
System.out.print(' ');
}
System.out.println("|");
}
System.out.println(" -----------------------");
}
public static void main(String[] args) {
int[][] board = {
{8, 5, 0, 0, 0, 2, 4, 0, 0},
{7, 2, 0, 0, 0, 0, 0, 0, 9},
{0, 0, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 1, 0, 7, 0, 0, 2},
{3, 0, 5, 0, 0, 0, 9, 0, 0},
{0, 4, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 8, 0, 0, 7, 0},
{0, 1, 7, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 3, 6, 0, 4, 0}
};
Sudoku s = new Sudoku(board);
System.out.print("Starting grid:\n");
s.print();
if (s.solve()) {
System.out.print("\nSolution:\n");
s.print();
} else {
System.out.println("\nUnsolvable!");
}
}
}</syntaxhighlight>
{{out}}
<pre>
Starting grid:
-----------------------
| 8 5 - | - - 2 | 4 - - |
| 7 2 - | - - - | - - 9 |
| - - 4 | - - - | - - - |
-----------------------
| - - - | 1 - 7 | - - 2 |
| 3 - 5 | - - - | 9 - - |
| - 4 - | - - - | - - - |
-----------------------
| - - - | - 8 - | - 7 - |
| - 1 7 | - - - | - - - |
| - - - | - 3 6 | - 4 - |
-----------------------
Solution:
-----------------------
| 8 5 9 | 6 1 2 | 4 3 7 |
| 7 2 3 | 8 5 4 | 1 6 9 |
| 1 6 4 | 3 7 9 | 5 2 8 |
-----------------------
| 9 8 6 | 1 4 7 | 3 5 2 |
| 3 7 5 | 2 6 8 | 9 1 4 |
| 2 4 1 | 5 9 3 | 7 8 6 |
-----------------------
| 4 3 2 | 9 8 1 | 6 7 5 |
| 6 1 7 | 4 2 5 | 8 9 3 |
| 5 9 8 | 7 3 6 | 2 4 1 |
-----------------------
</pre>
=={{header|JavaScript}}==
====ES6====
<syntaxhighlight lang="javascript">//-------------------------------------------[ Dancing Links and Algorithm X ]--
/**
* The doubly-doubly circularly linked data object.
* Data object X
*/
class DoX {
/**
* @param {string} V
* @param {!DoX=} H
*/
constructor(V, H) {
this.V = V;
this.L = this;
this.R = this;
this.U = this;
this.D = this;
this.S = 1;
this.H = H || this;
H && (H.S += 1);
}
}
/**
* Helper function to help build a horizontal doubly linked list.
* @param {!DoX} e An existing node in the list.
* @param {!DoX} n A new node to add to the right of the existing node.
* @return {!DoX}
*/
const addRight = (e, n) => {
n.R = e.R;
n.L = e;
e.R.L = n;
return e.R = n;
};
/**
* Helper function to help build a vertical doubly linked list.
* @param {!DoX} e An existing node in the list.
* @param {!DoX} n A new node to add below the existing node.
*/
const addBelow = (e, n) => {
n.D = e.D;
n.U = e;
e.D.U = n;
return e.D = n;
};
/**
* Verbatim copy of DK's search algorithm. The meat of the DLX algorithm.
* @param {!DoX} h The root node.
* @param {!Array<!DoX>} s The solution array.
*/
const search = function(h, s) {
if (h.R == h) {
printSol(s);
} else {
let c = chooseColumn(h);
cover(c);
for (let r = c.D; r != c; r = r.D) {
s.push(r);
for (let j = r.R; r !=j; j = j.R) {
cover(j.H);
}
search(h, s);
r = s.pop();
for (let j = r.R; j != r; j = j.R) {
uncover(j.H);
}
}
uncover(c);
}
};
/**
* Verbatim copy of DK's algorithm for choosing the next column object.
* @param {!DoX} h
* @return {!DoX}
*/
const chooseColumn = h => {
let s = Number.POSITIVE_INFINITY;
let c = h;
for(let j = h.R; j != h; j = j.R) {
if (j.S < s) {
c = j;
s = j.S;
}
}
return c;
};
/**
* Verbatim copy of DK's cover algorithm
* @param {!DoX} c
*/
const cover = c => {
c.L.R = c.R;
c.R.L = c.L;
for (let i = c.D; i != c; i = i.D) {
for (let j = i.R; j != i; j = j.R) {
j.U.D = j.D;
j.D.U = j.U;
j.H.S = j.H.S - 1;
}
}
};
/**
* Verbatim copy of DK's cover algorithm
* @param {!DoX} c
*/
const uncover = c => {
for (let i = c.U; i != c; i = i.U) {
for (let j = i.L; i != j; j = j.L) {
j.H.S = j.H.S + 1;
j.U.D = j;
j.D.U = j;
}
}
c.L.R = c;
c.R.L = c;
};
//-----------------------------------------------------------[ Print Helpers ]--
/**
* Given the standard string format of a grid, print a formatted view of it.
* @param {!string|!Array} a
*/
const printGrid = function(a) {
const getChar = c => {
let r = Number(c);
if (isNaN(r)) { return c }
let o = 48;
if (r > 9 && r < 36) { o = 55 }
if (r >= 36) { o = 61 }
return String.fromCharCode(r + o)
};
a = 'string' == typeof a ? a.split('') : a;
let U = Math.sqrt(a.length);
let N = Math.sqrt(U);
let line = new Array(N).fill('+').reduce((p, c) => {
p.push(... Array.from(new Array(1 + N*2).fill('-')));
p.push(c);
return p;
}, ['\n+']).join('') + '\n';
a = a.reduce(function(p, c, i) {
let d = i && !(i % U), G = i && !(i % N);
i = !(i % (U * N));
d && !i && (p += '|\n| ');
d && i && (p += '|');
i && (p = '' + p + line + '| ');
return '' + p + (G && !d ? '| ' : '') + getChar(c) + ' ';
}, '') + '|' + line;
console.log(a);
};
/**
* Given a search solution, print the resultant grid.
* @param {!Array<!DoX>} a An array of data objects
*/
const printSol = a => {
printGrid(a.reduce((p, c) => {
let [i, v] = c.V.split(':');
p[i * 1] = v;
return p;
}, new Array(a.length).fill('.')));
};
//----------------------------------------------[ Grid to Exact cover Matrix ]--
/**
* Helper to get some meta about the grid.
* @param {!string} s The standard string representation of a grid.
* @return {!Array}
*/
const gridMeta = s => {
const g = s.split('');
const cellCount = g.length;
const tokenCount = Math.sqrt(cellCount);
const N = Math.sqrt(tokenCount);
const g2D = g.map(e => isNaN(e * 1) ?
new Array(tokenCount).fill(1).map((_, i) => i + 1) :
[e * 1]);
return [cellCount, N, tokenCount, g2D];
};
/**
* Given a cell grid index, return the row, column and box indexes.
* @param {!number} n The n-value of the grid. 3 for a 9x9 sudoku.
* @return {!function(!number): !Array<!number>}
*/
const indexesN = n => i => {
let c = Math.floor(i / (n * n));
i %= n * n;
return [c, i, Math.floor(c / n) * n + Math.floor(i / n)];
};
/**
* Given a puzzle string, reduce it to an exact-cover matrix and use
* Donald Knuth's DLX algorithm to solve it.
* @param puzString
*/
const reduceGrid = puzString => {
printGrid(puzString);
const [
numCells, // The total number of cells in a grid (81 for a 9x9 grid)
N, // the 'n' value of the grid. (3 for a 9x9 grid)
U, // The total number of unique tokens to be placed.
g2D // A 2D array representation of the grid, with each element
// being an array of candidates for a cell. Known cells are
// single element arrays.
] = gridMeta(puzString);
const getIndex = indexesN(N);
/**
* The DLX Header row.
* Its length is 4 times the grid's size. This is to be able to encode
* each of the 4 Sudoku constrains, onto each of the cells of the grid.
* The array is initialised with unlinked DoX nodes, but in the next step
* those nodes are all linked.
* @type {!Array.<!DoX>}
*/
const headRow = new Array(4 * numCells)
.fill('')
.map((_, i) => new DoX(`H${i}`));
/**
* The header row root object. This is circularly linked to be to the left
* of the first header object in the header row array.
* It is used as the entry point into the DLX algorithm.
* @type {!DoX}
*/
let H = new DoX('ROOT');
headRow.reduce((p, c) => addRight(p, c), H);
/**
* Transposed the sudoku puzzle into a exact cover matrix, so it can be passed
* to the DLX algorithm to solve.
*/
for (let i = 0; i < numCells; i++) {
const [ri, ci, bi] = getIndex(i);
g2D[i].forEach(num => {
let id = `${i}:${num}`;
let candIdx = num - 1;
// The 4 columns that we will populate.
const A = headRow[i];
const B = headRow[numCells + candIdx + (ri * U)];
const C = headRow[(numCells * 2) + candIdx + (ci * U)];
const D = headRow[(numCells * 3) + candIdx + (bi * U)];
// The Row-Column Constraint
let rcc = addBelow(A.U, new DoX(id, A));
// The Row-Number Constraint
let rnc = addBelow(B.U, addRight(rcc, new DoX(id, B)));
// The Column-Number Constraint
let cnc = addBelow(C.U, addRight(rnc, new DoX(id, C)));
// The Block-Number Constraint
addBelow(D.U, addRight(cnc, new DoX(id, D)));
});
}
search(H, []);
};
</syntaxhighlight>
<syntaxhighlight lang="javascript">[
'819..5.....2...75..371.4.6.4..59.1..7..3.8..2..3.62..7.5.7.921..64...9.....2..438',
'53..247....2...8..1..7.39.2..8.72.49.2.98..7.79.....8.....3.5.696..1.3...5.69..1.',
'..3.2.6..9..3.5..1..18.64....81.29..7.......8..67.82....26.95..8..2.3..9..5.1.3..',
'394..267....3..4..5..69..2..45...9..6.......7..7...58..1..67..8..9..8....264..735',
'97.3...6..6.75.........8.5.......67.....3.....539..2..7...25.....2.1...8.4...73..',
'4......6.5...8.9..3....1....2.7....1.9.....4.8....3.5....2....7..6.5...8.1......6',
'85...24..72......9..4.........1.7..23.5...9...4...........8..7..17..........36.4.',
'..1..5.7.92.6.......8...6...9..2.4.1.........3.4.8..9...7...3.......7.69.1.8..7..',
'.9...4..7.....79..8........4.58.....3.......2.....97.6........4..35.....2..6...8.',
'12.3....435....1....4........54..2..6...7.........8.9...31..5.......9.7.....6...8',
'9..2..5...4..6..3...3.....6...9..2......5..8...7..4..37.....1...5..2..4...1..6..9',
'1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..',
'12.4..3..3...1..5...6...1..7...9.....4.6.3.....3..2...5...8.7....7.....5.......98',
'..............3.85..1.2.......5.7.....4...1...9.......5......73..2.1........4...9',
'.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7.....',
'....839..1......3...4....7..42.3....6.......4....7..1..2........8...92.....25...6',
'..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7..6..5..'
].forEach(reduceGrid);
// Or of you want to create all the grids of a particular n-size.
// I run out of stack space at n = 9
let n = 2;
let s = new Array(Math.pow(n, 4)).fill('.').join('');
reduceGrid(s);
</syntaxhighlight>
<pre>+-------+-------+-------+
| . . 3 | . . . | . . . |
| 4 . . | . 8 . | . 3 6 |
| . . 8 | . . . | 1 . . |
+-------+-------+-------+
| . 4 . | . 6 . | . 7 3 |
| . . . | 9 . . | . . . |
| . . . | . . 2 | . . 5 |
+-------+-------+-------+
| . . 4 | . 7 . | . 6 8 |
| 6 . . | . . . | . . . |
| 7 . . | 6 . . | 5 . . |
+-------+-------+-------+
+-------+-------+-------+
| 1 2 3 | 4 5 6 | 7 8 9 |
| 4 5 7 | 1 8 9 | 2 3 6 |
| 9 6 8 | 3 2 7 | 1 5 4 |
+-------+-------+-------+
| 2 4 9 | 5 6 1 | 8 7 3 |
| 5 7 6 | 9 3 8 | 4 1 2 |
| 8 3 1 | 7 4 2 | 6 9 5 |
+-------+-------+-------+
| 3 1 4 | 2 7 5 | 9 6 8 |
| 6 9 5 | 8 1 4 | 3 2 7 |
| 7 8 2 | 6 9 3 | 5 4 1 |
+-------+-------+-------+
</pre>
=={{header|jq}}==
{{works with|jq}}
'''Also works with gojq, the Go implementation of jq'''
'''Also works with fq, a Go implementation of a large subset of jq'''
The two solutions presented here take advantage of jq's built-in backtracking
mechanism.
The first solution uses a naive backtracking algorithm which can readily be modified to include more sophisticated
strategies.
The second solution modifies `next_row` to use a simple greedy algorithm,
namely, "select the row with the fewest gaps".
For the `tarx0134` problem (taken from the
[https://en.wikipedia.org/w/index.php?title=Sudoku_solving_algorithms#Exceptionally_difficult_Sudokus_.28hardest_Sudokus.29 Wikipedia collection] but googleable by that name),
the running time (u+s) is reduced from 264s to 180s on my 3GHz machine.
The memory usage statistics as produced by `/usr/bin/time -lp`
are also shown in the output section below.
<syntaxhighlight lang=jq>
## Utility Functions
def div($b): (. - (. % $b)) / $b;
def count(s): reduce s as $_ (0; .+1);
def row($i): .[$i];
def col($j): transpose | row($j);
# pretty print
def pp: .[:3][],"", .[3:6][], "", .[6:][];
# Input: 9 x 9 matrix
# Output: linear array corresponding to the specified 3x3 block using IO=0:
# 0,0 0,1 0,2
# 1,0 1,1 1,2
# 2,0 2,1 2,2
def block($i;$j):
def x: range(0;3) + 3*$i;
def y: range(0;3) + 3*$j;
[.[x][y]];
# Output: linear block containing .[$i][$j]
def blockOf($i;$j):
block($i|div(3); $j|div(3));
# Input: the entire Sudoku matrix
# Output: the update matrix after solving for row $i
def solveRow($i):
def s:
(.[$i] | index(0)) as $j
| if $j
then ((( [range(1;10)] - row($i)) - col($j)) - blockOf($i;$j) ) as $candidates
| if $candidates|length == 0 then empty
else $candidates[] as $x
| .[$i][$j] = $x
| s
end
else .
end;
s;
def distinct: map(select(. != 0)) | length - (unique|length) == 0;
# Is the Sudoku valid?
def valid:
. as $in
| length as $l
| all(.[]; distinct) and
all( range(0;9); . as $i | $in | col($i) | distinct ) and
all( range(0;3); . as $i | all(range(0;3); . as $j
| $in | block($i;$j) | distinct ));
# input: the full puzzle in its current state
# output: null if there is no candidate next row
def next_row:
first( range(0; length) as $i | select(row($i)|index(0)) | $i) // null;
def solve(problem):
def s:
next_row as $ix
| if $ix then solveRow($ix) | s
else .
end;
if problem|valid then first(problem|s) | pp
else "The Sukoku puzzle is invalid."
end;
# Rating Program: dukuso's suexratt
# Rating: 3311
# Poster: tarek
# Label: tarx0134
# ........8..3...4...9..2..6.....79.......612...6.5.2.7...8...5...1.....2.4.5.....3
def tarx0134:
[[0,0,0,0,0,0,0,0,8],
[0,0,3,0,0,0,4,0,0],
[0,9,0,0,2,0,0,6,0],
[0,0,0,0,7,9,0,0,0],
[0,0,0,0,6,1,2,0,0],
[0,6,0,5,0,2,0,7,0],
[0,0,8,0,0,0,5,0,0],
[0,1,0,0,0,0,0,2,0],
[4,0,5,0,0,0,0,0,3]];
# An invalid puzzle, for checking `valid`:
def unsolvable:
[[3,9,4,3,0,2,6,7,0],
[0,0,0,3,0,0,4,0,0],
[5,0,0,6,9,0,0,2,0],
[0,4,5,0,0,0,9,0,0],
[6,0,0,0,0,0,0,0,7],
[0,0,7,0,0,0,5,8,0],
[0,1,0,0,6,7,0,0,8],
[0,0,9,0,0,8,0,0,0],
[0,2,6,4,0,0,7,3,5]] ;
solve(tarx0134)
</syntaxhighlight>
====Greedy Algorithm====
Replace `def next_row:` with the following definition:
<syntaxhighlight lang=jq>
# select a row with the fewest number of unknowns
def next_row:
length as $len
| . as $in
| reduce range(0;length) as $i ([];
. + [ [ count( $in[$i][] | select(. != 0)), $i] ] )
| map(select(.[0] != $len))
| if length == 0 then null
else max_by(.[0]) | .[1]
end ;
</syntaxhighlight>
{{output}}
For the naive next_row:
<pre>
[6,2,1,9,4,3,7,5,8]
[7,8,3,6,1,5,4,9,2]
[5,9,4,7,2,8,3,6,1]
[1,4,2,8,7,9,6,3,5]
[3,5,7,4,6,1,2,8,9]
[8,6,9,5,3,2,1,7,4]
[2,3,8,1,9,7,5,4,6]
[9,1,6,3,5,4,8,2,7]
[4,7,5,2,8,6,9,1,3]
# Summary performance statistics:
user 260.89
sys 3.32
2240512 maximum resident set size
1302528 peak memory footprint
</pre>
For the greedy next_row algorithm, jq produces the same solution
with the following performance statistics:
<pre>
user 177.94
sys 2.12
2224128 maximum resident set size
1277952 peak memory footprint
</pre>
gojq stats for the greedy algorithm:
<pre>
user 62.19
sys 7.44
7458418688 maximum resident set size
7683284992 peak memory footprint
</pre>
fq stats for the greedy algorithm:
<pre>
user 73.56
sys 5.34
6084091904 maximum resident set size
6436892672 peak memory footprint
</pre>
=={{header|Julia}}==
<syntaxhighlight lang="julia">function check(i, j)
id, im = div(i, 9), mod(i, 9)
jd, jm = div(j, 9), mod(j, 9)
jd == id && return true
jm == im && return true
div(id, 3) == div(jd, 3) &&
div(jm, 3) == div(im, 3)
end
const lookup = zeros(Bool, 81, 81)
for i in 1:81
for j in 1:81
lookup[i,j] = check(i-1, j-1)
end
end
function solve_sudoku(callback::Function, grid::Array{Int64})
(function solve()
for i in 1:81
if grid[i] == 0
t = Dict{Int64, Nothing}()
for j in 1:81
if lookup[i,j]
t[grid[j]] = nothing
end
end
for k in 1:9
if !haskey(t, k)
grid[i] = k
solve()
end
end
grid[i] = 0
return
end
end
callback(grid)
end)()
end
function display(grid)
for i in 1:length(grid)
print(grid[i], " ")
i % 3 == 0 && print(" ")
i % 9 == 0 && print("\n")
i % 27 == 0 && print("\n")
end
end
grid = Int64[5, 3, 0, 0, 2, 4, 7, 0, 0,
0, 0, 2, 0, 0, 0, 8, 0, 0,
1, 0, 0, 7, 0, 3, 9, 0, 2,
0, 0, 8, 0, 7, 2, 0, 4, 9,
0, 2, 0, 9, 8, 0, 0, 7, 0,
7, 9, 0, 0, 0, 0, 0, 8, 0,
0, 0, 0, 0, 3, 0, 5, 0, 6,
9, 6, 0, 0, 1, 0, 3, 0, 0,
0, 5, 0, 6, 9, 0, 0, 1, 0]
solve_sudoku(display, grid)</syntaxhighlight>
{{out}}
<pre>
5 3 9 8 2 4 7 6 1
6 7 2 1 5 9 8 3 4
1 8 4 7 6 3 9 5 2
3 1 8 5 7 2 6 4 9
4 2 5 9 8 6 1 7 3
7 9 6 3 4 1 2 8 5
8 4 1 2 3 7 5 9 6
9 6 7 4 1 5 3 2 8
2 5 3 6 9 8 4 1 7
</pre>
=={{header|Kotlin}}==
{{trans|C++}}
<syntaxhighlight lang="scala">// version 1.2.10
class Sudoku(rows: List<String>) {
private val grid = IntArray(81)
private var solved = false
init {
require(rows.size == 9 && rows.all { it.length == 9 }) {
"Grid must be 9 x 9"
}
for (i in 0..8) {
for (j in 0..8 ) grid[9 * i + j] = rows[i][j] - '0'
}
}
fun solve() {
println("Starting grid:\n\n$this")
placeNumber(0)
println(if (solved) "Solution:\n\n$this" else "Unsolvable!")
}
private fun placeNumber(pos: Int) {
if (solved) return
if (pos == 81) {
solved = true
return
}
if (grid[pos] > 0) {
placeNumber(pos + 1)
return
}
for (n in 1..9) {
if (checkValidity(n, pos % 9, pos / 9)) {
grid[pos] = n
placeNumber(pos + 1)
if (solved) return
grid[pos] = 0
}
}
}
private fun checkValidity(v: Int, x: Int, y: Int): Boolean {
for (i in 0..8) {
if (grid[y * 9 + i] == v || grid[i * 9 + x] == v) return false
}
val startX = (x / 3) * 3
val startY = (y / 3) * 3
for (i in startY until startY + 3) {
for (j in startX until startX + 3) {
if (grid[i * 9 + j] == v) return false
}
}
return true
}
override fun toString(): String {
val sb = StringBuilder()
for (i in 0..8) {
for (j in 0..8) {
sb.append(grid[i * 9 + j])
sb.append(" ")
if (j == 2 || j == 5) sb.append("| ")
}
sb.append("\n")
if (i == 2 || i == 5) sb.append("------+-------+------\n")
}
return sb.toString()
}
}
fun main(args: Array<String>) {
val rows = listOf(
"850002400",
"720000009",
"004000000",
"000107002",
"305000900",
"040000000",
"000080070",
"017000000",
"000036040"
)
Sudoku(rows).solve()
}</syntaxhighlight>
{{out}}
<pre>
Starting grid:
8 5 0 | 0 0 2 | 4 0 0
7 2 0 | 0 0 0 | 0 0 9
0 0 4 | 0 0 0 | 0 0 0
------+-------+------
0 0 0 | 1 0 7 | 0 0 2
3 0 5 | 0 0 0 | 9 0 0
0 4 0 | 0 0 0 | 0 0 0
------+-------+------
0 0 0 | 0 8 0 | 0 7 0
0 1 7 | 0 0 0 | 0 0 0
0 0 0 | 0 3 6 | 0 4 0
Solution:
8 5 9 | 6 1 2 | 4 3 7
7 2 3 | 8 5 4 | 1 6 9
1 6 4 | 3 7 9 | 5 2 8
------+-------+------
9 8 6 | 1 4 7 | 3 5 2
3 7 5 | 2 6 8 | 9 1 4
2 4 1 | 5 9 3 | 7 8 6
------+-------+------
4 3 2 | 9 8 1 | 6 7 5
6 1 7 | 4 2 5 | 8 9 3
5 9 8 | 7 3 6 | 2 4 1
</pre>
=={{header|Lua}}==
===without FFI, slow===
<syntaxhighlight lang="lua">--9x9 sudoku solver in lua
--based on a branch and bound solution
--fields are not tried in plain order
Line 4,028 ⟶ 7,179:
if x then
return printer(x)
end</
Input:
<pre>
Line 4,059 ⟶ 7,210:
</pre>
Time with luajit: 9.245s
===with FFI, fast===
<syntaxhighlight lang="lua">#!/usr/bin/env luajit
ffi=require"ffi"
local printf=function(fmt, ...) io.write(string.format(fmt, ...)) end
local band, bor, lshift, rshift=bit.band, bit.bor, bit.lshift, bit.rshift
local function show(x)
for i=0,8 do
if i%3==0 then print() end
for j=0,8 do
printf(j%3~=0 and "%2d" or "%3d", x[j+9*i])
end
print()
end
end
local function trycell(x, pos)
local row=math.floor(pos/9)
local col=pos%9
local used=0
if pos==81 then return true end
if x[pos]~=0 then return trycell(x, pos+1) end
for i=0,8 do
used=bor(used,lshift(1,x[i*9+col]-1))
end
for j=0,8 do
used=bor(used,lshift(1,x[row*9+j]-1))
end
row=math.floor(row/3)*3
col=math.floor(col/3)*3
for i=row,row+2 do
for j=col,col+2 do
used=bor(used, lshift(1, x[i*9+j]-1))
end
end
x[pos]=1
while x[pos]<=9 do
if band(used,1)==0 and trycell(x, pos+1) then return true end
used=rshift(used,1)
x[pos]=x[pos]+1
end
x[pos]=0
return false
end
local function solve(str)
local x=ffi.new("char[?]", 81)
str=str:gsub("[%c%s]","")
for i=0,81 do
x[i]=tonumber(str:sub(i+1, i+1)) or 0
end
if trycell(x, 0) then
show(x)
else
print("no solution")
end
end
do -- MAIN
solve([[
5.. .7. ...
6.. 195 ...
.98 ... .6.
8.. .6. ..3
4.. 8.3 ..1
7.. .2. ..6
.6. ... 28.
... 419 ..5
... .8. .79
]])
end</syntaxhighlight>
{{out}}
<pre>> time ./sudoku_fast.lua
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9
./sudoku_fast.lua 0,01s user 0,00s system 90% cpu 0,007 total</pre>
Speed is about the speed of unoptimized C, half as fast as optimized C (C normal=0.007 C opt=0.004)
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
NestWhile[
Join @@ Table[
Line 4,070 ⟶ 7,307:
Extract[Partition[s, {3, 3}], Quotient[#, 3, -2]]]} & /@
Position[s, 0, {2}],
Length@Last@# &], {s, #}] &, {sudoku}, ! FreeQ[#, 0] &]</
Example:
<syntaxhighlight lang="text">solve[{{9, 7, 0, 3, 0, 0, 0, 6, 0},
{0, 6, 0, 7, 5, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 8, 0, 5, 0},
Line 4,080 ⟶ 7,317:
{7, 0, 0, 0, 2, 5, 0, 0, 0},
{0, 0, 2, 0, 1, 0, 0, 0, 8},
{0, 4, 0, 0, 0, 7, 3, 0, 0}}]</
{{out}}
<pre>{{{9, 7, 5, 3, 4, 2, 8, 6, 1}, {8, 6, 1, 7, 5, 9, 4, 3, 2}, {3, 2, 4,
Line 4,091 ⟶ 7,328:
For this to work, this code must be placed in a file named "sudokuSolver.m"
<
%Define what each of the sub-boxes of the sudoku grid are by defining
Line 4,443 ⟶ 7,680:
%% End of program
end %end sudokuSolver</
[http://www.menneske.no/sudoku/eng/showpuzzle.html?number=6903541 Test Input]:
All empty cells must have a value of NaN.
<
1 NaN NaN NaN NaN NaN NaN 3 NaN
NaN NaN 4 NaN NaN NaN NaN 7 NaN
Line 4,454 ⟶ 7,691:
NaN 2 NaN NaN NaN NaN NaN NaN NaN
NaN 8 NaN NaN NaN 9 2 NaN NaN
NaN NaN NaN 2 5 NaN NaN NaN 6]</
[http://www.menneske.no/sudoku/eng/solution.html?number=6903541 Output]:
<
7 6 5 4 8 3 9 2 1
Line 4,466 ⟶ 7,703:
9 2 6 1 4 7 5 8 3
5 8 1 3 6 9 2 4 7
4 7 3 2 5 8 1 9 6</
=={{header|Nim}}==
{{trans|Kotlin}}
<syntaxhighlight lang="nim">{.this: self.}
type
Sudoku = ref object
grid : array[81, int]
solved : bool
proc `$`(self: Sudoku): string =
var sb: string = ""
for i in 0..8:
for j in 0..8:
sb &= $grid[i * 9 + j]
sb &= " "
if j == 2 or j == 5:
sb &= "| "
sb &= "\n"
if i == 2 or i == 5:
sb &= "------+------+------\n"
sb
proc init(self: Sudoku, rows: array[9, string]) =
for i in 0..8:
for j in 0..8:
grid[9 * i + j] = rows[i][j].int - '0'.int
proc checkValidity(self: Sudoku, v, x, y: int): bool =
for i in 0..8:
if grid[y * 9 + i] == v or grid[i * 9 + x] == v:
return false
var startX = (x div 3) * 3
var startY = (y div 3) * 3
for i in startY..startY + 2:
for j in startX..startX + 2:
if grid[i * 9 + j] == v:
return false
result = true
proc placeNumber(self: Sudoku, pos: int) =
if solved:
return
if pos == 81:
solved = true
return
if grid[pos] > 0:
placeNumber(pos + 1)
return
for n in 1..9:
if checkValidity(n, pos mod 9, pos div 9):
grid[pos] = n
placeNumber(pos + 1)
if solved:
return
grid[pos] = 0
proc solve(self: Sudoku) =
echo "Starting grid:\n\n", $self
placeNumber(0)
if solved:
echo "Solution:\n\n", $self
else:
echo "Unsolvable!"
var rows = ["850002400",
"720000009",
"004000000",
"000107002",
"305000900",
"040000000",
"000080070",
"017000000",
"000036040"]
var puzzle = Sudoku()
puzzle.init(rows)
puzzle.solve()</syntaxhighlight>
{{out}}
<pre>Starting grid:
8 5 0 | 0 0 2 | 4 0 0
7 2 0 | 0 0 0 | 0 0 9
0 0 4 | 0 0 0 | 0 0 0
------+-------+------
0 0 0 | 1 0 7 | 0 0 2
3 0 5 | 0 0 0 | 9 0 0
0 4 0 | 0 0 0 | 0 0 0
------+-------+------
0 0 0 | 0 8 0 | 0 7 0
0 1 7 | 0 0 0 | 0 0 0
0 0 0 | 0 3 6 | 0 4 0
Solution:
8 5 9 | 6 1 2 | 4 3 7
7 2 3 | 8 5 4 | 1 6 9
1 6 4 | 3 7 9 | 5 2 8
------+-------+------
9 8 6 | 1 4 7 | 3 5 2
3 7 5 | 2 6 8 | 9 1 4
2 4 1 | 5 9 3 | 7 8 6
------+-------+------
4 3 2 | 9 8 1 | 6 7 5
6 1 7 | 4 2 5 | 8 9 3
5 9 8 | 7 3 6 | 2 4 1</pre>
=={{header|OCaml}}==
uses the library [http://ocamlgraph.lri.fr/index.en.html ocamlgraph]
<
Copyright 2004-2007 Sylvain Conchon, Jean-Christophe Filliatre, Julien Signoles
Line 4,539 ⟶ 7,883:
module C = Coloring.Mark(G)
let () = C.coloring g 9; display ()</
=={{header|Oz}}==
Using built-in constraint propagation and search.
<
%% a puzzle is a function that returns an initial board configuration
fun {Puzzle1}
Line 4,626 ⟶ 7,970:
end
in
{Inspect {Solve Puzzle1}.1}</
=={{header|PARI/GP}}==
Build plugin for PARI's function interface from C code: sudoku.c
<
typedef int SUDOKU [9][9];
Line 4,702 ⟶ 8,045:
return gen_0; /* no solution */
}
</syntaxhighlight>
Compile plugin: gcc -O2 -Wall -fPIC -shared sudoku.c -o libsudoku.so -lpari
Install plugin from home directory and play:
<
Output:<pre> gp > S=[5,3,0,0,7,0,0,0,0;6,0,0,1,9,5,0,0,0;0,9,8,0,0,0,0,6,0;8,0,0,0,6,0,0,0,3;4,0,0,8,0,3,0,0,1;7,0,0,0,2,0,0,0,6;0,6,0,0,0,0,2,8,0;0,0,0,4,1,9,0,0,5;0,0,0,0,8,0,0,7,9]
[5 3 0 0 7 0 0 0 0]
[6 0 0 1 9 5 0 0 0]
[0 9 8 0 0 0 0 6 0]
[8 0 0 0 6 0 0 0 3]
[4 0 0 8 0 3 0 0 1]
[7 0 0 0 2 0 0 0 6]
[0 6 0 0 0 0 2 8 0]
[0 0 0 4 1 9 0 0 5]
[0 0 0 0 8 0 0 7 9]
gp > sudoku(S)
[5 3 4 6 7 8 9 1 2]
[6 7 2 1 9 5 3 4 8]
[1 9 8 3 4 2 5 6 7]
[8 5 9 7 6 1 4 2 3]
[4 2 6 8 5 3 7 9 1]
[7 1 3 9 2 4 8 5 6]
[9 6 1 5 3 7 2 8 4]
[2 8 7 4 1 9 6 3 5]
[3 4 5 2 8 6 1 7 9]
</pre>
Line 4,752 ⟶ 8,077:
{{works with|Free Pascal}}
Simple backtracking implimentation, therefor it must be fast to be competetive.With doReverse = true same sequence for trycell. nearly 5 times faster than [[Sudoku#C|C]]-Version.
<
{$IFDEF FPC}
{$CODEALIGN proc=16,loop=8}
Line 5,008 ⟶ 8,333:
Outfield(solF);
writeln(86400*1000*(T1-T0)/k:10:3,' ms Test calls :',callCnt/k:8:0);
end.</
{{out}}
<pre>
Line 5,044 ⟶ 8,369:
=={{header|Perl}}==
<
use integer;
use strict;
Line 5,083 ⟶ 8,408:
}
}
solve();</
{{out}}
<pre>
Line 5,099 ⟶ 8,424:
</pre>
=={{header|
Simple brute force solution. Generally quite good but will struggle on some puzzles (eg see "the beast" below)
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">board</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"""
.......39
.....1..5
..3.5.8..
..8.9...6
.7...2...
1..4.....
..9.8..5.
.2....6..
4..7....."""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'\n'</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">valid_move</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">][</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">y</span> <span style="color: #0000FF;">-=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">x</span> <span style="color: #0000FF;">-=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">ys</span><span style="color: #0000FF;">=</span><span style="color: #000000;">y</span> <span style="color: #008080;">to</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">xs</span><span style="color: #0000FF;">=</span><span style="color: #000000;">x</span> <span style="color: #008080;">to</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ys</span><span style="color: #0000FF;">][</span><span style="color: #000000;">xs</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">solution</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">brute_solve</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">][</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]<=</span><span style="color: #008000;">'0'</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'1'</span> <span style="color: #008080;">to</span> <span style="color: #008000;">'9'</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">valid_move</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">][</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ch</span>
<span style="color: #000000;">brute_solve</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">][</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">' '</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">solution</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (already solved case)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">brute_solve</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n(solved in %3.2fs)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
751846239
892371465
643259871
238197546
974562318
165438927
319684752
527913684
486725193
(solved in 0.95s)
</pre>
OTT solution. Implements line/col and set exclusion, and x-wings. Blisteringly fast<BR>
The included program demo\rosetta\Sudoku.exw is an extended version of this that performs extended validation,
contains 339 puzzles, can be run as a command-line or gui program, check for multiple solutions, and produce
a more readable single-puzzle output (example below).
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #000080;font-style:italic;">-- Working directly on 81-character strings ultimately proves easier: Originally I
-- just wanted to simplify the final display, but later I realised that a 9x9 grid
-- encourages laborious indexing/looping everwhere whereas using a flat 81-element
-- approach encourages precomputation of index sets, and once you commit to that,
-- the rest of the code starts to get a whole lot cleaner. Below we create 27+18
-- sets and 5 tables of lookup indexes to locate them quickly.</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">nines</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000080;font-style:italic;">-- will be 27 in total</span>
<span style="color: #000000;">cols</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- remainder(i-1,9)+1</span>
<span style="color: #000000;">rows</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- floor((i-1)/9)+10</span>
<span style="color: #000000;">squares</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">sixes</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000080;font-style:italic;">-- will be 18 in total</span>
<span style="color: #000000;">dotcol</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- same col, diff square</span>
<span style="color: #000000;">dotrow</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- same row, diff square</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">set_nines</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">nine</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">six</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">idx</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ndx</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- columns</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #000000;">ndx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">81</span> <span style="color: #008080;">by</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">x</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">,</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cols</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ndx</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">nines</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">81</span> <span style="color: #008080;">by</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- rows</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #000000;">ndx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">x</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">,</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">rows</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ndx</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">nines</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">18</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">by</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- small squares [19..27]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">by</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #000000;">ndx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">sy</span><span style="color: #0000FF;">=</span><span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span> <span style="color: #008080;">to</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">+</span><span style="color: #000000;">18</span> <span style="color: #008080;">by</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">sx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">x</span> <span style="color: #008080;">to</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sy</span><span style="color: #0000FF;">+</span><span style="color: #000000;">sx</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">,</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">squares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ndx</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">nines</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">27</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">six</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cols</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span> <span style="color: #000080;font-style:italic;">-- dotcol</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">squares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">squares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">six</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">six</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">ndx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">six</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sixes</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ndx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">sixes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sixes</span><span style="color: #0000FF;">,</span><span style="color: #000000;">six</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">ndx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sixes</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">dotcol</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ndx</span>
<span style="color: #000000;">six</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rows</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span> <span style="color: #000080;font-style:italic;">-- dotrow</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">squares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">squares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">six</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">six</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nine</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">ndx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">six</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sixes</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ndx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">sixes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sixes</span><span style="color: #0000FF;">,</span><span style="color: #000000;">six</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">ndx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sixes</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">dotrow</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ndx</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">set_nines</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">improved</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">eliminate_in</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">..</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #000000;">improved</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">valid</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">test_comb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">chosen</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">pool</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--
-- (see deep_logic()/set elimination)
-- chosen is a sequence of length 2..4 of integers 1..9: ordered elements of pool.
-- pool is a set of elements of the sequence valid, each of which is a sequence.
-- (note that elements of valid in pool not in chosen are not necessarily sequences)
--</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">contains</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ccount</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">set</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">pool</span><span style="color: #0000FF;">[</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">contains</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">contains</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">ccount</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ccount</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pool</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">pool</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- (reverse order so deletions don't foul indexes)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">contains</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">pool</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">..</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #000000;">improved</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">valid</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">-- from [[Combinations#Phix|Combinations]]
-- from http://rosettacode.org/wiki/Combinations#Phix</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">comb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">pool</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">needed</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">done</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">chosen</span><span style="color: #0000FF;">={})</span>
<span style="color: #000080;font-style:italic;">-- (used by deep_logic()/set elimination)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">needed</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- got a full set</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">test_comb</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pool</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">done</span><span style="color: #0000FF;">+</span><span style="color: #000000;">needed</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pool</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">valid</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- cannot fulfil
-- get all combinations with and without the next item:</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">pool</span><span style="color: #0000FF;">[</span><span style="color: #000000;">done</span><span style="color: #0000FF;">]])</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">comb</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pool</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">needed</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">done</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">),</span><span style="color: #000000;">done</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">comb</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pool</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">needed</span><span style="color: #0000FF;">,</span><span style="color: #000000;">done</span><span style="color: #0000FF;">,</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">deep_logic</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--
-- Create a grid of valid moves. Note this does not modify board, but instead creates
-- sets of permitted values for each cell, which can also be and are used for hints.
-- Apply standard eliminations of known cells, then try some more advanced tactics:
--
-- 1) row/col elimination
-- If in any of the 9 small squares a number can only occur in one row or column,
-- then that number cannot occur in that row or column in two other corresponding
-- small squares. Example
--
-- 840|000|000
--
--
--
--
-- 000|600|400
-- ---+---+---
-- 000|410|050
-- 003|000|200
-- 600|000|000 <-- 3
--
-- Naively, the br can contain a 3 in the four corners, but looking at mid-right and
-- mid-bottom leads us to eliminating 3s in column 9 and row 9, leaving 7,7 as the
-- only square in the br that can be a 3. Uses dotcol and dotrow.
-- Without this, brute force on the above takes ~8s, but with it ~0s
--
-- 2) set elimination
-- If in any 9-set there is a set of n blank squares that can only contain n digits,
-- then no other squares can contain those digits. Example (with some benefit):
-- 75.|.9.|.46
-- 961|...|352
-- 4..|...|79.
-- ---+---+---
-- 2..|6.1|..7
-- .8.|...|.2.
-- 1..|328|.65
-- ---+---+---
-- ...|...|... <-- [7,8] is {1,3,8}, [7,9] is {1,3,8}
-- 3.9|...|2.4 <-- [8,8] is {1,8}
-- 84.|.3.|.79
-- The three cells above the br 479 can only contain {1,3,8}, so the .. of the .2.
-- in column 7 of that square are {5,6} (not 1) and hence [9,4] must be a 1.
-- (Relies on plain_logic to spot that "must be a 1", and serves as a clear example
-- of why this routine should not bother to attempt updating the board itself - as
-- it spends almost all of its time looking in a completely different place.)
-- (One could argue that [7,7] and [9,7] are the only places that can hold {5,6} and
-- therefore we should eliminate all non-{5,6} from those squares, as an alternative
-- strategy. However I think that would be harder to code and cannot imagine a case
-- said complementary logic covers, that the above does not, cmiiw.)
--
-- 3) x-wings
-- If a pair of rows or columns can only contain a given number in two matching places,
-- then once filled they will occupy opposite diagonal corners, hence that said number
-- cannot occur elsewhere in those two columns/rows. Example (with a benefit):
-- .43|98.|25. <-- 6 in [1,{6,9}]
-- 6..|425|...
--
--
-- 9..|..4|.7. <-- hence 6 not in [4,9]
-- 3..|6.8|...
-- 41.|2.9|..3
-- ---+---+---
-- 82.|5..|... <-- hence 6 not in [7,6],[7,9]
-- ...|.4.|..5 <-- hence 6 not in [8,6]
-- 534|89.|71. <-- 6 in [9,{6,9}]
-- A 6 must be in [1,6] or [1,9] and [9,6] or [9,9], hence [7,9] is not 6 and must be 9.
-- (we also eliminate 6 from [4,9], [7,6] and [8,6] to no great use)
-- In practice this offers little benefit over a single trial-and-error step, as
-- obviously trying either 6 in row 1 or 9 immediately pinpoints that 9 anyway.
--
-- 4) swordfish (not attempted)
-- There is an extension to x-wings known as swordfish: three (or more) pairs form
-- a staggered pair (or more) of rectangles that exhibit similar properties, eg:
-- 8-1|-5-|-3-
-- 953|-68|---
-- -4-|-*3|5*8
-- ---+---+---
-- 6--|9-2|---
-- -8-|-3-|-4-
-- 3*-|5-1|-*7 <-- hence [6,3] is not 9, must be 4
-- ---+---+---
-- 5*2|-*-|-8-
-- --8|37-|--9
-- -3-|82-|1--
-- ^---^---^-- 3 pairs of 9s (marked with *) on 3 rows (only)
-- It is not a swordfish if the 3 pairs are on >3 rows, I trust that is obvious.
-- Logically you can extend this to N pairs on N rows, however I cannot imagine a
-- case where this is not immediately solved by a single trial-step being invalid.
-- (eg above if you try [3,5]:=9 it is quickly proved to be invalid, and the same
-- goes for [6,8]:=9 and [7,2]:=9, since they are all entirely inter-dependent.)
-- Obviously where I have said rows, the same concept can be applied to columns.
-- Likewise there are "Alternate Pairs" and "Hook or X-Y wing" strategies, which
-- are easily solved with a single trial-and-error step, and of course the brute
-- force algorithm is going to select pairs first anyway. [Erm, no it doesn't,
-- it selects shortest - I've noted the possible improvement below.]
--</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #000080;font-style:italic;">-- (scratch)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- initialise/start again from scratch</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"123456789"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">--
-- First perform standard eliminations of any known cells:
-- (repeated every time so plain_logic() does not have to worry about it)
--</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">></span><span style="color: #008000;">'0'</span>
<span style="color: #008080;">and</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ch</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">eliminate_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cols</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]],</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">eliminate_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rows</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]],</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">eliminate_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">squares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]],</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000080;font-style:italic;">--
-- 1) row/col elimination
--</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">19</span> <span style="color: #008080;">to</span> <span style="color: #000000;">27</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- 0 = none seen, 1..9 this col only, -1: >1 col</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- "" row row</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nine</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">vk</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vk</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vk</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">vk</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">col</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dotcol</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dotrow</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">],{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">col</span><span style="color: #0000FF;">})!=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #000000;">col</span><span style="color: #0000FF;">:-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">],{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">row</span><span style="color: #0000FF;">})!=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #000000;">row</span><span style="color: #0000FF;">:-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">col</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">eliminate_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sixes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">],</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">eliminate_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sixes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">],</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000080;font-style:italic;">--
-- 2) set elimination
--</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">--
-- Practical note: Meticulously counting empties to eliminate larger set sizes
-- would at best reduce 6642 tests to 972, not deemed worth it.
--</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">set_size</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">4</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">--if floor(count_empties(nines[i])/2)>=set_size then -- (untested)</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">comb</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">set_size</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--end if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000080;font-style:italic;">--
-- 3) x-wings
--</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'1'</span> <span style="color: #008080;">to</span> <span style="color: #008000;">'9'</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">prevsets</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">set</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">idx</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">+</span><span style="color: #000000;">x</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prevsets</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">sx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sx</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">k</span> <span style="color: #008080;">and</span> <span style="color: #000000;">sx</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">x</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">eliminate_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">+</span><span style="color: #000000;">sx</span><span style="color: #0000FF;">},</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">prevsets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">prevsets</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">+</span><span style="color: #000000;">x</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prevsets</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">sy</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sy</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">k</span> <span style="color: #008080;">and</span> <span style="color: #000000;">sy</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">y</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">eliminate_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">sy</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">+</span><span style="color: #000000;">x</span><span style="color: #0000FF;">},</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">prevsets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">valid</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">permitted_in</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">sets</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">pos</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">bch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">bch</span><span style="color: #0000FF;">></span><span style="color: #008000;">'0'</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">bch</span><span style="color: #0000FF;">=</span><span style="color: #000000;">ch</span> <span style="color: #008080;">then</span> <span style="color: #000000;">pos</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">elsif</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">pos</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">pos</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">pos</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">idx</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">pos</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ch</span>
<span style="color: #000000;">improved</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">board</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">INVALID</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">INCOMPLETE</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">SOLVED</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">MULTIPLE</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">BRUTE</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">plain_logic</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--
-- Responsible for:
-- 1) cells with only one option
-- 2) numbers with only one home
--</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">solved</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">solved</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">SOLVED</span>
<span style="color: #000000;">improved</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">deep_logic</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- 1) cells with only one option:</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">vi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vi</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vi</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,{},</span><span style="color: #000000;">INVALID</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vi</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">vi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">improved</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]<=</span><span style="color: #008000;">'0'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">solved</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">INCOMPLETE</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">=</span><span style="color: #000000;">SOLVED</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,{},</span><span style="color: #000000;">SOLVED</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- 2) numbers with only one home</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'1'</span> <span style="color: #008080;">to</span> <span style="color: #008000;">'9'</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">board</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">permitted_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cols</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">board</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">permitted_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rows</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">board</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">permitted_in</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,</span><span style="color: #000000;">squares</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">improved</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,</span><span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">solved</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">validate</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- (sum9 should be sufficient - if you want, get rid of nine/nines)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">sum9</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">nine</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nines</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- columns</span>
<span style="color: #000000;">sum9</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">81</span> <span style="color: #008080;">by</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;"><</span><span style="color: #000000;">1</span> <span style="color: #008080;">or</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">></span><span style="color: #000000;">9</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sum9</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ch</span>
<span style="color: #000000;">nine</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ch</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sum9</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">45</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nine</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">nines</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">81</span> <span style="color: #008080;">by</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- rows</span>
<span style="color: #000000;">sum9</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">sum9</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ch</span>
<span style="color: #000000;">nine</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ch</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sum9</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">45</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nine</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">nines</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">by</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- small squares</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">by</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">sum9</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">nine</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">sy</span><span style="color: #0000FF;">=</span><span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span> <span style="color: #008080;">to</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">+</span><span style="color: #000000;">18</span> <span style="color: #008080;">by</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">sx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">x</span> <span style="color: #008080;">to</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sy</span><span style="color: #0000FF;">+</span><span style="color: #000000;">sx</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">sum9</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ch</span>
<span style="color: #000000;">nine</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ch</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sum9</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">45</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nine</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">nines</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">solution</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">plain_logic</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">=</span><span style="color: #000000;">INVALID</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{{},</span><span style="color: #000000;">INVALID</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">=</span><span style="color: #000000;">SOLVED</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">},</span><span style="color: #000000;">SOLVED</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">=</span><span style="color: #000000;">BRUTE</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">},</span><span style="color: #000000;">BRUTE</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">INCOMPLETE</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- find the cell with the fewest options:
-- (a possible improvement here would be to select the shortest
-- with the "most pairs" set, see swordfish etc above.)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">minopt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mindx</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">vi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vi</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vi</span><span style="color: #0000FF;">)<=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- should be caught above</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vi</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">minopt</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">minopt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vi</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">mindx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">solutions</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">minopt</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mindx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">valid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mindx</span><span style="color: #0000FF;">][</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">,</span><span style="color: #000000;">solved</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">=</span><span style="color: #000000;">MULTIPLE</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">,</span><span style="color: #000000;">MULTIPLE</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">=</span><span style="color: #000000;">SOLVED</span>
<span style="color: #008080;">or</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">=</span><span style="color: #000000;">BRUTE</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">and</span> <span style="color: #000000;">validate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">solutions</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">,</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">)></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">,</span><span style="color: #000000;">MULTIPLE</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">elsif</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">,</span><span style="color: #000000;">BRUTE</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">,</span><span style="color: #000000;">BRUTE</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{{},</span><span style="color: #000000;">INVALID</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">test_one</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">solutions</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">solution</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">desc</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">=</span><span style="color: #000000;">SOLVED</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">desc</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"(logic)"</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">solved</span><span style="color: #0000FF;">=</span><span style="color: #000000;">BRUTE</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">desc</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"(brute force)"</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">desc</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"???"</span> <span style="color: #000080;font-style:italic;">-- INVALID/INCOMPLETE/MULTIPLE</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">solution</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">board</span>
<span style="color: #000000;">desc</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"*** NO SOLUTIONS ***"</span>
<span style="color: #008080;">elsif</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solutions</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">solution</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">solutions</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">validate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">desc</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"*** ERROR ***"</span> <span style="color: #000080;font-style:italic;">-- (should never happen)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">solution</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">board</span>
<span style="color: #000000;">desc</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"*** MULTIPLE SOLUTIONS ***"</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">,</span><span style="color: #000000;">desc</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">--NB Blank cells can be represented by any character <'1'. Spaces are not recommended since
-- they can all too easily be converted to tabs by copy/paste/save. In particular, ? and
-- _ are NOT valid characters for representing a blank square. Use any of .0-* instead.</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span>
<span style="color: #008000;">"..............3.85..1.2.......5.7.....4...1...9.......5......73..2.1........4...9"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.01s, (logic))
-- row/col elimination (was 8s w/o logic first)</span>
<span style="color: #008000;">"000000036840000000000000020000203000010000700000600400000410050003000200600000000"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.04s, (brute force))</span>
<span style="color: #008000;">".......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7....."</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (1.12s, (brute force))</span>
<span style="color: #008000;">"000037600000600090008000004090000001600000009300000040700000800010009000002540000"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))</span>
<span style="color: #008000;">"....839..1......3...4....7..42.3....6.......4....7..1..2........8...92.....25...6"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.04s, (brute force))</span>
<span style="color: #008000;">"..1..5.7.92.6.......8...6...9..2.4.1.........3.4.8..9...7...3.......7.69.1.8..7.."</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))
-- (the following takes ~8s when checking for multiple solutions)</span>
<span style="color: #008000;">"--3------4---8--36--8---1---4--6--73---9----------2--5--4-7--686--------7--6--5--"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.01s, (brute force))</span>
<span style="color: #008000;">"..3.2.6..9..3.5..1..18.64....81.29..7.......8..67.82....26.95..8..2.3..9..5.1.3.."</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))</span>
<span style="color: #008000;">"--4-5--6--6-1--8-93----7----8----5-----4-3-----6----7----2----61-5--4-3--2--7-1--"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))
-- x-wings</span>
<span style="color: #008000;">".4398.25.6..425...2....1.949....4.7.3..6.8...41.2.9..382.5.........4...553489.71."</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))</span>
<span style="color: #008000;">".9...4..7.....79..8........4.58.....3.......2.....97.6........4..35.....2..6...8."</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))
-- "AL Escargot", so-called "hardest sudoku"</span>
<span style="color: #008000;">"1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3.."</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.26s, (brute force))</span>
<span style="color: #008000;">"12.3....435....1....4........54..2..6...7.........8.9...31..5.......9.7.....6...8"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.48s, (brute force))</span>
<span style="color: #008000;">"12.4..3..3...1..5...6...1..7...9.....4.6.3.....3..2...5...8.7....7.....5.......98"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (1.07s, (brute force))</span>
<span style="color: #008000;">"394..267....3..4..5..69..2..45...9..6.......7..7...58..1..67..8..9..8....264..735"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))</span>
<span style="color: #008000;">"4......6.5...8.9..3....1....2.7....1.9.....4.8....3.5....2....7..6.5...8.1......6"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.01s, (brute force))</span>
<span style="color: #008000;">"5...7....6..195....98....6.8...6...34..8.3..17...2...6.6....28....419..5....8..79"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))</span>
<span style="color: #008000;">"503600009010002600900000080000700005006804100200003000030000008004300050800006702"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))</span>
<span style="color: #008000;">"53..247....2...8..1..7.39.2..8.72.49.2.98..7.79.....8.....3.5.696..1.3...5.69..1."</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))</span>
<span style="color: #008000;">"530070000600195000098000060800060003400803001700020006060000280000419005000080079"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))
-- set exclusion</span>
<span style="color: #008000;">"75..9..46961...3524.....79.2..6.1..7.8.....2.1..328.65.........3.9...2.484..3..79"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))
-- Worlds hardest sudoku:</span>
<span style="color: #008000;">"800000000003600000070090200050007000000045700000100030001000068008500010090000400"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.21s, (brute force))</span>
<span style="color: #008000;">"819--5-----2---75--371-4-6-4--59-1--7--3-8--2--3-62--7-5-7-921--64---9-----2--438"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))</span>
<span style="color: #008000;">"85...24..72......9..4.........1.7..23.5...9...4...........8..7..17..........36.4."</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.01s, (logic))</span>
<span style="color: #008000;">"9..2..5...4..6..3...3.....6...9..2......5..8...7..4..37.....1...5..2..4...1..6..9"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.17s, (brute force))</span>
<span style="color: #008000;">"97.3...6..6.75.........8.5.......67.....3.....539..2..7...25.....2.1...8.4...73.."</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.00s, (logic))
-- "the beast" (an earlier algorithm took 318s (5min 18s) on this):</span>
<span style="color: #008000;">"000060080020000000001000000070000102500030000000000400004201000300700600000000050"</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (0.03s, (brute force))</span>
<span style="color: #0000FF;">$},</span>
<span style="color: #000000;">lt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">run_one_test</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">" x x x | x x x | x x x "</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"-------+-------+-------"</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">l3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">({</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">substitute</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">({</span><span style="color: #000000;">l3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l3</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"x"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%c"</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"\n"</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (81 characters)</span>
<span style="color: #000000;">solution</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">desc</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">run_one_test</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">board</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">run_one_test</span><span style="color: #0000FF;">]</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">,</span><span style="color: #000000;">desc</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">test_one</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"solution:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s, %3.2fs\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">desc</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">else</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lt</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">board</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">,</span><span style="color: #000000;">desc</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">test_one</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" \"%s\", -- (%3.2fs, %s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">desc</span><span style="color: #0000FF;">})</span>
<span style="color: #000080;font-style:italic;">-- printf(1," \"%s\", -- (%3.2fs, %s)\n",{solution,time()-t1,desc})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d puzzles solved in %3.2fs (av %3.2fs)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">lt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">/</span><span style="color: #000000;">lt</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
"..............3.85..1.2.......5.7.....4...1...9.......5......73..2.1........4...9", -- (0.02s, (logic))
"000000036840000000000000020000203000010000700000600400000410050003000200600000000", -- (0.03s, (brute force))
".......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7.....", -- (1.31s, (brute force))
"000037600000600090008000004090000001600000009300000040700000800010009000002540000", -- (0.00s, (logic))
"....839..1......3...4....7..42.3....6.......4....7..1..2........8...92.....25...6", -- (0.03s, (brute force))
"..1..5.7.92.6.......8...6...9..2.4.1.........3.4.8..9...7...3.......7.69.1.8..7..", -- (0.00s, (logic))
"--3------4---8--36--8---1---4--6--73---9----------2--5--4-7--686--------7--6--5--", -- (0.03s, (brute force))
"..3.2.6..9..3.5..1..18.64....81.29..7.......8..67.82....26.95..8..2.3..9..5.1.3..", -- (0.00s, (logic))
"--4-5--6--6-1--8-93----7----8----5-----4-3-----6----7----2----61-5--4-3--2--7-1--", -- (0.01s, (logic))
".4398.25.6..425...2....1.949....4.7.3..6.8...41.2.9..382.5.........4...553489.71.", -- (0.00s, (logic))
".9...4..7.....79..8........4.58.....3.......2.....97.6........4..35.....2..6...8.", -- (0.00s, (logic))
"1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..", -- (0.26s, (brute force))
"12.3....435....1....4........54..2..6...7.........8.9...31..5.......9.7.....6...8", -- (0.40s, (brute force))
"12.4..3..3...1..5...6...1..7...9.....4.6.3.....3..2...5...8.7....7.....5.......98", -- (1.12s, (brute force))
"394..267....3..4..5..69..2..45...9..6.......7..7...58..1..67..8..9..8....264..735", -- (0.00s, (logic))
"4......6.5...8.9..3....1....2.7....1.9.....4.8....3.5....2....7..6.5...8.1......6", -- (0.03s, (brute force))
"5...7....6..195....98....6.8...6...34..8.3..17...2...6.6....28....419..5....8..79", -- (0.00s, (logic))
"503600009010002600900000080000700005006804100200003000030000008004300050800006702", -- (0.01s, (logic))
"53..247....2...8..1..7.39.2..8.72.49.2.98..7.79.....8.....3.5.696..1.3...5.69..1.", -- (0.00s, (logic))
"530070000600195000098000060800060003400803001700020006060000280000419005000080079", -- (0.00s, (logic))
"75..9..46961...3524.....79.2..6.1..7.8.....2.1..328.65.........3.9...2.484..3..79", -- (0.01s, (logic))
"800000000003600000070090200050007000000045700000100030001000068008500010090000400", -- (0.21s, (brute force))
"819--5-----2---75--371-4-6-4--59-1--7--3-8--2--3-62--7-5-7-921--64---9-----2--438", -- (0.00s, (logic))
"85...24..72......9..4.........1.7..23.5...9...4...........8..7..17..........36.4.", -- (0.01s, (logic))
"9..2..5...4..6..3...3.....6...9..2......5..8...7..4..37.....1...5..2..4...1..6..9", -- (0.18s, (brute force))
"97.3...6..6.75.........8.5.......67.....3.....539..2..7...25.....2.1...8.4...73..", -- (0.00s, (logic))
"000060080020000000001000000070000102500030000000000400004201000300700600000000050", -- (0.01s, (brute force))
27 puzzles solved in 3.74s (av 0.14s)
</pre>
Running the fuller version mentioned above:
<pre>
"008002000000600040064000092017005004200000008800100730470000910080001000000900200", -- (0.05s, *** MULTIPLE SOLUTIONS ***)
338 puzzles solved in 36.20s (av 0.11s)
--or
338 puzzles solved in 16.46s (av 0.05s) (w/o check for multiple solutions)
</pre>
Running a single puzzle (run_one_test set non-zero) produces:
<pre>
. . .
. . . | . . 3 | . 8 5
. . 1 | .
-------+-------+-------
. . . | 5 .
. . 4 | . . .
. 9 . | . . .
-------+-------+-------
5 . . | . . .
. . 2 | . 1 . | . . .
. . . | .
solution:
9 8 7 | 6 5 4 | 3 2 1
2 4 6 | 1 7 3 | 9 8 5
3 5 1 | 9 2 8 | 7 4 6
-------+-------+-------
1 2 8 | 5 3 7 | 6 9 4
6 3 4 | 8 9 2 | 1 5 7
7 9 5 | 4 6 1 | 8 3 2
-------+-------+-------
5 1 9 | 2 8 6 | 4 7 3
8 6 3 | 7 4 5 | 2 1 9
(logic), 0.02s
</pre>
=={{header|PHP}}==
{{trans|C++}}
<
protected $grid = [];
protected $emptySymbol;
Line 5,911 ⟶ 9,333:
$solver = new SudokuSolver('009170000020600001800200000200006053000051009005040080040000700006000320700003900');
$solver->solve();
$solver->display();</
{{out}}
<pre>
Line 5,928 ⟶ 9,350:
</pre>
=={{header|
Using constraint programming.
<syntaxhighlight lang="picat">import util.
import cp.
main => go.
go =>
sudokus(Sudokus),
foreach([Comment,SudokuS] in Sudokus)
println(SudokuS),
println(Comment),
% Convert string to numbers and "." to _ (unknown)
Sudoku = [ [cond(S == '.',_,S.to_integer()) :
S in slice(SudokuS,(I*9)+1,(I+1)*9)] : I in
print_board(Sudoku),
% Ensure unicity of the solution (check that it is a unique
All = findall(Sudoku,sudoku(Sudoku)),
if All.length > 1
printf("Problem has %d solutions!\n", All.length)
print("Solution:")
print_board(A)
end,
nl
end,
nl.
sudoku(Board) =>
N = ceiling(sqrt(Board.len)),
N2 = N*N,
Vars = Board.vars(),
Vars :: 1..N2,
foreach(Row in Board) all_different(Row) end,
foreach(Column in transpose(Board)) all_different(Column) end,
foreach(I in 1..N..N2, J in 1..N..N2)
all_different([Board[I+K,J+L] : K in 0..N-1, L in 0..N-1])
end,
solve([ffd,inout], Vars).
print_board(Board) =>
N = Board.length,
foreach(I in 1..N)
foreach(J in
X = Board[I,J],
end,
nl
end,
nl.
% (Problems from the Groovy implementation)
sudokus(Sudokus) => Sudokus =
[
"819..5.....2...75..371.4.6.4..59.1..7..3.8..2..3.62..7.5.7.921..64...9.....2..438",
"53..247....2...8..1..7.39.2..8.72.49.2.98..7.79.....8.....3.5.696..1.3...5.69..1.",
"..3.2.6..9..3.5..1..18.64....81.29..7.......8..67.82....26.95..8..2.3..9..5.1.3..",
"394..267....3..4..5..69..2..45...9..6.......7..7...58..1..67..8..9..8....264..735",
"97.3...6..6.75.........8.5.......67.....3.....539..2..7...25.....2.1...8.4...73..",
"4......6.5...8.9..3....1....2.7....1.9.....4.8....3.5....2....7..6.5...8.1......6",
"85...24..72......9..4.........1.7..23.5...9...4...........8..7..17..........36.4.",
"..1..5.7.92.6.......8...6...9..2.4.1.........3.4.8..9...7...3.......7.69.1.8..7..",
".9...4..7.....79..8........4.58.....3.......2.....97.6........4..35.....2..6...8.",
"12.3....435....1....4........54..2..6...7.........8.9...31..5.......9.7.....6...8",
"9..2..5...4..6..3...3.....6...9..2......5..8...7..4..37.....1...5..2..4...1..6..9",
"1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..",
"12.4..3..3...1..5...6...1..7...9.....4.6.3.....3..2...5...8.7....7.....5.......98",
"..............3.85..1.2.......5.7.....4...1...9.......5......73..2.1........4...9",
".......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7.....",
"....839..1......3...4....7..42.3....6.......4....7..1..2........8...92.....25...6",
"..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7..6..5.."
].</syntaxhighlight>
{{out}}
All problems are solved (and proved/checked for unicity) in 0.043s.
<pre>
819..5.....2...75..371.4.6.4..59.1..7..3.8..2..3.62..7.5.7.921..64...9.....2..438
8 1 9 _ _ 5 _ _ _
_ _ 2 _ _ _ 7 5 _
_ 3 7 1 _ 4 _ 6 _
4 _ _ 5 9 _ 1 _ _
7 _ _ 3 _ 8 _ _ 2
_ _ 3 _ 6 2 _ _ 7
_ 5 _ 7 _ 9 2 1 _
_ 6 4 _ _ _ 9 _ _
_ _ _ 2 _ _ 4 3 8
Solution:
8
6 4 2
5 3 7
4 2 6 5 9
7 9 5 3 1
1 8 3 4 6 2 5
3 5 8 7 4 9 2
2 6 4 8 3
9 7 1
...
</pre>
=={{header|PicoLisp}}==
<
### Fields/Board ###
Line 6,803 ⟶ 9,536:
(0 6 0 0 0 0 2 8 0)
(0 0 0 4 1 9 0 0 5)
(0 0 0 0 8 0 0 7 9) ) )</
{{out}}
<pre> +---+---+---+---+---+---+---+---+---+
Line 6,825 ⟶ 9,558:
+---+---+---+---+---+---+---+---+---+
a b c d e f g h i</pre>
<syntaxhighlight lang
{{out}}
<pre> +---+---+---+---+---+---+---+---+---+
Line 6,850 ⟶ 9,583:
=={{header|PL/I}}==
Working PL/I version, derived from the Rosetta Fortran version.
<
declare grid (9,9) fixed (1) static initial (
Line 6,933 ⟶ 9,666:
end sudoku;
</syntaxhighlight>
{{out}}
<pre>
Line 6,967 ⟶ 9,700:
Another PL/I version, reads sudoku from the text data file as 81 character record.
<
*PROCESS MARGINS(1,120) LIBS(SINGLE,STATIC);
*PROCESS OPTIMIZE(2) DFT(REORDER);
Line 7,106 ⟶ 9,839:
end sudoku;
</syntaxhighlight>
=={{header|Prolog}}==
<
sudoku(Rows) :-
Line 7,134 ⟶ 9,867:
[5,_,_,_,_,_,_,7,3],
[_,_,2,_,1,_,_,_,_],
[_,_,_,_,4,_,_,_,9]]).</
===GNU Prolog version===
{{works with|GNU Prolog|1.4.4}}
<
Line 7,191 ⟶ 9,924:
main :- test(T), solve(T), maplist(show,T), halt.
show(X) :- write(X), nl.</
{{Out}}
<pre>[1,2,3,4,5,6,7,8,9]
Line 7,206 ⟶ 9,939:
=={{header|PureBasic}}==
A brute force method is used, it seemed the fastest as well as the simplest.
<
puzzle:
Data.s "394002670"
Line 7,316 ⟶ 10,049:
Input()
CloseConsole()
EndIf</
{{out}}
<pre>+-----+-----+-----+
Line 7,348 ⟶ 10,081:
=={{header|Python}}==
See [http://www2.warwick.ac.uk/fac/sci/moac/currentstudents/peter_cock/python/sudoku/ Solving Sudoku puzzles with Python] for GPL'd solvers of increasing complexity of algorithm.
===Backtrack===
A simple backtrack algorithm -- Quick but may take longer if the grid had been more than 9 x 9
<
def initiate():
box.append([0, 1, 2, 9, 10, 11, 18, 19, 20])
Line 7,434 ⟶ 10,169:
print grid[i*9:i*9+9]
raw_input()
</syntaxhighlight>
===Search + Wave Function Collapse===
A Sudoku solver using search guided by the principles of wave function collapse.
<syntaxhighlight lang="python">
sudoku = [
# cell value # cell number
0, 0, 4, 0, 5, 0, 0, 0, 0, # 0, 1, 2, 3, 4, 5, 6, 7, 8,
9, 0, 0, 7, 3, 4, 6, 0, 0, # 9, 10, 11, 12, 13, 14, 15, 16, 17,
0, 0, 3, 0, 2, 1, 0, 4, 9, # 18, 19, 20, 21, 22, 23, 24, 25, 26,
0, 3, 5, 0, 9, 0, 4, 8, 0, # 27, 28, 29, 30, 31, 32, 33, 34, 35,
0, 9, 0, 0, 0, 0, 0, 3, 0, # 36, 37, 38, 39, 40, 41, 42, 43, 44,
0, 7, 6, 0, 1, 0, 9, 2, 0, # 45, 46, 47, 48, 49, 50, 51, 52, 53,
3, 1, 0, 9, 7, 0, 2, 0, 0, # 54, 55, 56, 57, 58, 59, 60, 61, 62,
0, 0, 9, 1, 8, 2, 0, 0, 3, # 63, 64, 65, 66, 67, 68, 69, 70, 71,
0, 0, 0, 0, 6, 0, 1, 0, 0, # 72, 73, 74, 75, 76, 77, 78, 79, 80
# zero = empty.
]
numbers = {1,2,3,4,5,6,7,8,9}
def options(cell,sudoku):
""" determines the degree of freedom for a cell. """
column = {v for ix, v in enumerate(sudoku) if ix % 9 == cell % 9}
row = {v for ix, v in enumerate(sudoku) if ix // 9 == cell // 9}
box = {v for ix, v in enumerate(sudoku) if (ix // (9 * 3) == cell // (9 * 3)) and ((ix % 9) // 3 == (cell % 9) // 3)}
return numbers - (box | row | column)
initial_state = sudoku[:] # the sudoku is our initial state.
job_queue = [initial_state] # we need the jobqueue in case of ambiguity of choice.
while job_queue:
state = job_queue.pop(0)
if not any(i==0 for i in state): # no missing values means that the sudoku is solved.
break
# determine the degrees of freedom for each cell.
degrees_of_freedom = [0 if v!=0 else len(options(ix,state)) for ix,v in enumerate(state)]
# find cell with least freedom.
least_freedom = min(v for v in degrees_of_freedom if v > 0)
cell = degrees_of_freedom.index(least_freedom)
for option in options(cell, state): # for each option we add the new state to the queue.
new_state = state[:]
new_state[cell] = option
job_queue.append(new_state)
# finally - print out the solution
for i in range(9):
print(state[i*9:i*9+9])
# [2, 6, 4, 8, 5, 9, 3, 1, 7]
# [9, 8, 1, 7, 3, 4, 6, 5, 2]
# [7, 5, 3, 6, 2, 1, 8, 4, 9]
# [1, 3, 5, 2, 9, 7, 4, 8, 6]
# [8, 9, 2, 5, 4, 6, 7, 3, 1]
# [4, 7, 6, 3, 1, 8, 9, 2, 5]
# [3, 1, 8, 9, 7, 5, 2, 6, 4]
# [6, 4, 9, 1, 8, 2, 5, 7, 3]
# [5, 2, 7, 4, 6, 3, 1, 9, 8]
</syntaxhighlight>
This solver found the 45 unknown values in 45 steps.
=={{header|Racket}}==
A [http://schemecookbook.org/view/Cookbook/SudokuSolver Sudoku Solver in Racket].
=={{header|Raku}}==
(formerly Perl 6)
===Brute Force===
{{trans|Perl}}
<syntaxhighlight lang="raku" line>my @A = <
5 3 0 0 2 4 7 0 0
0 0 2 0 0 0 8 0 0
1 0 0 7 0 3 9 0 2
0 0 8 0 7 2 0 4 9
0 2 0 9 8 0 0 7 0
7 9 0 0 0 0 0 8 0
0 0 0 0 3 0 5 0 6
9 6 0 0 1 0 3 0 0
0 5 0 6 9 0 0 1 0
>;
my &I = * div 9; # line number
my &J = * % 9; # column number
my &K = { ($_ div 27) * 3 + $_ % 9 div 3 }; # bloc number
sub solve {
for ^@A -> $i {
next if @A[$i];
my @taken-values = @A[
grep {
I($_) == I($i) || J($_) == J($i) || K($_) == K($i)
}, ^@A
];
for grep none(@taken-values), 1..9 {
@A[$i] = $_;
solve;
}
return @A[$i] = 0;
}
my $i = 1;
for ^@A {
print "@A[$_] ";
print " " if $i %% 3;
print "\n" if $i %% 9;
print "\n" if $i++ %% 27;
}
}
solve;</syntaxhighlight>
{{out}}
<pre>5 3 9 8 2 4 7 6 1
6 7 2 1 5 9 8 3 4
1 8 4 7 6 3 9 5 2
3 1 8 5 7 2 6 4 9
4 2 5 9 8 6 1 7 3
7 9 6 3 4 1 2 8 5
8 4 1 2 3 7 5 9 6
9 6 7 4 1 5 3 2 8
2 5 3 6 9 8 4 1 7</pre>
===Finesse It===
This is an alternative solution that uses a more ellaborate set of choices instead of brute-forcing it.
<syntaxhighlight lang="raku" line>#
# In this code, a sudoku puzzle is represented as a two-dimentional
# array. The cells that are not yet solved are represented by yet
# another array of all the possible values.
#
# This implementation is not a simple brute force evaluation of all
# the options, but rather makes four extra attempts to guide the
# solution:
#
# 1) For every change in the grid, usually made by an attempt at a
# solution, we will reduce the search space of the possible values
# in all the other cells before going forward.
#
# 2) When a cell that is not yet resolved is the only one that can
# hold a specific value, resolve it immediately instead of
# performing the regular search.
#
# 3) Instead of trying from cell 1,1 and moving in sequence, this
# implementation will start trying on the cell that is the closest
# to being solved already.
#
# 4) Instead of trying all possible values in sequence, start with
# the value that is the most unique. I.e.: If the options for this
# cell are 1,4,6 and 6 is only a candidate for two of the
# competing cells, we start with that one.
#
# keep a list with all the cells, handy for traversal
my @cells = do for (flat 0..8 X 0..8) -> $x, $y { [ $x, $y ] };
#
# Try to solve this puzzle and return the resolved puzzle if it is at
# all solvable in this configuration.
sub solve($sudoku, Int $level) {
# cleanup the impossible values first,
if (cleanup-impossible-values($sudoku, $level)) {
# try to find implicit answers
while (find-implicit-answers($sudoku, $level)) {
# and every time you find some, re-do the cleanup and try again
cleanup-impossible-values($sudoku, $level);
}
# Now let's actually try to solve a new value. But instead of
# going in sequence, we select the cell that is the closest to
# being solved already. This will reduce the overall number of
# guesses.
for sort { solution-complexity-factor($sudoku, $_[0], $_[1]) },
grep { $sudoku[$_[0]][$_[1]] ~~ Array },
@cells -> $cell
{
my Int ($x, $y) = @($cell);
# Now let's try the possible values in the order of
# uniqueness.
for sort { matches-in-competing-cells($sudoku, $x, $y, $_) }, @($sudoku[$x][$y]) -> $val {
trace $level, "Trying $val on "~($x+1)~","~($y+1)~" "~$sudoku[$x][$y].raku;
my $solution = clone-sudoku($sudoku);
$solution[$x][$y] = $val;
my $solved = solve($solution, $level+1);
if $solved {
trace $level, "Solved... ($val on "~($x+1)~","~($y+1)~")";
return $solved;
}
}
# if we fell through, it means that we found no valid
# value for this cell
trace $level, "Backtrack, path unsolvable... (on "~($x+1)~" "~($y+1)~")";
return False;
}
# all cells are already solved.
return $sudoku;
} else {
# if the cleanup failed, it means this is an invalid grid.
return False;
}
}
# This function reduces the search space from values that are already
# assigned to competing cells.
sub cleanup-impossible-values($sudoku, Int $level = 1) {
my Bool $resolved;
repeat {
$resolved = False;
for grep { $sudoku[$_[0]][$_[1]] ~~ Array },
@cells -> $cell {
my Int ($x, $y) = @($cell);
# which block is this cell in
my Int $bx = Int($x / 3);
my Int $by = Int($y / 3);
# A unfilled cell is not resolved, so it shouldn't match
my multi match-resolved-cell(Array $other, Int $this) {
return False;
}
my multi match-resolved-cell(Int $other, Int $this) {
return $other == $this;
}
# Reduce the possible values to the ones that are still
# valid
my @r =
grep { !match-resolved-cell($sudoku[any(0..2)+3*$bx][any(0..2)+3*$by], $_) }, # same block
grep { !match-resolved-cell($sudoku[any(0..8)][$y], $_) }, # same line
grep { !match-resolved-cell($sudoku[$x][any(0..8)], $_) }, # same column
@($sudoku[$x][$y]);
if (@r.elems == 1) {
# if only one element is left, then make it resolved
$sudoku[$x][$y] = @r[0];
$resolved = True;
} elsif (@r.elems == 0) {
# This is an invalid grid
return False;
} else {
$sudoku[$x][$y] = @r;
}
}
} while $resolved; # repeat if there was any change
return True;
}
sub solution-complexity-factor($sudoku, Int $x, Int $y) {
my Int $bx = Int($x / 3); # this block
my Int $by = Int($y / 3);
my multi count-values(Array $val) {
return $val.elems;
}
my multi count-values(Int $val) {
return 1;
}
# the number of possible values should take precedence
my Int $f = 1000 * count-values($sudoku[$x][$y]);
for (flat 0..2 X 0..2) -> $lx, $ly {
$f += count-values($sudoku[$lx+$bx*3][$ly+$by*3])
}
for 0..^($by*3), (($by+1)*3)..8 -> $ly {
$f += count-values($sudoku[$x][$ly])
}
for 0..^($bx*3), (($bx+1)*3)..8 -> $lx {
$f += count-values($sudoku[$lx][$y])
}
return $f;
}
sub matches-in-competing-cells($sudoku, Int $x, Int $y, Int $val) {
my Int $bx = Int($x / 3); # this block
my Int $by = Int($y / 3);
# Function to decide which possible value to try first
my multi cell-matching(Int $cell) {
return $val == $cell ?? 1 !! 0;
}
my multi cell-matching(Array $cell) {
return $cell.grep({ $val == $_ }) ?? 1 !! 0;
}
my Int $c = 0;
for (flat 0..2 X 0..2) -> $lx, $ly {
$c += cell-matching($sudoku[$lx+$bx*3][$ly+$by*3])
}
for 0..^($by*3), (($by+1)*3)..8 -> $ly {
$c += cell-matching($sudoku[$x][$ly])
}
for 0..^($bx*3), (($bx+1)*3)..8 -> $lx {
$c += cell-matching($sudoku[$lx][$y])
}
return $c;
}
sub find-implicit-answers($sudoku, Int $level) {
my Bool $resolved = False;
for grep { $sudoku[$_[0]][$_[1]] ~~ Array },
@cells -> $cell {
my Int ($x, $y) = @($cell);
for @($sudoku[$x][$y]) -> $val {
# If this is the only cell with this val as a possibility,
# just make it resolved already
if (matches-in-competing-cells($sudoku, $x, $y, $val) == 1) {
$sudoku[$x][$y] = $val;
$resolved = True;
}
}
}
return $resolved;
}
my $puzzle =
map { [ map { $_ == 0 ?? [1..9] !! $_+0 }, @($_) ] },
[ 0,0,0,0,3,7,6,0,0 ],
[ 0,0,0,6,0,0,0,9,0 ],
[ 0,0,8,0,0,0,0,0,4 ],
[ 0,9,0,0,0,0,0,0,1 ],
[ 6,0,0,0,0,0,0,0,9 ],
[ 3,0,0,0,0,0,0,4,0 ],
[ 7,0,0,0,0,0,8,0,0 ],
[ 0,1,0,0,0,9,0,0,0 ],
[ 0,0,2,5,4,0,0,0,0 ];
my $solved = solve($puzzle, 0);
if $solved {
print-sudoku($solved,0);
} else {
say "unsolvable.";
}
# Utility functions, not really part of the solution
sub trace(Int $level, Str $message) {
# say '.' x $level, $message; # un-comment for verbose logging
}
sub clone-sudoku($sudoku) {
my $clone;
for (flat 0..8 X 0..8) -> $x, $y {
$clone[$x][$y] = $sudoku[$x][$y];
}
return $clone;
}
sub print-sudoku($sudoku, Int $level = 1) {
trace $level, '-' x 5*9;
for @($sudoku) -> $row {
trace $level, join " ", do for @($row) -> $cell {
$cell ~~ Array ?? "#{$cell.elems}#" !! " $cell "
}
}
}</syntaxhighlight>
{{out}}
<pre> 9 5 4 1 3 7 6 8 2
2 7 3 6 8 4 1 9 5
1 6 8 2 9 5 7 3 4
4 9 5 7 2 8 3 6 1
6 8 1 4 5 3 2 7 9
3 2 7 9 6 1 5 4 8
7 4 9 3 1 2 8 5 6
5 1 6 8 7 9 4 2 3
8 3 2 5 4 6 9 1 7
</pre>
=={{header|Rascal}}==
Line 7,443 ⟶ 10,542:
A sudoku is represented as a matrix, see Rascal solutions to matrix related problems for examples.
<
import vis::Figure;
import vis::Render;
Line 7,526 ⟶ 10,625:
<0,7,0>, <1,7,0>, <2,7,9>, <3,7,0>, <4,7,0>, <5,7,8>, <6,7,0>, <7,7,0>, <8,7,0>,
<0,8,0>, <1,8,2>, <2,8,6>, <3,8,4>, <4,8,0>, <5,8,0>, <6,8,7>, <7,8,3>, <8,8,5>
};</
Example
Line 7,534 ⟶ 10,633:
=={{header|REXX}}==
The '''SUDOKU''' REXX programs (and output) are included here ──► [[Sudoku/REXX]].
<br><br>
=={{header|RPN (HP-15c)}}==
Line 7,813 ⟶ 10,913:
RDN ; get rid of the sum from the stack
RTN
</pre>
=={{header|Ruby}}==
Example of a back-tracking solver, from [[wp:Algorithmics of sudoku]]
{{works with|Ruby|2.0+}}
<
lines = data.lines
9.times.collect { |i| 9.times.collect { |j| lines[i][j].to_i } }
Line 7,908 ⟶ 11,008:
print_matrix(matrix)
puts
print_matrix(solve_sudoku(matrix))</
{{out}}
Line 7,939 ⟶ 11,039:
|8 2 6|4 1 9|7 3 5|
+-----+-----+-----+</pre>
=={{header|Rust}}==
{{trans|Ada}}
<syntaxhighlight lang="rust">type Sudoku = [u8; 81];
fn is_valid(val: u8, x: usize, y: usize, sudoku_ar: &mut Sudoku) -> bool {
(0..9).all(|i| sudoku_ar[y * 9 + i] != val && sudoku_ar[i * 9 + x] != val) && {
let (start_x, start_y) = ((x / 3) * 3, (y / 3) * 3);
(start_y..start_y + 3).all(|i| (start_x..start_x + 3).all(|j| sudoku_ar[i * 9 + j] != val))
}
}
fn place_number(pos: usize, sudoku_ar: &mut Sudoku) -> bool {
(pos..81).find(|&p| sudoku_ar[p] == 0).map_or(true, |pos| {
let (x, y) = (pos % 9, pos / 9);
for n in 1..10 {
if is_valid(n, x, y, sudoku_ar) {
sudoku_ar[pos] = n;
if place_number(pos + 1, sudoku_ar) {
return true;
}
sudoku_ar[pos] = 0;
}
}
false
})
}
fn pretty_print(sudoku_ar: Sudoku) {
let line_sep = "------+-------+------";
println!("{}", line_sep);
for (i, e) in sudoku_ar.iter().enumerate() {
print!("{} ", e);
if (i + 1) % 3 == 0 && (i + 1) % 9 != 0 {
print!("| ");
}
if (i + 1) % 9 == 0 {
println!(" ");
}
if (i + 1) % 27 == 0 {
println!("{}", line_sep);
}
}
}
fn solve(sudoku_ar: &mut Sudoku) -> bool {
place_number(0, sudoku_ar)
}
fn main() {
let mut sudoku_ar: Sudoku = [
8, 5, 0, 0, 0, 2, 4, 0, 0,
7, 2, 0, 0, 0, 0, 0, 0, 9,
0, 0, 4, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 7, 0, 0, 2,
3, 0, 5, 0, 0, 0, 9, 0, 0,
0, 4, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 8, 0, 0, 7, 0,
0, 1, 7, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 3, 6, 0, 4, 0
];
if solve(&mut sudoku_ar) {
pretty_print(sudoku_ar);
} else {
println!("Unsolvable");
}
}</syntaxhighlight>
{{out}}
<pre>
------+-------+------
8 5 9 | 6 1 2 | 4 3 7
7 2 3 | 8 5 4 | 1 6 9
1 6 4 | 3 7 9 | 5 2 8
------+-------+------
9 8 6 | 1 4 7 | 3 5 2
3 7 5 | 2 6 8 | 9 1 4
2 4 1 | 5 9 3 | 7 8 6
------+-------+------
4 3 2 | 9 8 1 | 6 7 5
6 1 7 | 4 2 5 | 8 9 3
5 9 8 | 7 3 6 | 2 4 1
------+-------+------
</pre>
=={{header|SAS}}==
Use CLP solver in SAS/OR:
<syntaxhighlight lang="sas">/* define SAS data set */
data Indata;
input C1-C9;
datalines;
. . 5 . . 7 . . 1
. 7 . . 9 . . 3 .
. . . 6 . . . . .
. . 3 . . 1 . . 5
. 9 . . 8 . . 2 .
1 . . 2 . . 4 . .
. . 2 . . 6 . . 9
. . . . 4 . . 8 .
8 . . 1 . . 5 . .
;
/* call OPTMODEL procedure in SAS/OR */
proc optmodel;
/* declare variables */
set ROWS = 1..9;
set COLS = ROWS;
var X {ROWS, COLS} >= 1 <= 9 integer;
/* declare nine row constraints */
con RowCon {i in ROWS}:
alldiff({j in COLS} X[i,j]);
/* declare nine column constraints */
con ColCon {j in COLS}:
alldiff({i in ROWS} X[i,j]);
/* declare nine 3x3 block constraints */
con BlockCon {s in 0..2, t in 0..2}:
alldiff({i in 3*s+1..3*s+3, j in 3*t+1..3*t+3} X[i,j]);
/* fix variables to cell values */
/* X[i,j] = c[i,j] if c[i,j] is not missing */
num c {ROWS, COLS};
read data indata into [_N_] {j in COLS} <c[_N_,j]=col('C'||j)>;
for {i in ROWS, j in COLS: c[i,j] ne .}
fix X[i,j] = c[i,j];
/* call CLP solver */
solve;
/* print solution */
print X;
quit;</syntaxhighlight>
Output:
<pre>
X
1 2 3 4 5 6 7 8 9
1 9 8 5 3 2 7 6 4 1
2 6 7 1 5 9 4 2 3 8
3 3 2 4 6 1 8 9 5 7
4 2 4 3 7 6 1 8 9 5
5 5 9 7 4 8 3 1 2 6
6 1 6 8 2 5 9 4 7 3
7 4 5 2 8 3 6 7 1 9
8 7 1 6 9 4 5 3 8 2
9 8 3 9 1 7 2 5 6 4
</pre>
=={{header|Scala}}==
Line 7,944 ⟶ 11,194:
This solver works with normally 9x9 sudokus as well as with sudokus of jigsaw type or sudokus with additional condition like diagonal constraint.
{{works with|Scala|2.9.1}}
<
class Solver {
Line 8,075 ⟶ 11,325:
println(solution match {case Nil => "no solution!!!" case _ => f2Str(solution)})
}</
{{out}}
<pre>riddle:
Line 8,109 ⟶ 11,359:
The implementation above doesn't work so effective for sudokus like Bracmat version, therefore I implemented a second version inspired by Java section:
{{works with|Scala|2.9.1}}
<
object Solver {
Line 8,226 ⟶ 11,476:
+("\n"*2))
}
}</
{{out}}
<pre>riddle used in Ada section:
Line 8,354 ⟶ 11,604:
no solution!!!</pre>
=={{header|
The grid should be input in <code>Init_board</code> as a 9x9 matrix. The blanks should be represented by 0. A rule that the initial game should have at least 17 givens is enforced, for it guarantees a unique solution. It is also possible to set a maximum number of steps to the solver using <code>break_point</code>. If it is set to 0, there will be no break until it finds the solution.
<syntaxhighlight lang="text">Init_board=[...
5 3 0 0
6 0 0 1 9 5 0 0 0;...
0 9 8 0 0 0 0 6 0;...
8 0 0 0 6 0 0 0 3;...
4 0 0 8 0 3 0 0 1;...
7 0 0 0 2 0 0 0 6;...
0 6 0 0 0 0 2 8 0;...
0 0 0 4 1 9 0 0 5;...
0 0 0 0 8 0 0 7 9];
break_point=1.0d5; //if 0 there will be no break
function []=disp_board(board)
StringBoard=string(board);
for i=1:9
for j=1:9
if board(i,j)==0 then
StringBoard(i,j)='×';
end
end
end
StringBoard=[StringBoard, string(zeros(9,2))];
StringBoard=[StringBoard; string(zeros(2,11))];
for i=1:9
StringBoard(i,:)=[StringBoard(i,1:3), '|', StringBoard(i,4:6), '|', StringBoard(i,7:9)]
end
StringBoard(9:11,:)=StringBoard(7:9,:);
StringBoard(8,:)=strsplit('-----------');
StringBoard(5:7,:)=StringBoard(4:6,:);
StringBoard(4,:)=strsplit('-----------');
disp(StringBoard)
endfunction
function varargout=validate_input(input,position,board)
row=board(position(1),:);
column=board(:,position(2));
block=zeros(3,3);
if position(1)>=1 & position(1)<=3 then
i=0;
elseif position(1)>=4 & position(1)<=6 then
i=3;
else
i=6;
end
if position(2)>=1 & position(2)<=3 then
j=0;
elseif position(2)>=4 & position(2)<=6 then
j=3;
else
j=6;
end
block=board(i+1:i+3,j+1:j+3)
valid_input=%F;
valid_row=%F;
valid_col=%F;
valid_block=%F;
if find(input==row)==[] then
valid_row=%T;
end
if find(input==column)==[] then
valid_col=%T;
end
if find(input==block)==[] then
valid_block=%T;
end
if valid_row & valid_col & valid_block then
valid_input=%T;
end
varargout=list(valid_input,valid_row,valid_col,valid_block)
endfunction
function varargout=validate_board(board)
valid_flag1=%T;
for i=1:9
for j=1:9
if board(i,j)~= 0 then
check_board=Init_board;
check_board(i,j)=0;
valid_flag1=validate_input(board(i,j),[i j],check_board);
if ~valid_flag1 then
break
end
end
end
if ~valid_flag1 then
break
end
end
valid_flag2 = (length( find(board) ) >= 17); //enforces rule of minimum of 17 givens
//set it to always %T to ignore this rule
valid_board = (valid_flag1 & valid_flag2);
varargout=list(valid_board)
endfunction
disp('Initial board:');
disp_board(Init_board);
valid_init_board=validate_board(Init_board);
if ~valid_init_board then
error('Invalid initial board. Should follow sudoku rules and have at least 17 clues.');
end
blank=[];
for i=1:9
for j=1:9
if Init_board(i,j)== 0 then
blank=[blank; i j];
end
end
end
Solved_board=Init_board;
tic();
i=0; counter=0; breaked=%F;
while i<size(blank,'r')
i=i+1;
counter=counter+1;
pos=blank(i,:);
value=Solved_board(pos(1),pos(2));
valid_value=%F;
while valid_value==%F
value=value+1;
if value>=10
break
else
valid_value=validate_input(value,pos,Solved_board);
end
end
if valid_value & value<10 then
Solved_board(pos(1),pos(2))=value
else
Solved_board(pos(1),pos(2))=0;
i=i-2;
end
if counter==break_point
breaked=%T;
break
end
end
valid_solved_board=validate_board(Solved_board);
t2=toc();
if valid_solved_board & ~breaked then
disp('Solved!');
disp('Solution:');
disp_board(Solved_board);
disp('Time: '+string(t2)+'s.');
disp('Steps: '+string(counter)+'.');
elseif breaked
disp('Break point reached.');
disp('Time: '+string(t2)+'s.');
disp_board(Solved_board);
elseif ~valid_solved_board & ~breaked
disp('Invalid solution found.');
disp_board(Solved_board);
end</syntaxhighlight>
{{out}}
<pre> Initial board:
!5 3 × | × 7 × | × × × !
! !
!6 × × | 1 9 5 | × × × !
! !
!× 9 8 | × × × | × 6 × !
! !
!- - - - - - - - - - - !
! !
!8 × × | × 6 × | × × 3 !
! !
!4 × × | 8 × 3 | × × 1 !
! !
!7 × × | × 2 × | × × 6 !
! !
!- - - - - - - - - - - !
! !
!× 6 × | × × × | 2 8 × !
! !
!× × × | 4 1 9 | × × 5 !
! !
!× × × | × 8 × | × 7 9 !
Solved!
Solution:
!5 3 4 | 6 7 8 | 9 1 2 !
! !
!6 7 2 | 1 9 5 | 3 4 8 !
! !
!1 9 8 | 3 4 2 | 5 6 7 !
! !
!- - - - - - - - - - - !
! !
!8 5 9 | 7 6 1 | 4 2 3 !
! !
!4 2 6 | 8 5 3 | 7 9 1 !
! !
!7 1 3 | 9 2 4 | 8 5 6 !
! !
!- - - - - - - - - - - !
! !
!9 6 1 | 5 3 7 | 2 8 4 !
! !
!2 8 7 | 4 1 9 | 6 3 5 !
! !
!3 4 5 | 2 8 6 | 1 7 9 !
Time: 1.7142502s.
Steps: 8365.</pre>
=={{header|Sidef}}==
{{trans|Raku}}
<syntaxhighlight lang="ruby">func check(i, j) is cached {
var (id, im) = i.divmod(9)
var (jd, jm) = j.divmod(9)
jd == id && return true
jm == im && return true
(id//3 == jd//3) &&
(jm//3 == im//3)
}
func solve(
for i in ^grid {
var t =
{
} << 1..9
return nil
}
for i in ^grid {
print "#{
print " " if (3 -> divides(i+1))
print "\n" if (9 -> divides(i+1))
print "\n" if (27 -> divides(i+1))
}
}
var
5 3 0 0 2 4 7 0 0
0 0 2 0 0 0 8 0 0
Line 8,405 ⟶ 11,885:
9 6 0 0 1 0 3 0 0
0 5 0 6 9 0 0 1 0
)
solve(
{{out}}
<pre>5 3 9 8 2 4 7 6 1
Line 8,420 ⟶ 11,900:
9 6 7 4 1 5 3 2 8
2 5 3 6 9 8 4 1 7 </pre>
=={{header|Shale}}==
<syntaxhighlight lang="shale">
#!/usr/local/bin/shale
time library
// This solves a sudoku with:
// row/column/3x3box constraints (standard sudoku)
// row/column/irregular, or jigsaw, region constraints
// optionally with a Chess Knight's move constraint.
// It is based on the python code from the Computerphile video
// https://www.youtube.com/watch?v=G_UYXzGuqvM
// The sudoku example from this video is used below, along with
// a couple of Cracking The Cryptic examples and one from Andrew Stuart.
// The sudoku grid is stored in a multi-dimensional array under the grid:: namespace.
// The row and column of each cell is represented by:
//
// row column:: grid::
//
// A 0 value represents an empty cell, and a 1 to 9 value represents a cell value.
// You can specify which of the sudokus to solve by specifying s={n} on the command line.
// If it is not specified then you get a text explaining how to specify an option
// and what the options are and the default (s=1) option is solved.
startTime dup var now time::() =
whichSudoku var
s initialised {
whichSudoku s =
} {
"You can choose to solve one of several sudokus by adding s=n to the command line," println
"where n is" println
" 1: standard sudoku from Computerphile (the default)" println
" 2: standard sudoku from Cracking The Cryptic" println
" 3: standard sudoku from Cracking The Cryptic, with Knight's move constraint" println
" 4: standard sudoku from Cracking The Cryptic" println
" 5: irregular sudoku from Cracking The Cryptic" println
" 6: irregular sudoku from Andrew Stuart" println
"" println
"You can also enable colour output by adding colour=true or color=true to the command line." println
"" println
"For example," println
file arg:: shale:: " %s s=3 colour=true\n" printf
"will solve the CTC sudoku with the Knight's move constraint" println
"" println
whichSudoku 1 =
} if
// Prints the sudoku grid.
printGrid dup var {
r var
c var
doColour var
irregular var
region var
colour initialised {
doColour colour =
} {
color initialised {
doColour color =
} {
doColour false =
} if
} if
irregular 0 0:: regions:: initialised =
r 0 =
{ r 9 < } {
c 0 =
{ c 9 < } {
doColour {
irregular {
region r.value c.value:: regions:: =
region.value colour:: 0x1b "%c[1;%dm" printf
} {
r 3 / c 3 / + 1 + 2 % 3 * 31 + 0x1b "%c[1;%dm" printf
} if
} ifthen
r.value c.value:: grid:: dup 0 == { pop " ." } { " %d" } if printf
doColour {
0x1b "%c[0m" printf
} ifthen
c++
} while
"" println
r++
} while
} =
// This sets up the colour map for irregular sudokus.
1 colour:: dup var 30 =
2 colour:: dup var 31 =
3 colour:: dup var 32 =
4 colour:: dup var 33 =
5 colour:: dup var 34 =
6 colour:: dup var 35 =
7 colour:: dup var 36 =
8 colour:: dup var 30 = // skip 37 (too light) and reuse 30 and 31 (with luck they won't be close to regions 1 and 2).
9 colour:: dup var 31 =
// Assign the cell values to one row of the grid.
setRow dup var {
8$ dup var swap = // cell 9 of the row
7$ dup var swap = // cell 8 of the row
6$ dup var swap = // ...
5$ dup var swap =
4$ dup var swap =
3$ dup var swap =
2$ dup var swap =
1$ dup var swap = // ...
0$ dup var swap = // cell 1 of the row
r dup var swap = // the row number
ns dup var swap &= // the namespace to use
i var // loop counter
r 0 < r 8 > or {
r "Illegal row %d\n" printf
1 exit
} ifthen
i 0 =
{ i 9 < } {
i.value$ 0 < i.value$ 9 > or {
i r i.value$ "Illegal value %d specified for r%dc%d\n" printf
1 exit
} ifthen
r.value i.value:: ns->:: defined not { // define this grid cell if not already defined
r.value i.value:: ns->:: var
} ifthen
r.value i.value:: ns->:: i.value$ = // assign the value to the grid cell
i++
} while
} =
// Standard 3x3 box region checker.
// This only works when called from within possible().
standardRegions dup var {
r0 var
c0 var
r0 r 3 / 3 * =
c0 c 3 / 3 * =
i 0 =
{ i 3 < } {
j 0 =
{ j 3 < } {
r0 i + c0 j +:: grid:: n == {
false return
} ifthen
j++
} while
i++
} while
} =
// Irregular region checker.
// This only works when called from within possible().
irregularRegions dup var {
region var
i var
region r.value c.value:: regions:: = // The region we are in.
i 0 =
{ i 9 < } {
i.value r:: region.value:: region:: value i.value c:: region.value:: region:: value:: grid:: n == {
false return
} ifthen
i++
} while
} =
// Convert the regions:: namespace into something a little more cpu-time friendly.
// Only optimise if there are irregular regions defined.
optimiseRegions dup var {
0 0:: regions:: initialised {
region var
r var
c var
i var
region 1 =
{ region 10 < } {
i 0 =
r 0 =
{ r 9 < } {
c 0 =
{ c 9 < } {
r.value c.value:: regions:: region == {
i.value r:: region.value:: region:: dup var r =
i.value c:: region.value:: region:: dup var c =
i++
} ifthen
c++
} while
r++
} while
i 9 != {
i region "Region %d contains the wrong number of cells (%d)\n" printf
1 exit
} ifthen
region++
} while
} ifthen
} =
// Is it possible to place a digit in a given cell?
possible dup var { function
n dup var swap =
c dup var swap =
r dup var swap =
i var
j var
// Check the column doesn't already contain this value.
i 0 =
{ i 9 < } {
r.value i.value:: grid:: n == {
false return
} ifthen
i++
} while
// Check the row doesn't already contain this value.
i 0 =
{ i 9 < } {
i.value c.value:: grid:: n == {
false return
} ifthen
i++
} while
// Check that the region doesn't already contain this value.
regionChecker()
// Check for any other constraint.
constraint initialised { r c n constraint() not } and {
false return
} ifthen
true
} =
// This is a Knight's move constraint.
knightsMoveConstraint dup var { function
0$ dup var swap = // n
1$ dup var swap = // column
2$ dup var swap = // row
nr var
nc var
// Check Knight's move 2 left and 1 up and down.
nc 1$ 2 - =
nc 0 >= {
nr 2$ 1 - =
nr 0 >= {
nr.value nc.value:: grid:: 0$ == {
false return
} ifthen
} ifthen
nr 2$ 1 + =
nr 9 < {
nr.value nc.value:: grid:: 0$ == {
false return
} ifthen
} ifthen
} ifthen
// Check Knight's move 1 left and 2 up and down.
nc 1$ 1 - =
nc 0 >= {
nr 2$ 2 - =
nr 0 >= {
nr.value nc.value:: grid:: 0$ == {
false return
} ifthen
} ifthen
nr 2$ 2 + =
nr 9 < {
nr.value nc.value:: grid:: 0$ == {
false return
} ifthen
} ifthen
} ifthen
// Check Knight's move 1 right and 2 up and down.
nc 1$ 1 + =
nc 9 < {
nr 2$ 2 - =
nr 0 >= {
nr.value nc.value:: grid:: 0$ == {
false return
} ifthen
} ifthen
nr 2$ 2 + =
nr 9 < {
nr.value nc.value:: grid:: 0$ == {
false return
} ifthen
} ifthen
} ifthen
// Check Knight's move 2 right and 1 up and down.
nc 1$ 2 + =
nc 9 < {
nr 2$ 1 - =
nr 0 >= {
nr.value nc.value:: grid:: 0$ == {
false return
} ifthen
} ifthen
nr 2$ 1 + =
nr 9 < {
nr.value nc.value:: grid:: 0$ == {
false return
} ifthen
} ifthen
} ifthen
true
} =
// Set this to standardRegions for the usual 3x3 boxes,
// or irregularRegions to handle irregular, or jigsaw, regions.
regionChecker var
// Leave this undefined to get the standard sudoku rules, or set this
// to constraint code such as knightsMoveConstraint defined above.
constraint var
solve dup var { function
r var
c var
n var
r 0 =
{ r 9 < } {
c 0 =
{ c 9 < } {
r.value c.value:: grid:: dup 0 == { // dup r.value c.value:: grid:: so we don't have to recalculate it in the inner loop.
n 1 =
{ n 10 < } {
r.value c.value n.value possible() {
dup n = // picking up r.value c.value:: grid:: again.
solve()
dup 0 = // picking up r.value c.value:: grid:: again.
} ifthen
n++
} while
pop // get rid of r.value c.value:: grid::
return
} ifthen
pop // get rid of r.value c.value:: grid::
c++
} while
r++
} while
"" println
printGrid()
now time::() startTime - 1000.0 / "Solution in %0.3f seconds\n" printf
} =
found var
found false =
// As mentioned above, this is the example taken from the Computerphile video.
// Raspberry Pi3 Model A time: 17s to the solution, 19s to finish.
// The time spent between the solution and the finish is the script searching
// of other, non-existant, soultion.
whichSudoku 1 == {
found true =
"From Computerphile: https://www.youtube.com/watch?v=G_UYXzGuqvM" println
regionChecker standardRegions =
grid 0 5 3 0 0 7 0 0 0 0 setRow()
grid 1 6 0 0 1 9 5 0 0 0 setRow()
grid 2 0 9 8 0 0 0 0 6 0 setRow()
grid 3 8 0 0 0 6 0 0 0 3 setRow()
grid 4 4 0 0 8 0 3 0 0 1 setRow()
grid 5 7 0 0 0 2 0 0 0 6 setRow()
grid 6 0 6 0 0 0 0 2 8 0 setRow()
grid 7 0 0 0 4 1 9 0 0 5 setRow()
grid 8 0 0 0 0 8 0 0 7 9 setRow()
} ifthen
// From https://www.youtube.com/watch?v=MXUgYxHmKq4&t=0s
// This sudoku was featured on Cracking The Cryptic, and takes considerably longer than the one above.
// Pi3 Model A time: 3m 23s to the solution, 15m 11s to finish.
whichSudoku 2 == {
found true =
"From Cracking The Cryptic: https://www.youtube.com/watch?v=MXUgYxHmKq4&t=0s" println
regionChecker standardRegions =
grid 0 0 6 8 0 0 0 0 1 3 setRow()
grid 1 0 0 0 9 0 1 0 0 0 setRow()
grid 2 0 0 0 0 0 8 0 0 4 setRow()
grid 3 0 1 0 0 4 0 5 0 0 setRow()
grid 4 0 3 0 0 0 9 0 0 0 setRow()
grid 5 0 8 5 0 0 0 0 7 0 setRow()
grid 6 0 2 0 0 0 7 3 0 0 setRow()
grid 7 0 0 0 0 9 4 0 0 6 setRow()
grid 8 4 0 0 0 6 0 0 0 0 setRow()
} ifthen
// From https://www.youtube.com/watch?v=rQHV-gIAG_0
// Another Cracking The Cryptic video, this one with a Knight's move constraint.
// Pi3 Model A time: 48s to the solution, 6m 10s to finish.
whichSudoku 3 == {
found true =
"From Cracking The Cryptic: https://www.youtube.com/watch?v=rQHV-gIAG_0" println
"This includes a Chess Knight's move constraint." println
regionChecker standardRegions =
constraint knightsMoveConstraint =
grid 0 0 0 0 0 0 6 0 0 0 setRow()
grid 1 0 0 3 0 0 0 0 0 7 setRow()
grid 2 2 0 0 3 0 0 4 9 0 setRow()
grid 3 6 0 0 0 0 0 0 4 5 setRow()
grid 4 0 0 2 0 0 0 8 0 0 setRow()
grid 5 0 0 0 1 0 0 0 0 0 setRow()
grid 6 3 0 0 0 0 0 0 0 0 setRow()
grid 7 7 0 0 0 0 1 0 0 9 setRow()
grid 8 0 0 0 0 0 0 5 0 0 setRow()
} ifthen
// Another CTC sudoku: https://www.youtube.com/watch?v=vH-JooV8RA4&t=0s
// Pi3 Model A time: 1m 6s to the solution, 48m 35s to finish.
whichSudoku 4 == {
found true =
"From Cracking The Cryptic: https://www.youtube.com/watch?v=vH-JooV8RA4&t=0s" println
regionChecker standardRegions =
grid 0 0 0 0 0 0 0 0 0 0 setRow()
grid 1 0 0 9 8 0 0 0 0 7 setRow()
grid 2 0 8 0 0 6 0 0 5 0 setRow()
grid 3 0 5 0 0 4 0 0 3 0 setRow()
grid 4 0 0 7 9 0 0 0 0 2 setRow()
grid 5 0 0 0 0 0 0 0 0 0 setRow()
grid 6 0 0 2 7 0 0 0 0 9 setRow()
grid 7 0 4 0 0 5 0 0 6 0 setRow()
grid 8 3 0 0 0 0 6 2 0 0 setRow()
} ifthen
// Another Cracking The Cryptic sudoku: https://www.youtube.com/watch?v=eJIu8w3ZXo8
// This is an irregular (jigsaw) sudoku.
// Pi3 Model A time: 2m 5s to the solution, 7m 5s to finish.
whichSudoku 5 == {
found true =
"From Cracking The Cryptic: https://www.youtube.com/watch?v=eJIu8w3ZXo8" println
"An irregular sudoku." println
regionChecker irregularRegions =
regions 0 1 1 1 1 1 2 2 2 2 setRow()
regions 1 1 3 3 3 6 6 2 2 2 setRow()
regions 2 1 3 3 3 6 7 7 7 2 setRow()
regions 3 1 3 3 3 6 7 7 7 2 setRow()
regions 4 1 6 6 6 6 7 7 7 8 setRow()
regions 5 9 6 4 4 4 8 8 8 8 setRow()
regions 6 9 9 4 4 4 8 5 5 5 setRow()
regions 7 9 9 4 4 4 8 5 5 5 setRow()
regions 8 9 9 9 9 8 8 5 5 5 setRow()
grid 0 3 0 0 0 0 0 0 0 1 setRow()
grid 1 0 9 0 1 7 2 0 0 0 setRow()
grid 2 0 0 3 0 0 0 9 0 0 setRow()
grid 3 0 7 0 0 0 0 0 4 0 setRow()
grid 4 0 4 0 0 3 0 0 6 0 setRow()
grid 5 0 5 0 0 0 0 0 9 0 setRow()
grid 6 0 0 6 0 0 0 5 0 0 setRow()
grid 7 0 0 0 8 5 6 0 2 0 setRow()
grid 8 7 0 0 0 0 0 0 0 8 setRow()
} ifthen
// This is taken from Andrew Stuart's web site https://www.sudokuwiki.org/Daily_Jigsaw_Sudoku
// No. 4294, dated 13 Nov 2020. It is rated 5-star out of 6: Diabolical.
// The archived version is here: https://www.sudokuwiki.org/Print_Daily_Jigsaw.asp?day=13/11/2020
// At the time of writing, Andrew only archives sudoku's for 31 days, then they are deleted.
// The region layout is called "Andrew Stuart 24" and the numbering is taken directly
// from Andrew's solver page. A big thanks goes to Andrew for giving me permission to include this sudoku.
// The region numbers must be between 1 and 9 inclusive.
// Pi3 Model A time: 26m 23s to the solution, 1h 15m 20s to finish.
whichSudoku 6 == {
found true =
"From Andrew Stuart's web page: https://www.sudokuwiki.org/Daily_Jigsaw_Sudoku" println
"No. 4294, dated 13 Nov 2020" println
regionChecker irregularRegions =
regions 0 1 1 2 2 2 2 3 3 4 setRow()
regions 1 1 1 2 2 2 3 3 3 4 setRow()
regions 2 1 1 1 2 3 3 3 4 4 setRow()
regions 3 1 1 5 2 3 7 4 4 4 setRow()
regions 4 5 5 5 6 6 7 7 4 4 setRow()
regions 5 5 5 5 6 6 7 7 7 9 setRow()
regions 6 8 5 5 6 6 7 7 7 9 setRow()
regions 7 8 8 6 6 6 9 9 9 9 setRow()
regions 8 8 8 8 8 8 8 9 9 9 setRow()
grid 0 0 0 0 0 0 0 0 9 0 setRow()
grid 1 5 0 0 0 8 1 0 0 0 setRow()
grid 2 0 0 0 9 0 4 5 0 0 setRow()
grid 3 0 0 0 0 0 0 0 0 5 setRow()
grid 4 0 1 0 0 0 8 0 0 0 setRow()
grid 5 7 0 6 0 0 0 0 0 0 setRow()
grid 6 0 0 0 1 0 0 6 0 0 setRow()
grid 7 1 0 0 7 2 0 0 0 0 setRow()
grid 8 0 9 0 0 0 0 0 0 0 setRow()
} ifthen
// If you want to add your own sudoku, add it here.
whichSudoku 7 == {
found true =
// add it here
// regionChecker standardRegions = // Include a region checker
// regionChecker irregularRegions =
// constraint knightsMoveConstraint = // Include any extra contraints, as appropriate
} ifthen
// Don't change anything from here to the end.
found {
optimiseRegions()
"" println
"Initial grid" println
printGrid()
solve()
now time::() startTime - 1000.0 / "Total runtime was %0.3f seconds\n" printf
} {
whichSudoku "Sudoku %d not found\n" printf
} if
// I'd like to see an irregular sudoku with a knight's move constraint. Any takers...
</syntaxhighlight>
'''Output'''
<pre>
From Cracking The Cryptic: https://www.youtube.com/watch?v=rQHV-gIAG_0
This includes a Chess Knight's move constraint.
Initial grid
. . . . . 6 . . .
. . 3 . . . . . 7
2 . . 3 . . 4 9 .
6 . . . . . . 4 5
. . 2 . . . 8 . .
. . . 1 . . . . .
3 . . . . . . . .
7 . . . . 1 . . 9
. . . . . . 5 . .
1 9 7 8 4 6 2 5 3
8 4 3 5 9 2 6 1 7
2 6 5 3 1 7 4 9 8
6 1 9 2 3 8 7 4 5
5 7 2 4 6 9 8 3 1
4 3 8 1 7 5 9 2 6
3 8 6 9 5 4 1 7 2
7 5 4 6 2 1 3 8 9
9 2 1 7 8 3 5 6 4
Solution in 7.241 seconds
Total runtime was 53.995 seconds
</pre>
=={{header|SQL}}==
{{works with|oracle|11.2 and higher}}
The implementation below uses a recursive WITH clause (aka recursive CTE, recursive query, recursive factored subquery). This is supported - with minimal syntactical differences - by some (perhaps many) but not all SQL dialects. The code was written and tested in Oracle SQL; Oracle has supported recursive subqueries since version 11.2.
The code implements a brute force algorithm. It can solve most problems in less than half a second (depending on hardware too), although I found a few that take 2-3 and up to 6 seconds. The output may either be empty (when the problem is impossible), a single completed grid (for a "correct" problem), or all the correct solutions to problems that admit more than one solution.
The input and output are presented as strings of 81 characters, where each character is either a digit or a space (indicating an empty cell in the grid). The translation between grids and such strings is trivial (convert grid to string by concatenating rows, reading left to right and then top to bottom), and not covered in the solution. The input is given as a bind variable, ''':game'''.
<syntaxhighlight lang="sql">with
symbols (d) as (select to_char(level) from dual connect by level <= 9)
, board (i) as (select level from dual connect by level <= 81)
, neighbors (i, j) as (
select b1.i, b2.i
from board b1 inner join board b2
on b1.i != b2.i
and (
mod(b1.i - b2.i, 9) = 0
or ceil(b1.i / 9) = ceil(b2.i / 9)
or ceil(b1.i / 27) = ceil(b2.i / 27) and trunc(mod(b1.i - 1, 9) / 3) = trunc(mod(b2.i - 1, 9) / 3)
)
)
, r (str, pos) as (
select :game, instr(:game, ' ')
from dual
union all
select substr(r.str, 1, r.pos - 1) || s.d || substr(r.str, r.pos + 1), instr(r.str, ' ', r.pos + 1)
from r inner join symbols s
on r.pos > 0 and not exists (
select *
from neighbors n
where r.pos = n.i and s.d = substr(r.str, n.j, 1)
)
)
select str
from r
where pos = 0
;</syntaxhighlight>
A better (faster) approach - taking advantage of database-specific features - is to create a '''table''' NEIGHBORS (similar to the inline view in the WITH clause) and an index on column I of that table; then the query execution time drops by more than half in most cases.
=={{header|Stata}}==
In this implementation, a Sudoku is a 9x9 matrix a, with either digits 1-9 or missing values. A cell is any element of a. A cell can be reference with indices i,j, or with a single index n between 1 and 81.
Three functions are defined:
* sudoku(a) will return 0 if there is no solution, 1 if there is '''at least''' one solution, and then a is modified in place with the solution found. This function builds several tables before calling the main "solver" function.
* solve(a,s,t,v,w) is made of two parts: first, all cells that can be filled without any assumption are considered known. Then, if not all cells are known, a cell with minimal number of choices is found, and a recursive call to solve is made with all possibilities in turn for this cell.
* push(a,s,t,v,w,n,z) is an auxiliary function, which pushes the value z in the nth cell of matrix a. Here n is a value between 1 and 81.
Fixed tables:
* t(n,.) is a row i,j,k: the cell n (1-81) has row index i, column index j, and square index k, where i, j, k are all in 1-9.
* s(n,.) is a row that contains the indices of the 20 "neighbors" of cell n: these are the cells in the same row, column or square.
Varying tables:
* v(n,z)=1 if the cell n may have the value z, otherwise 0. When a value z is pushed into the matrix, all neighboring cells are updated, as they can't take the value z anymore.
* w(n)=1 if cell n is not yet known, otherwise 0.
* In the initialization step of the sudoku() function, w has another meaning: it stores the column index of the last entry in row n of the array s while it is built. When it's done, every element of w is thus twenty.
The example grid given below is taken from [https://en.wikipedia.org/wiki/Sudoku_solving_algorithms Wikipedia]. It does not require any recursive call (it's entirely filled in the first step of ''solve''), as can be seen with additional ''printf'' in the code to follow the algorithm.
<syntaxhighlight lang="stata">mata
function sudoku(a) {
s = J(81,20,.)
t = J(81,3,.)
v = J(81,9,1)
w = J(81,1,0)
for (i=1; i<=9; i++) {
for (j=1; j<=9; j++) {
n = (i-1)*9+j
k = floor((i-1)/3)*3+floor((j-1)/3)+1
t[n,.] = i,j,k
}
}
for (i=1; i<=81; i++) {
for (j=i+1; j<=81; j++) {
if (any(t[i,.]:==t[j,.])) {
w[i]=w[i]+1
w[j]=w[j]+1
s[i,w[i]] = j
s[j,w[j]] = i
}
}
}
w = J(81,1,1)
for (i=1; i<=9; i++) {
for (j=1; j<=9; j++) {
if (a[i,j]<.) {
push(a,s,t,v,w,(i-1)*9+j,a[i,j])
}
}
}
return(solve(a,s,t,v,w))
}
function solve(a,s,t,v,w) {
for (q=1; q;) {
q = 0
for (n=1; n<=81; n++) {
if (w[n]) {
r = sum(v[n,.])
if (r==0) {
return(0)
}
else if (r==1) {
q = 1
push(a,s,t,v,w,n,selectindex(v[n,.]))
}
}
}
}
if (all(w:==0)) {
return(1)
}
else {
m0 = n0 = .
for (n=1; n<=81; n++) {
m = sum(v[n,.])
if (w[n] & m>1 & m<m0) {
m0 = m
n0 = n
}
}
z = selectindex(v[n0,.])
for (i=1; i<=m0; i++) {
a2 = a
v2 = v
w2 = w
push(a2,s,t,v2,w2,n0,z[i])
if (solve(a2,s,t,v2,w2)) {
a = a2
return(1)
}
}
return(0)
}
}
function push(a,s,t,v,w,n,z) {
w[n] = 0
i = t[n,1]
j = t[n,2]
a[i,j] = z
for (k=1; k<=20; k++) {
v[s[n,k],z] = 0
}
}
a = 5,3,.,.,7,.,.,.,.\
6,.,.,1,9,5,.,.,.\
.,9,8,.,.,.,.,6,.\
8,.,.,.,6,.,.,.,3\
4,.,.,8,.,3,.,.,1\
7,.,.,.,2,.,.,.,6\
.,6,.,.,.,.,2,8,.\
.,.,.,4,1,9,.,.,5\
.,.,.,.,8,.,.,7,9
sudoku(a)
a
end</syntaxhighlight>
'''Output'''
<pre>1
1 2 3 4 5 6 7 8 9
+-------------------------------------+
1 | 5 3 4 6 7 8 9 1 2 |
2 | 6 7 2 1 9 5 3 4 8 |
3 | 1 9 8 3 4 2 5 6 7 |
4 | 8 5 9 7 6 1 4 2 3 |
5 | 4 2 6 8 5 3 7 9 1 |
6 | 7 1 3 9 2 4 8 5 6 |
7 | 9 6 1 5 3 7 2 8 4 |
8 | 2 8 7 4 1 9 6 3 5 |
9 | 3 4 5 2 8 6 1 7 9 |
+-------------------------------------+</pre>
Two more examples, from [http://www.7sudoku.com/very-difficult here] and [http://www.extremesudoku.info/sudoku.html there].
<syntaxhighlight lang="stata">a = 7,9,.,.,.,3,.,.,2\
.,6,.,5,1,.,.,.,.\
.,.,.,.,.,2,.,.,6\
.,.,.,8,.,1,.,4,.\
.,.,.,.,.,.,1,.,3\
5,.,.,.,2,.,.,.,.\
.,.,.,.,.,.,.,7,4\
.,.,1,.,.,.,.,6,5\
.,.,8,.,9,7,.,.,.
sudoku(a)
a
1 2 3 4 5 6 7 8 9
+-------------------------------------+
1 | 7 9 5 6 8 3 4 1 2 |
2 | 2 6 4 5 1 9 7 3 8 |
3 | 1 8 3 7 4 2 5 9 6 |
4 | 9 3 6 8 5 1 2 4 7 |
5 | 8 4 2 9 7 6 1 5 3 |
6 | 5 1 7 3 2 4 6 8 9 |
7 | 3 2 9 1 6 5 8 7 4 |
8 | 4 7 1 2 3 8 9 6 5 |
9 | 6 5 8 4 9 7 3 2 1 |
+-------------------------------------+
a = .,.,4,1,.,.,.,.,9\
.,9,.,.,8,.,.,6,.\
6,.,.,.,.,3,7,.,.\
5,.,.,.,.,2,8,.,.\
.,4,.,.,3,.,.,2,.\
.,.,1,8,.,.,.,.,5\
.,.,2,5,.,.,.,.,3\
.,8,.,.,7,.,.,1,.\
7,.,.,.,.,1,4,.,.
sudoku(a)
a
1 2 3 4 5 6 7 8 9
+-------------------------------------+
1 | 2 7 4 1 5 6 3 8 9 |
2 | 1 9 3 7 8 4 5 6 2 |
3 | 6 5 8 2 9 3 7 4 1 |
4 | 5 3 7 6 1 2 8 9 4 |
5 | 8 4 6 9 3 5 1 2 7 |
6 | 9 2 1 8 4 7 6 3 5 |
7 | 4 1 2 5 6 8 9 7 3 |
8 | 3 8 5 4 7 9 2 1 6 |
9 | 7 6 9 3 2 1 4 5 8 |
+-------------------------------------+</syntaxhighlight>
=={{header|Swift}}==
{{trans|Java}}
<
typealias SodukuPuzzle = [[Int]]
Line 8,536 ⟶ 12,815:
[5, 0, 0, 0, 8, 0, 9, 0, 0],
[3, 0, 0, 0, 0, 1, 0, 0, 0],
[0, 2, 0, 7, 0, 0, 0, 0, 1],
[0, 9, 0, 0, 0, 0, 0, 4, 0],
Line 8,547 ⟶ 12,825:
let puzzle = Soduku(board: board)
puzzle.solve()
puzzle.printBoard()</
{{out}}
<pre>
Line 8,564 ⟶ 12,842:
-----------------------
</pre>
{{works with|Swift 3}}
<syntaxhighlight lang="swift">
func solving(board: [[Int]]) -> [[Int]] {
var board = board
var isSolved = false
while !isSolved {
for x in 0 ..< 9 {
for y in 0 ..< 9 {
if board[x][y] == 0 {
let known = Set(board.map { $0[y] } + board[x] + subgrid(board, pos: (x, y)))
let possible = Set(Array(1...9)).subtracting(known)
if possible.count == 1 {
board[x][y] = possible.first!
}
}
}
isSolved = 45 == board[x].reduce(0, +)
}
}
return board
}
func subgrid(_ board: [[Int]], pos: (Int, Int)) -> [Int] {
var r = [Int]()
var (x, y) = pos
x = x / 3 * 3
y = y / 3 * 3
for i in x ..< x + 3 {
for j in y ..< y + 3 {
r.append(board[i][j])
}
}
return r
}
func print(_ board: [[Int]]) {
for i in board.indices {
if i % 9 == 0 {
print(" -------------------")
}
for j in board.indices {
if j % board.count == 0 {
print("| ", terminator: "")
}
let digit = board[i][j]
print(digit != 0 ? digit : " ", terminator: "")
print(" ", terminator: "")
}
print("|")
}
print(" -------------------")
}
let puzzle = [
[0,2,0,4,5,0,7,0,9],
[0,0,0,1,0,9,0,3,0],
[0,0,8,0,0,0,1,0,4],
[0,4,0,0,6,1,0,7,0],
[5,0,6,0,3,0,0,1,0],
[0,3,0,0,0,2,0,9,0],
[3,0,4,0,7,5,0,6,8],
[0,9,0,0,1,0,3,0,7],
[0,0,2,0,0,3,0,0,1]
]
print(solving(board: puzzle))
</syntaxhighlight>
{{out}}
<pre>
-------------------
| 1 2 3 4 5 6 7 8 9 |
| 4 5 7 1 8 9 2 3 6 |
| 9 6 8 3 2 7 1 5 4 |
| 2 4 9 5 6 1 8 7 3 |
| 5 7 6 9 3 8 4 1 2 |
| 8 3 1 7 4 2 6 9 5 |
| 3 1 4 2 7 5 9 6 8 |
| 6 9 5 8 1 4 3 2 7 |
| 7 8 2 6 9 3 5 4 1 |
-------------------
</pre>
=={{header|SystemVerilog}}==
<syntaxhighlight lang="systemverilog">
//////////////////////////////////////////////////////////////////////////////
/// SudokuSolver ///
/// A class that fills up a sudoku board, the initial board is given ///
/// as an array preset_rows, the positions where preset_rows is zero ///
/// are to be determined. Three views of the sudoku board are created ///
/// and the uniqueness of its elements are defined by on constraint for ///
/// each view, one constraint ensures that the values are between 1 and ///
/// 9, and two other constraints are used to ensure that the values in ///
/// all three views agree to each other. ///
/// ///
/// ///
/// A solution using only the "rows" array would be possible, however ///
/// this illustrates better how one can relate different variables in ///
/// SystemVerilog Constrained randomization. ///
//////////////////////////////////////////////////////////////////////////////
class SudokuSolver;
rand int tiles[0:8][0:8];
rand int rows[0:8][0:8];
rand int cols[0:8][0:8];
int preset_rows[0:8][0:8];
constraint board_input {
foreach(preset_rows[i])foreach(preset_rows[i][j])
if(preset_rows[i][j] != 0) rows[i][j] == preset_rows[i][j];
}
constraint range {
foreach(rows[i]) foreach(rows[i][j])
rows[i][j] inside {[1:9]};
}
////////////////////////////////////////////////
/// Every number in a row is unique ///
////////////////////////////////////////////////
constraint rows_permutation {
foreach(rows[i]) foreach(rows[i][j1])
foreach(rows[i][j2])
if(j1 != j2) rows[i][j1] != rows[i][j2];
}
///////////////////////////////////////////////
/// Every number in a column is unique ///
///////////////////////////////////////////////
constraint cols_permutation {
foreach(cols[i]) foreach(cols[i][j1])
foreach(cols[i][j2])
if(j1 != j2) cols[i][j1] != cols[i][j2];
}
/////////////////////////////////////////////////
/// Every number in a tile (square) is unique ///
/////////////////////////////////////////////////
constraint tiles_permutation {
foreach(tiles[i]) foreach(tiles[i][j1])
foreach(tiles[i][j2])
if(j1 != j2) tiles[i][j1] != tiles[i][j2];
}
///////////////////////////////////////////////////
/// Makes sure that sure that the numbers in ///
/// each view agree with other views ///
///////////////////////////////////////////////////
constraint rows_vs_tiles {
foreach(tiles[i]) foreach(tiles[i][j])
tiles[i][j] == rows[(i/3) * 3 + (j/3)][3*(i%3)+(j%3)];
}
constraint rows_vs_cols {
foreach(cols[i]) foreach(cols[i][j])
cols[i][j] == rows[j][i];
}
///////////////////////////////////////////////////
/// Print the current state of the board in the ///
/// standard output ///
///////////////////////////////////////////////////
function void printBoard;
int i, j;
for(i = 0; i < 9; ++i) begin
if(i % 3 == 0)$display(" -------------");
$write(" ");
for(j = 0; j < 9; ++j) begin
if(j % 3 == 0) $write("|");
$write("%c", "0" + rows[i][j]);
end
$display("|");
end
$display(" -------------");
endfunction
function void printInitial;
int i, j;
for(i = 0; i < 9; ++i) begin
if(i % 3 == 0)$display("-------------");
for(j = 0; j < 9; ++j) begin
if(j % 3 == 0) $write("|");
if(preset_rows[i][j]) begin
$write("%c", "0" + preset_rows[i][j]);
end
else begin
$write(".");
end
end
$display("|");
end
$display("-------------");
endfunction
endclass
//////////////////////////////////////////////////////
/// Simple program instantiating the sudoku object ///
//////////////////////////////////////////////////////
program SudokuTest;
SudokuSolver board;
initial begin
board = new;
foreach(board.preset_rows[0][i]) board.preset_rows[i][i] = i+1;
$display("Initial Board:");
board.printInitial();
// Generate two different solutions for the board
if(board.randomize())begin
$display("One solution:");
board.printBoard();
end
else begin
$display("ERROR: Failed to generate first solution");
end
if(board.randomize())begin
$display("Another solution:");
board.printBoard();
end
else begin
$display("ERROR: Failed to generate second solution");
end
end
endprogram
</syntaxhighlight>
It can be seen that SystemVerilog randomization is a very powerfull tool, in this implementation I directly described the game constraints and the randomization engine takes care of producing solutions, and when multiple solutions are possible they will be chosen at random.
Running the above code using Cadence ncverilog I get
<pre>
> ncverilog +sv sudoku.sv
Initial Board:
-------------
|1..|...|...|
|.2.|...|...|
|..3|...|...|
-------------
|...|4..|...|
|...|.5.|...|
|...|..6|...|
-------------
|...|...|7..|
|...|...|.8.|
|...|...|..9|
-------------
One solution:
-------------
|168|547|392|
|925|631|478|
|743|928|156|
-------------
|832|479|561|
|671|852|934|
|459|316|827|
-------------
|396|284|715|
|214|795|683|
|587|163|249|
-------------
Another solution:
-------------
|197|642|358|
|425|389|176|
|683|715|294|
-------------
|956|431|827|
|842|957|631|
|731|826|945|
-------------
|214|598|763|
|569|173|482|
|378|264|519|
-------------
</pre>
=={{header|Tailspin}}==
There is a blog post about how this code was developed: https://tobega.blogspot.com/2020/05/creating-algorithm.html
<syntaxhighlight lang="tailspin">
templates deduceRemainingDigits
templates findOpenPosition
@:{options: 10"1"};
$ -> \[i;j](when <[]?($::length <..~$@findOpenPosition.options::raw>)> do @findOpenPosition: {row: $i, col: $j, options: ($::length)"1"}; \) -> !VOID
$@ !
end findOpenPosition
templates selectFirst&{pos:}
def digit: $($pos.row;$pos.col) -> $(1);
$ -> \[i;j](
when <?($i <=$pos.row>)?($j <=$pos.col>)> do $digit !
when <[]?($i <=$pos.row>)
|[]?($j <=$pos.col>)
|[]?(($i::raw-1)~/3 <=($pos.row::raw-1)~/3>)?(($j::raw-1)~/3 <=($pos.col::raw-1)~/3>)> do [$... -> \(when <~=$digit> do $! \)] !
when <> do $ !
\) !
end selectFirst
@: $;
$ -> findOpenPosition -> #
when <{options: <=0"1">}> do row´1:[] !
when <{options: <=10"1">}> do $@ !
when <> do def next: $;
$@ -> selectFirst&{pos: $next} -> deduceRemainingDigits
-> \(when <~=row´1:[]> do @deduceRemainingDigits: $; {options: 10"1"} !
when <=row´1:[]> do ^@deduceRemainingDigits($next.row;$next.col;1)
-> { $next..., options: $next.options-1"1"} ! \) -> #
end deduceRemainingDigits
test 'internal solver'
def sample: row´1:[
col´1:[5,3,4,6,7,8,9,1,2],
col´1:[6,7,2,1,9,5,3,4,8],
col´1:[1,9,8,3,4,2,5,6,7],
col´1:[8,5,9,7,6,1,4,2,3],
col´1:[4,2,6,8,5,3,7,9,1],
col´1:[7,1,3,9,2,4,8,5,6],
col´1:[9,6,1,5,3,7,2,8,4],
col´1:[2,8,7,4,1,9,6,3,5],
col´1:[3,4,5,2,8,6,1,7,9]
];
assert $sample -> deduceRemainingDigits <=$sample> 'completed puzzle unchanged'
assert row´1:[
col´1:[[5],3,4,6,7,8,9,1,2],
$sample(row´2..last)...] -> deduceRemainingDigits <=$sample> 'final digit gets placed'
assert row´1:[
col´1:[[],3,4,6,7,8,9,1,2],
$sample(row´2..last)...] -> deduceRemainingDigits <=row´1:[]> 'no remaining options returns empty'
assert row´1:[
col´1:[[5],3,4,6,[2,5,7],8,9,1,[2,5]],
$sample(row´2..last)...] -> deduceRemainingDigits <=$sample> 'solves 3 digits on row'
assert row´1:[
col´1:[5,3,4,6,7,8,9,1,2],
col´1:[[6,7,9],7,2,1,9,5,3,4,8],
col´1:[1,9,8,3,4,2,5,6,7],
col´1:[8,5,9,7,6,1,4,2,3],
col´1:[4,2,6,8,5,3,7,9,1],
col´1:[[7],1,3,9,2,4,8,5,6],
col´1:[[7,9],6,1,5,3,7,2,8,4],
col´1:[2,8,7,4,1,9,6,3,5],
col´1:[3,4,5,2,8,6,1,7,9]
] -> deduceRemainingDigits <=$sample> 'solves 3 digits on column'
assert row´1:[
col´1:[5,3,[4,6],6,7,8,9,1,2],
col´1:[[6],7,2,1,9,5,3,4,8],
col´1:[1,[4,6,9],8,3,4,2,5,6,7],
$sample(row´4..last)...
] -> deduceRemainingDigits <=$sample> 'solves 3 digits in block'
// This gives a contradiction if 3 gets chosen out of [3,5]
assert row´1:[
col´1:[[3,5],[3,4,6],[3,4,6],[3,4,6],7,8,9,1,2],
$sample(row´2..last)...] -> deduceRemainingDigits <=$sample> 'contradiction is backtracked'
end 'internal solver'
composer parseSudoku
row´1:[<section>=3]
rule section: <row>=3 (<'-+'>? <WS>?)
rule row: col´1:[<triple>=3] (<WS>?)
rule triple: <digit|dot>=3 (<'\|'>?)
rule digit: [<'\d'>]
rule dot: <'\.'> -> [1..9 -> '$;']
end parseSudoku
test 'input sudoku'
def parsed:
'53.|.7.|...
6..|195|...
.98|...|.67
-----------
8..|.6.|..3
4..|8.3|..1
7..|.2.|..6
-----------
.6.|...|28.
...|419|..5
...|.8.|.79' -> parseSudoku;
assert $parsed <[<[<[]>=9](9)>=9](9)> 'parsed sudoku has 9 rows containing 9 columns of lists'
assert $parsed(row´1;col´1) <=['5']> 'a digit'
assert $parsed(row´1;col´3) <=['1','2','3','4','5','6','7','8','9']> 'a dot'
end 'input sudoku'
templates solveSudoku
$ -> parseSudoku -> deduceRemainingDigits -> #
when <=row´1:[]> do 'No result found' !
when <> do $ -> \[i](
'$(col´1..col´3)...;|$(col´4..col´6)...;|$(col´7..col´9)...;$#10;' !
$i -> \(when <=row´3|=row´6> do '-----------$#10;' !\) !
\) -> '$...;' !
end solveSudoku
test 'sudoku solver'
assert
'53.|.7.|...
6..|195|...
.98|...|.67
-----------
8..|.6.|..3
4..|8.3|..1
7..|.2.|..6
-----------
.6.|...|28.
...|419|..5
...|.8.|.79'
-> solveSudoku <=
'534|678|912
672|195|348
198|342|567
-----------
859|761|423
426|853|791
713|924|856
-----------
961|537|284
287|419|635
345|286|179
'> 'solves sudoku and outputs pretty solution'
end 'sudoku solver'
</syntaxhighlight>
=={{header|Tcl}}==
Line 8,570 ⟶ 13,268:
Note that you can implement more rules if you want. Just make another subclass of <code>Rule</code> and the solver will pick it up and use it automatically.
{{works with|Tcl|8.6}} or {{libheader|TclOO}}
<
oo::class create Sudoku {
variable idata
Line 8,818 ⟶ 13,516:
return 0
}
}</
Demonstration code:
<
sudoku load {
{3 9 4 @ @ 2 6 7 @}
Line 8,843 ⟶ 13,541:
}
}
sudoku destroy</
{{out}}
<pre>+-----+-----+-----+
Line 8,859 ⟶ 13,557:
+-----+-----+-----+</pre>
If we'd added a logger method (after creating the <code>sudoku</code> object but before running the solver) like this:
<
Then this additional logging output would have been produced prior to the result being printed:
<pre>::RuleOnlyChoice solved ::sudoku at 8,0 for 1
Line 8,912 ⟶ 13,610:
Finished solving!</pre>
=={{header|Uiua}}==
{{Works with |Uiua|0.12.0-dev.1}}
Uses experimental '''⮌ orient''' and '''astar''' (only as a lazy way of managing the iteration :-).
<syntaxhighlight lang="uiua">
# Solves Sudoku using brute force.
# Experimental!
S ← [[8 5 0 0 0 2 4 0 0]
[7 2 0 0 0 0 0 0 9]
[0 0 4 0 0 0 0 0 0]
[0 0 0 1 0 7 0 0 2]
[3 0 5 0 0 0 9 0 0]
[0 4 0 0 0 0 0 0 0]
[0 0 0 0 8 0 0 7 0]
[0 1 7 0 0 0 0 0 0]
[0 0 0 0 3 6 0 4 0]]
Ps ← ⊞⊟.⇡9
Boxes ← ↯∞_9_2 ⊡⊞⊂.0_3_6 ◫3_3Ps
Nines ← ⊂Boxes⊂⟜(⮌1_0)Ps # 27 lists of pos's: one per row, col, box.
IsIn ← ☇1▽:⟜≡(∊:)Nines ¤ # (pos) -> pos's of all peers for a pos.
Peers ← ⊞(IsIn ⊟).⇡9 # For each pos, the pos of every peer (by row, col, box)
Free ← ▽:⟜(¬∊)+1⇡9◴▽⊸(>0)⊡⊡:Peers # Free values at pos (pos board) -> [n]
Next ← (
=/↧.≡(⧻Free) ⊙¤,,⊚=0. # Find most constrained pos.
Free,,⊙◌⊢▽⊙. # Get free values at pos.
≡(⍜⊡⋅∘)λBCa # Generate node for each.
)
End ← =0/+/+=0
astar(⍣Next⋅[]|0|End)S
↙¯1°□⊢⊙◌
</syntaxhighlight>
{{out}}
<pre>
╭─
╷ 8 5 1 3 9 2 4 6 7
╷ 7 2 3 4 6 1 5 8 9
6 9 4 7 5 8 2 3 1
9 6 8 1 4 7 3 0 2
3 0 5 0 0 0 9 0 0
0 4 0 0 0 0 0 0 0
0 0 0 0 8 0 0 7 0
0 1 7 0 0 0 0 0 0
0 0 0 0 3 6 0 4 0
╯
</pre>
=={{header|Ursala}}==
<
#import nat
Line 8,925 ⟶ 13,668:
~&rgg&& ~&irtPFXlrjrXPS; ~&lrK2tkZ2g&& ~&llrSL2rDrlPrrPljXSPTSL)+-,
//~&p ^|DlrDSLlrlPXrrPDSL(~&,num*+ rep2 block3)*= num block27 ~&iiK0 iota9,
* `0?=\~&iNC ! ~&t digits+-</
test program:
<
example =
Line 8,942 ⟶ 13,685:
010067008
009008000
026400735]-</
{{out}}
<pre>
Line 8,958 ⟶ 13,701:
</pre>
=={{
{{trans|Fortran}}
<
Dim gridSolved(9, 9)
Line 9,061 ⟶ 13,804:
Debug.Print
Next i
End Sub</
{{out}}
<pre>
Line 9,080 ⟶ 13,823:
{{trans|VBA}}
To run in console mode with cscript.
<
Dim gridSolved(9, 9)
Line 9,181 ⟶ 13,924:
End Sub 'Sudoku
Call sudoku</
{{out}}
<pre>Problem:
Line 9,203 ⟶ 13,946:
2 4 3 1 5 7 8 6 9
5 1 9 8 3 6 7 2 4</pre>
===Alternate version===
A faster version adapted from the C solution
<syntaxhighlight lang="vb">
'VBScript Sudoku solver. Fast recursive algorithm adapted from the C version
'It can read a problem passed in the command line or from a file /f:textfile
'if no problem passed it solves a hardwired problem (See the prob0 string)
'problem string can have 0's or dots in the place of unknown values. All chars different from .0123456789 are ignored
Option explicit
Sub print(s):
On Error Resume Next
WScript.stdout.Write (s)
If err= &h80070006& Then WScript.Echo " Please run this script with CScript": WScript.quit
End Sub
function parseprob(s)'problem string to array
Dim i,j,m
print "parsing: " & s & vbCrLf & vbcrlf
j=0
For i=1 To Len(s)
m=Mid(s,i,1)
Select Case m
Case "0","1","2","3","4","5","6","7","8","9"
sdku(j)=cint(m)
j=j+1
Case "."
sdku(j)=0
j=j+1
Case Else 'all other chars are ignored as separators
End Select
Next
' print j
If j<>81 Then parseprob=false Else parseprob=True
End function
sub getprob 'get problem from file or from command line or from
Dim s,s1
With WScript.Arguments.Named
If .exists("f") Then
s1=.item("f")
If InStr(s1,"\")=0 Then s1= Left(WScript.ScriptFullName, InStrRev(WScript.ScriptFullName, "\"))&s1
On Error Resume Next
s= CreateObject("Scripting.FileSystemObject").OpenTextFile (s1, 1).readall
If err Then print "can't open file " & s1 : parseprob(prob0): Exit sub
If parseprob(s) =True Then Exit sub
End if
End With
With WScript.Arguments.Unnamed
If .count<>0 Then
s1=.Item(0)
If parseprob(s1)=True Then exit sub
End if
End With
parseprob(prob0)
End sub
function solve(x,ByVal pos)
'print pos & vbcrlf
'display(x)
Dim row,col,i,j,used
solve=False
If pos=81 Then solve= true :Exit function
row= pos\9
col=pos mod 9
If x(pos) Then solve=solve(x,pos+1):Exit Function
used=0
For i=0 To 8
used=used Or pwr(x(i * 9 + col))
Next
For i=0 To 8
used=used Or pwr(x(row*9 + i))
next
row = (row\ 3) * 3
col = (col \3) * 3
For i=row To row+2
For j=col To col+2
' print i & " " & j &vbcrlf
used = used Or pwr(x(i*9+j))
Next
Next
'print pos & " " & Hex(used) & vbcrlf
For i=1 To 9
If (used And pwr(i))=0 Then
x(pos)=i
'print pos & " " & i & " " & num2bin((used)) & vbcrlf
solve= solve(x,pos+1)
If solve=True Then Exit Function
'x(pos)=0
End If
Next
x(pos)=0
solve=False
End Function
Sub display(x)
Dim i,s
For i=0 To 80
If i mod 9=0 Then print s & vbCrLf :s=""
If i mod 27=0 Then print vbCrLf
If i mod 3=0 Then s=s & " "
s=s& x(i)& " "
Next
print s & vbCrLf
End Sub
Dim pwr:pwr=Array(1,2,4,8,16,32,64,128,256,512,1024,2048)
Dim prob0:prob0= "001005070"&"920600000"& "008000600"&"090020401"& "000000000" & "304080090" & "007000300" & "000007069" & "010800700"
Dim sdku(81),Time
getprob
print "The problem"
display(sdku)
Time=Timer
If solve (sdku,0) Then
print vbcrlf &"solution found" & vbcrlf
display(sdku)
Else
print "no solution found " & vbcrlf
End if
print vbcrlf & "time: " & Timer-Time & " seconds" & vbcrlf
</syntaxhighlight>
{{out}}
<small>
<pre>
parsing: 001005070920600000008000600090020401000000000304080090007000300000007069010800700
The problem
0 0 1 0 0 5 0 7 0
9 2 0 6 0 0 0 0 0
0 0 8 0 0 0 6 0 0
0 9 0 0 2 0 4 0 1
0 0 0 0 0 0 0 0 0
3 0 4 0 8 0 0 9 0
0 0 7 0 0 0 3 0 0
0 0 0 0 0 7 0 6 9
0 1 0 8 0 0 7 0 0
solution found
6 3 1 2 4 5 9 7 8
9 2 5 6 7 8 1 4 3
4 7 8 3 1 9 6 5 2
7 9 6 5 2 3 4 8 1
1 8 2 9 6 4 5 3 7
3 5 4 7 8 1 2 9 6
8 6 7 4 9 2 3 1 5
2 4 3 1 5 7 8 6 9
5 1 9 8 3 6 7 2 4
time: 0.3710938 seconds
</pre>
</small>
=={{header|Wren}}==
{{trans|Kotlin}}
<syntaxhighlight lang="wren">class Sudoku {
construct new(rows) {
if (rows.count != 9 || rows.any { |r| r.count != 9 }) {
Fiber.abort("Grid must be 9 x 9")
}
_grid = List.filled(81, null)
for (i in 0..8) {
for (j in 0..8 ) _grid[9 * i + j] = rows[i][j]
}
_solved = false
}
checkValidity_(v, x, y) {
for (i in 0..8) {
if (_grid[y * 9 + i] == v || _grid[i * 9 + x] == v) return false
}
var startX = (x / 3).floor * 3
var startY = (y / 3).floor * 3
for (i in startY...startY + 3) {
for (j in startX...startX + 3) {
if (_grid[i * 9 + j] == v) return false
}
}
return true
}
placeNumber_(pos) {
if (_solved) return
if (pos == 81) {
_solved = true
return
}
if (_grid[pos].bytes[0] > 48) {
placeNumber_(pos + 1)
return
}
for (n in 1..9) {
if (checkValidity_(n.toString, pos % 9, (pos/9).floor)) {
_grid[pos] = n.toString
placeNumber_(pos + 1)
if (_solved) return
_grid[pos] = "0"
}
}
}
solve() {
System.print("Starting grid:\n\n%(this)")
placeNumber_(0)
System.print(_solved ? "Solution:\n\n%(this)" : "Unsolvable!")
}
toString {
var sb = ""
for (i in 0..8) {
for (j in 0..8) {
sb = sb + _grid[i * 9 + j] + " "
if (j == 2 || j == 5) sb = sb + "| "
}
sb = sb + "\n"
if (i == 2 || i == 5) sb = sb + "------+-------+------\n"
}
return sb
}
}
var rows = [
"850002400",
"720000009",
"004000000",
"000107002",
"305000900",
"040000000",
"000080070",
"017000000",
"000036040"
]
Sudoku.new(rows).solve()</syntaxhighlight>
{{out}}
<pre>
Starting grid:
8 5 0 | 0 0 2 | 4 0 0
7 2 0 | 0 0 0 | 0 0 9
0 0 4 | 0 0 0 | 0 0 0
------+-------+------
0 0 0 | 1 0 7 | 0 0 2
3 0 5 | 0 0 0 | 9 0 0
0 4 0 | 0 0 0 | 0 0 0
------+-------+------
0 0 0 | 0 8 0 | 0 7 0
0 1 7 | 0 0 0 | 0 0 0
0 0 0 | 0 3 6 | 0 4 0
Solution:
8 5 9 | 6 1 2 | 4 3 7
7 2 3 | 8 5 4 | 1 6 9
1 6 4 | 3 7 9 | 5 2 8
------+-------+------
9 8 6 | 1 4 7 | 3 5 2
3 7 5 | 2 6 8 | 9 1 4
2 4 1 | 5 9 3 | 7 8 6
------+-------+------
4 3 2 | 9 8 1 | 6 7 5
6 1 7 | 4 2 5 | 8 9 3
5 9 8 | 7 3 6 | 2 4 1
</pre>
=={{header|XPL0}}==
Line 9,208 ⟶ 14,221:
can be verified by several other examples.
{{trans|C}}
<
proc Show(X);
Line 9,278 ⟶ 14,291:
..9 ..8 ...
.26 4.. 735 ");
]</
{{out}}
Line 9,297 ⟶ 14,310:
=={{header|zkl}}==
{{trans|C}} Note: Unlike in the C solution, 1<<-1 is defined (as 0).
<
row,col:=pos/9, pos%9;
Line 9,318 ⟶ 14,331:
sdku[pos]=0;
return(False);
}</
<
#<<<
" 5 3 0 0 7 0 0 0 0
Line 9,337 ⟶ 14,350:
s[n*27,27].pump(Console.println,T(Void.Read,8),("| " + "%s%s%s | "*3).fmt); // 3 lines
println("+-----+-----+-----+");
}</
{{out}}
<pre>
|