Sudoku
You are encouraged to solve this task according to the task description, using any language you may know.
Solve a partially filled-in normal 9x9 Sudoku grid and display the result in a human-readable format. Algorithmics of Sudoku may help implement this.
AutoHotkey
<lang AutoHotkey>#SingleInstance OFF SetBatchLines, -1 SetTitleMatchMode, 3 Loop 9 {
r := A_Index, y := r*17-8
Loop 9 {
c := A_Index, x := c*17+5
Gui, Add, Edit, x%x% y%y% w17 h17 v%r%%c% Center Number Limit1
}
} Gui, Add, Button, vButton gSolve w175 x10 Center, Solve Gui, Add, Text, vMsg, Enter Sudoku puzzle and click Solve Gui, Show,, Sudoku Solver Return Solve: Gui, Submit, NoHide Loop 9 {
r := A_Index
Loop 9
If (%r%%A_Index% = "")
puzzle .= "@"
Else
puzzle .= %r%%A_Index%
} s := A_TickCount answer := Sudoku(puzzle) e := A_TickCount seconds := (e-s)/1000 StringSplit, a, answer, | Loop 9 {
r := A_Index
Loop 9
{
b := (r*9)+A_Index-9
GuiControl,, %r%%A_Index%, % a%b%
GuiControl, +ReadOnly, %r%%A_Index%
}
} GuiControl,, Msg, Solved! Time: %seconds% GuiControl,, Button, Close GuiControl, +gClose, Button return GuiClose: Close: ExitApp
- IfWinActive, Sudoku Solver
~Up:: GuiControlGet, f, focus StringTrimLeft, f, f, 4 f := ((f >= 1 && f <= 9) ? f+72 : f-9) GuiControl, Focus, Edit%f% return ~Down:: GuiControlGet, f, focus StringTrimLeft, f, f, 4 f := ((f >= 73 && f <= 81) ? f-72 : f + 9) GuiControl, Focus, Edit%f% return ~Left:: GuiControlGet, f, focus StringTrimLeft, f, f, 4 copyf := f While copyf > 0
copyf -= 9
f := ((copyf = 1) ? f+9 : f-1) f := ((f < 1) ? 81 : f) GuiControl, Focus, Edit%f% return ~Right:: GuiControlGet, f, focus StringTrimLeft, f, f, 4 copyf := f While copyf >= 9
copyf -= 9
f := ((copyf = 9) ? f-9 : f+1) f := Mod(f, 81) GuiControl, Focus, Edit%f% return
- IfWinActive
- Functions Start here
Sudoku( p ) { ;ErrorLevel contains the number of iterations p := RegExReplace(p, "[^1-9@]") ;format puzzle as single line string return Sudoku_Display(Sudoku_Solve(p)) }
Sudoku_Solve( p, d = 0 ) { ;d is 0-based
- http://www.autohotkey.com/forum/topic46679.html
- p
- 81 character puzzle string
- (concat all 9 rows of 9 chars each)
- givens represented as chars 1-9
- fill-ins as any non-null, non 1-9 char
- d
- used internally. omit on initial call
- returns
- 81 char string with non-givens replaced with valid solution
If (d >= 81) return p ;this is 82nd iteration, so it has successfully finished iteration 81 If InStr( "123456789", SubStr(p, d+1, 1) ) ;this depth is a given, skip through return Sudoku_Solve(p, d+1) m := Sudoku_Constraints(p,d) ;a string of this level's constraints. ; (these will not change for all 9 loops) Loop 9 { If InStr(m, A_Index) Continue NumPut(Asc(A_Index), p, d, "Char") If r := Sudoku_Solve(p, d+1) return r } return 0 }
Sudoku_Constraints( ByRef p, d ) {
- returns a string of the constraints for a particular position
c := Mod(d,9) , r := (d - c) // 9 , b := r//3*27 + c//3*3 + 1 ;convert to 1-based , c++ return "" ; row: . SubStr(p, r * 9 + 1, 9) ; column: . SubStr(p,c ,1) SubStr(p,c+9 ,1) SubStr(p,c+18,1) . SubStr(p,c+27,1) SubStr(p,c+36,1) SubStr(p,c+45,1) . SubStr(p,c+54,1) SubStr(p,c+63,1) SubStr(p,c+72,1) ;box . SubStr(p, b, 3) SubStr(p, b+9, 3) SubStr(p, b+18, 3) }
Sudoku_Display( p ) { If StrLen(p) = 81 loop 81 r .= SubStr(p, A_Index, 1) . "|" return r }</lang>
C
See e.g. this GPLed solver written in C.
Common Lisp
A simple solver without optimizations (except for pre-computing the possible entries of a cell).
<lang lisp>(defun row-neighbors (row column grid &aux (neighbors '()))
(dotimes (i 9 neighbors)
(let ((x (aref grid row i)))
(unless (or (eq '_ x) (= i column))
(push x neighbors)))))
(defun column-neighbors (row column grid &aux (neighbors '()))
(dotimes (i 9 neighbors)
(let ((x (aref grid i column)))
(unless (or (eq x '_) (= i row))
(push x neighbors)))))
(defun square-neighbors (row column grid &aux (neighbors '()))
(let* ((rmin (* 3 (floor row 3))) (rmax (+ rmin 3))
(cmin (* 3 (floor column 3))) (cmax (+ cmin 3)))
(do ((r rmin (1+ r))) ((= r rmax) neighbors)
(do ((c cmin (1+ c))) ((= c cmax))
(let ((x (aref grid r c)))
(unless (or (eq x '_) (= r row) (= c column))
(push x neighbors)))))))
(defun choices (row column grid)
(nset-difference
(list 1 2 3 4 5 6 7 8 9)
(nconc (row-neighbors row column grid)
(column-neighbors row column grid)
(square-neighbors row column grid))))
(defun solve (grid &optional (row 0) (column 0))
(cond
((= row 9)
grid)
((= column 9)
(solve grid (1+ row) 0))
((not (eq '_ (aref grid row column)))
(solve grid row (1+ column)))
(t (dolist (choice (choices row column grid) (setf (aref grid row column) '_))
(setf (aref grid row column) choice)
(when (eq grid (solve grid row (1+ column)))
(return grid))))))</lang>
Example:
> (defparameter *puzzle*
#2A((3 9 4 _ _ 2 6 7 _)
(_ _ _ 3 _ _ 4 _ _)
(5 _ _ 6 9 _ _ 2 _)
(_ 4 5 _ _ _ 9 _ _)
(6 _ _ _ _ _ _ _ 7)
(_ _ 7 _ _ _ 5 8 _)
(_ 1 _ _ 6 7 _ _ 8)
(_ _ 9 _ _ 8 _ _ _)
(_ 2 6 4 _ _ 7 3 5)))
*PUZZLE*
> (pprint (solve *puzzle*))
#2A((3 9 4 8 5 2 6 7 1)
(2 6 8 3 7 1 4 5 9)
(5 7 1 6 9 4 8 2 3)
(1 4 5 7 8 3 9 6 2)
(6 8 2 9 4 5 3 1 7)
(9 3 7 1 2 6 5 8 4)
(4 1 3 5 6 7 2 9 8)
(7 5 9 2 3 8 1 4 6)
(8 2 6 4 1 9 7 3 5))
D
<lang d> import std.stdio;
bool[char]genFull() {
return ['1':true,
'2':true,
'3':true,
'4':true,
'5':true,
'6':true,
'7':true,
'8':true,
'9':true];
} // these three functions assume that the number has not already been found bool[char]availRow(int x,int y,bool[char]available=genFull()) {
// x designates row, y designates column
foreach(ele;puzzle[x]) {
if (ele != '_') available.remove(ele);
}
return available;
}
bool[char]availCol(int x,int y,bool[char]available=genFull()) {
// x designates row, y designates column
for(int i = 0;i<9;i++) {
if (puzzle[i][y] != '_') available.remove(puzzle[i][y]);
}
return available;
}
bool[char]availBox(int x,int y,bool[char]available=genFull()) {
// x designates row, y designates column
// get a base index for the boxes
int bx = x/3;bx*=3;
int by = y/3;by*=3;
for(int i = 0;i<3;i++) for(int j = 0;j<3;j++) {
if (puzzle[bx+i][by+j] != '_') available.remove(puzzle[bx+i][by+j]);
}
return available;
}
char[][]puzzle; void main() {
puzzle ~= "394__267_".dup;
puzzle ~= "___3__4__".dup;
puzzle ~= "5__69__2_".dup;
puzzle ~= "_45___9__".dup;
puzzle ~= "6_______7".dup;
puzzle ~= "__7___58_".dup;
puzzle ~= "_1__67__8".dup;
puzzle ~= "__9__8___".dup;
puzzle ~= "_264__735".dup;
while(1) {
bool done = true;
foreach(i,row;puzzle) foreach(j,ref ele;row) if (ele == '_') {
// poke at the elements that are _
auto remaining = availBox(i,j,availRow(i,j,availCol(i,j)));
if (remaining.keys.length == 1) ele = remaining.keys[0];
else done = false;
}
if (done) break;
}
// write out completed puzzle
writefln("Completed puzzle:");
foreach(row;puzzle) writefln("%s",row);
} </lang>
J
See Solving Sudoku in J.
OCaml
uses the library ocamlgraph <lang ocaml>(* Ocamlgraph demo program: solving the Sudoku puzzle using graph coloring
Copyright 2004-2007 Sylvain Conchon, Jean-Christophe Filliatre, Julien Signoles
This software is free software; you can redistribute it and/or modify it under the terms of the GNU Library General Public License version 2, with the special exception on linking described in file LICENSE.
This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *)
open Format open Graph
(* We use undirected graphs with nodes containing a pair of integers
(the cell coordinates in 0..8 x 0..8). The integer marks of the nodes will store the colors. *)
module G = Imperative.Graph.Abstract(struct type t = int * int end)
(* The Sudoku grid = a graph with 9x9 nodes *) let g = G.create ()
(* We create the 9x9 nodes, add them to the graph and keep them in a matrix
for later access *)
let nodes =
let new_node i j = let v = G.V.create (i, j) in G.add_vertex g v; v in Array.init 9 (fun i -> Array.init 9 (new_node i))
let node i j = nodes.(i).(j) (* shortcut for easier access *)
(* We add the edges:
two nodes are connected whenever they can't have the same value, i.e. they belong to the same line, the same column or the same 3x3 group *)
let () =
for i = 0 to 8 do for j = 0 to 8 do
for k = 0 to 8 do
if k <> i then G.add_edge g (node i j) (node k j);
if k <> j then G.add_edge g (node i j) (node i k);
done;
let gi = 3 * (i / 3) and gj = 3 * (j / 3) in
for di = 0 to 2 do for dj = 0 to 2 do
let i' = gi + di and j' = gj + dj in
if i' <> i || j' <> j then G.add_edge g (node i j) (node i' j')
done done
done done
(* Displaying the current state of the graph *) let display () =
for i = 0 to 8 do for j = 0 to 8 do printf "%d" (G.Mark.get (node i j)) done; printf "\n"; done; printf "@?"
(* We read the initial constraints from standard input and we display g *) let () =
for i = 0 to 8 do
let s = read_line () in
for j = 0 to 8 do match s.[j] with
| '1'..'9' as ch -> G.Mark.set (node i j) (Char.code ch - Char.code '0')
| _ -> ()
done
done;
display ();
printf "---------@."
(* We solve the Sudoku by 9-coloring the graph g and we display the solution *) module C = Coloring.Mark(G)
let () = C.coloring g 9; display ()</lang>
Python
See Solving Sudoku puzzles with Python for GPL'd solvers of increasing complexity of algorithm.
Tcl
Adapted from a page on the Tcler's Wiki to use a standard object system.
Note that you can implement more rules if you want. Just make another subclass of Rule and the solver will pick it up and use it automatically.
<lang tcl>package require Tcl 8.6 oo::class create Sudoku {
variable idata
method clear {} {
for {set y 0} {$y < 9} {incr y} { for {set x 0} {$x < 9} {incr x} { my set $x $y {} } }
}
method load {data} {
set error "data must be a 9-element list, each element also being a\ list of 9 numbers from 1 to 9 or blank or an @ symbol." if {[llength $data] != 9} { error $error } for {set y 0} {$y<9} {incr y} { set row [lindex $data $y] if {[llength $row] != 9} { error $error } for {set x 0} {$x<9} {incr x} { set d [lindex $row $x] if {![regexp {^[@1-9]?$} $d]} { error $d-$error } if {$d eq "@"} {set d ""} my set $x $y $d } }
}
method dump {} {
set rows {} for {set y 0} {$y < 9} {incr y} { lappend rows [my getRow 0 $y] } return $rows
}
method Log msg {
# Chance to print message
}
method set {x y value} {
if {[catch {set value [format %d $value]}]} {set value 0} if {$value<1 || $value>9} { set idata(sq$x$y) {} } else { set idata(sq$x$y) $value }
}
method get {x y} {
if {![info exists idata(sq$x$y)]} { return {} } return $idata(sq$x$y)
}
method getRow {x y} {
set row {} for {set x 0} {$x<9} {incr x} { lappend row [my get $x $y] } return $row
}
method getCol {x y} {
set col {} for {set y 0} {$y<9} {incr y} { lappend col [my get $x $y] } return $col
}
method getRegion {x y} {
set xR [expr {($x/3)*3}] set yR [expr {($y/3)*3}] set regn {} for {set x $xR} {$x < $xR+3} {incr x} { for {set y $yR} {$y < $yR+3} {incr y} { lappend regn [my get $x $y] } } return $regn
}
}
- SudokuSolver inherits from Sudoku, and adds the ability to filter
- possibilities for a square by looking at all the squares in the row, column,
- and region that the square is a part of. The method 'solve' contains a list
- of rule-objects to use, and iterates over each square on the board, applying
- each rule sequentially until the square is allocated.
oo::class create SudokuSolver {
superclass Sudoku
method validchoices {x y} {
if {[my get $x $y] ne {}} { return [my get $x $y] }
set row [my getRow $x $y] set col [my getCol $x $y] set regn [my getRegion $x $y] set eliminate [list {*}$row {*}$col {*}$regn] set eliminate [lsearch -all -inline -not $eliminate {}] set eliminate [lsort -unique $eliminate]
set choices {} for {set c 1} {$c < 10} {incr c} { if {$c ni $eliminate} { lappend choices $c } } if {[llength $choices]==0} { error "No choices left for square $x,$y" } return $choices
}
method completion {} {
return [expr { 81-[llength [lsearch -all -inline [join [my dump]] {}]] }]
}
method solve {} {
foreach ruleClass [info class subclass Rule] { lappend rules [$ruleClass new] }
while {1} { set begin [my completion] for {set y 0} {$y < 9} {incr y} { for {set x 0} {$x < 9} {incr x} { if {[my get $x $y] eq ""} { foreach rule $rules { set c [$rule solve [self] $x $y] if {$c} { my set $x $y $c my Log "[info object class $rule] solved [self] at $x,$y for $c" break } } } } } set end [my completion] if {$end==81} { my Log "Finished solving!" break } elseif {$begin==$end} { my Log "A round finished without solving any squares, giving up." break } } foreach rule $rules { $rule destroy }
}
}
- Rule is the template for the rules used in Solver. The other rule-objects
- apply their logic to the values passed in and return either '0' or a number
- to allocate to the requested square.
oo::class create Rule {
method solve {hSudoku x y} {
if {![info object isa typeof $hSudoku SudokuSolver]} { error "hSudoku must be an instance of class SudokuSolver." }
tailcall my Solve $hSudoku $x $y [$hSudoku validchoices $x $y]
}
}
- Get all the allocated numbers for each square in the the row, column, and
- region containing $x,$y. If there is only one unallocated number among all
- three groups, it must be allocated at $x,$y
oo::class create RuleOnlyChoice {
superclass Rule
method Solve {hSudoku x y choices} {
if {[llength $choices]==1} { return $choices } else { return 0 }
}
}
- Test each column to determine if $choice is an invalid choice for all other
- columns in row $X. If it is, it must only go in square $x,$y.
oo::class create RuleColumnChoice {
superclass Rule
method Solve {hSudoku x y choices} {
foreach choice $choices { set failed 0 for {set x2 0} {$x2<9} {incr x2} { if {$x2 != $x && $choice in [$hSudoku validchoices $x2 $y]} { set failed 1 break } } if {!$failed} {return $choice} } return 0
}
}
- Test each row to determine if $choice is an invalid choice for all other
- rows in column $y. If it is, it must only go in square $x,$y.
oo::class create RuleRowChoice {
superclass Rule
method Solve {hSudoku x y choices} {
foreach choice $choices { set failed 0 for {set y2 0} {$y2<9} {incr y2} { if {$y2 != $y && $choice in [$hSudoku validchoices $x $y2]} { set failed 1 break } } if {!$failed} {return $choice} } return 0
}
}
- Test each square in the region occupied by $x,$y to determine if $choice is
- an invalid choice for all other squares in that region. If it is, it must
- only go in square $x,$y.
oo::class create RuleRegionChoice {
superclass Rule
method Solve {hSudoku x y choices} {
foreach choice $choices { set failed 0 set regnX [expr {($x/3)*3}] set regnY [expr {($y/3)*3}] for {set y2 $regnY} {$y2 < $regnY+3} {incr y2} { for {set x2 $regnX} {$x2 < $regnX+3} {incr x2} { if { ($x2!=$x || $y2!=$y) && $choice in [$hSudoku validchoices $x2 $y2] } then { set failed 1 break } } } if {!$failed} {return $choice} } return 0
}
}</lang> Demonstration code: <lang tcl>SudokuSolver create sudoku sudoku load {
{3 9 4 @ @ 2 6 7 @}
{@ @ @ 3 @ @ 4 @ @}
{5 @ @ 6 9 @ @ 2 @}
{@ 4 5 @ @ @ 9 @ @}
{6 @ @ @ @ @ @ @ 7}
{@ @ 7 @ @ @ 5 8 @}
{@ 1 @ @ 6 7 @ @ 8}
{@ @ 9 @ @ 8 @ @ @}
{@ 2 6 4 @ @ 7 3 5}
} sudoku solve
- Simple pretty-printer for completed sudokus
puts +-----+-----+-----+ foreach line [sudoku dump] postline {0 0 1 0 0 1 0 0 1} {
puts |[lrange $line 0 2]|[lrange $line 3 5]|[lrange $line 6 8]|
if {$postline} {
puts +-----+-----+-----+
}
} sudoku destroy</lang> Sample output:
+-----+-----+-----+ |3 9 4|8 5 2|6 7 1| |2 6 8|3 7 1|4 5 9| |5 7 1|6 9 4|8 2 3| +-----+-----+-----+ |1 4 5|7 8 3|9 6 2| |6 8 2|9 4 5|3 1 7| |9 3 7|1 2 6|5 8 4| +-----+-----+-----+ |4 1 3|5 6 7|2 9 8| |7 5 9|2 3 8|1 4 6| |8 2 6|4 1 9|7 3 5| +-----+-----+-----+
If we'd added a logger method (after creating the sudoku object but before running the solver) like this:
<lang tcl>oo::objdefine sudoku method Log msg {puts $msg}</lang>
Then this additional logging output would have been produced prior to the result being printed:
::RuleOnlyChoice solved ::sudoku at 8,0 for 1 ::RuleColumnChoice solved ::sudoku at 1,1 for 6 ::RuleRegionChoice solved ::sudoku at 4,1 for 7 ::RuleRowChoice solved ::sudoku at 7,1 for 5 ::RuleOnlyChoice solved ::sudoku at 8,1 for 9 ::RuleColumnChoice solved ::sudoku at 1,2 for 7 ::RuleColumnChoice solved ::sudoku at 5,2 for 4 ::RuleRowChoice solved ::sudoku at 6,2 for 8 ::RuleOnlyChoice solved ::sudoku at 8,2 for 3 ::RuleColumnChoice solved ::sudoku at 3,3 for 7 ::RuleRowChoice solved ::sudoku at 1,4 for 8 ::RuleRowChoice solved ::sudoku at 5,4 for 5 ::RuleRowChoice solved ::sudoku at 6,4 for 3 ::RuleRowChoice solved ::sudoku at 0,5 for 9 ::RuleOnlyChoice solved ::sudoku at 1,5 for 3 ::RuleOnlyChoice solved ::sudoku at 0,6 for 4 ::RuleOnlyChoice solved ::sudoku at 2,6 for 3 ::RuleColumnChoice solved ::sudoku at 3,6 for 5 ::RuleOnlyChoice solved ::sudoku at 6,6 for 2 ::RuleOnlyChoice solved ::sudoku at 7,6 for 9 ::RuleOnlyChoice solved ::sudoku at 0,7 for 7 ::RuleOnlyChoice solved ::sudoku at 1,7 for 5 ::RuleColumnChoice solved ::sudoku at 4,7 for 3 ::RuleOnlyChoice solved ::sudoku at 6,7 for 1 ::RuleOnlyChoice solved ::sudoku at 0,8 for 8 ::RuleOnlyChoice solved ::sudoku at 4,8 for 1 ::RuleOnlyChoice solved ::sudoku at 5,8 for 9 ::RuleOnlyChoice solved ::sudoku at 3,0 for 8 ::RuleOnlyChoice solved ::sudoku at 4,0 for 5 ::RuleColumnChoice solved ::sudoku at 2,1 for 8 ::RuleOnlyChoice solved ::sudoku at 5,1 for 1 ::RuleOnlyChoice solved ::sudoku at 2,2 for 1 ::RuleRowChoice solved ::sudoku at 0,3 for 1 ::RuleColumnChoice solved ::sudoku at 4,3 for 8 ::RuleColumnChoice solved ::sudoku at 5,3 for 3 ::RuleOnlyChoice solved ::sudoku at 7,3 for 6 ::RuleOnlyChoice solved ::sudoku at 8,3 for 2 ::RuleOnlyChoice solved ::sudoku at 2,4 for 2 ::RuleColumnChoice solved ::sudoku at 3,4 for 9 ::RuleOnlyChoice solved ::sudoku at 4,4 for 4 ::RuleOnlyChoice solved ::sudoku at 7,4 for 1 ::RuleColumnChoice solved ::sudoku at 3,5 for 1 ::RuleOnlyChoice solved ::sudoku at 4,5 for 2 ::RuleOnlyChoice solved ::sudoku at 5,5 for 6 ::RuleOnlyChoice solved ::sudoku at 8,5 for 4 ::RuleOnlyChoice solved ::sudoku at 3,7 for 2 ::RuleOnlyChoice solved ::sudoku at 7,7 for 4 ::RuleOnlyChoice solved ::sudoku at 8,7 for 6 ::RuleOnlyChoice solved ::sudoku at 0,1 for 2 Finished solving!
Ursala
<lang Ursala>
- import std
- import nat
sudoku =
@FL mat0+ block3+ mat` *+ block3*+ block9+ -+
~&rSL+ (psort (nleq+)* <~&blrl,~&blrr>)+ ~&arg^& -+
~&al?\~&ar ~&aa^&~&afahPRPfafatPJPRY+ ~&farlthlriNCSPDPDrlCS2DlrTS2J,
^|J/~& ~&rt!=+ ^= ~&s+ ~&H(
-+.|=&lrr;,|=&lrl;,|=≪+-,
~&rgg&& ~&irtPFXlrjrXPS; ~&lrK2tkZ2g&& ~&llrSL2rDrlPrrPljXSPTSL)+-,
//~&p ^|DlrDSLlrlPXrrPDSL(~&,num*+ rep2 block3)*= num block27 ~&iiK0 iota9,
* `0?=\~&iNC ! ~&t digits+-
</lang> test program: <lang Ursala>
- show+
example =
sudoku
-[ 394002670 000300400 500690020 045000900 600000007 007000580 010067008 009008000 026400735]- </lang> output:
394 852 671 268 371 459 571 694 823 145 783 962 682 945 317 937 126 584 413 567 298 759 238 146 826 419 735