Sudoku: Difference between revisions
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=={{header|Forth}}== |
=={{header|Forth}}== |
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{{works with|4tH|3.60.0}} |
{{works with|4tH|3.60.0}} |
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<lang forth> |
<lang forth>include lib/interprt.4th |
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\ No special extensions were used. |
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\ Tested on in win32forth, VFX and Swift (evaluation). |
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\ No locals were harmed during this experiment. |
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\ Version: 1900 01092005 - Robert Spykerman |
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\ Modifier: David N. Williams |
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\ Email: robspyke_nospam@iprimus_no_spam.com.au |
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\ (delete the obvious) |
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\ 4tH version: 2005,2008 J.L. Bezemer |
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include lib/interprt.4th |
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include lib/istype.4th |
include lib/istype.4th |
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include lib/argopen.4th |
include lib/argopen.4th |
Revision as of 23:59, 27 February 2010
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, Force SetBatchLines, -1 SetTitleMatchMode, 3
Loop 9 { r := A_Index, y := r*17-8 + (A_Index >= 7 ? 4 : A_Index >= 4 ? 2 : 0) Loop 9 { c := A_Index, x := c*17+5 + (A_Index >= 7 ? 4 : A_Index >= 4 ? 2 : 0) Gui, Add, Edit, x%x% y%y% w17 h17 v%r%_%c% Center Number Limit1 gNext } } Gui, Add, Button, vButton gSolve w175 x10 Center, Solve Gui, Add, Text, vMsg r3, 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) iterations := ErrorLevel 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% } } if answer GuiControl,, Msg, Solved!`nTime: %seconds%s`nIterations: %iterations% else GuiControl,, Msg, Failed! :(`nTime: %seconds%s`nIterations: %iterations% GuiControl,, Button, Again! GuiControl, +gAgain, Button
return
GuiClose:
ExitApp
Again:
Reload
- IfWinActive, Sudoku Solver
~*Enter::GoSub % GetKeyState( "Shift", "P" ) ? "~Up" : "~Down" ~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 f := Mod(f + 79, 81) + 1 GuiControl, Focus, Edit%f%
return Next: ~Right::
GuiControlGet, f, focus StringTrimLeft, f, f, 4 f := Mod(f, 81) + 1 GuiControl, Focus, Edit%f%
return
- IfWinActive
- Functions Start here
Sudoku( p ) { ;ErrorLevel contains the number of iterations
p := RegExReplace(p, "[^1-9@]"), ErrorLevel := 0 ;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), ErrorLevel++ 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>
Forth
<lang forth>include lib/interprt.4th include lib/istype.4th include lib/argopen.4th
\ --------------------- \ Variables \ ---------------------
81 string sudokugrid 9 array sudoku_row 9 array sudoku_col 9 array sudoku_box
\ ------------- \ 4tH interface \ -------------
- >grid ( n2 a1 n1 -- n3)
rot dup >r 9 chars * sudokugrid + dup >r swap 0 do ( a1 a2) over i chars + c@ dup is-digit ( a1 a2 c f) if [char] 0 - over c! char+ else drop then loop ( a1 a2) nip r> - 9 / r> + ( n3)
0 s" 090004007" >grid s" 000007900" >grid s" 800000000" >grid s" 405800000" >grid s" 300000002" >grid s" 000009706" >grid s" 000000004" >grid s" 003500000" >grid s" 200600080" >grid drop
\ --------------------- \ Logic \ --------------------- \ Basically : \ Grid is parsed. All numbers are put into sets, which are \ implemented as bitmaps (sudoku_row, sudoku_col, sudoku_box) \ which represent sets of numbers in each row, column, box. \ only one specific instance of a number can exist in a \ particular set.
\ SOLVER is recursively called \ SOLVER looks for the next best guess using FINDNEXTSPACE \ tries this trail down... if fails, backtracks... and tries \ again.
\ Grid Related
- xy 9 * + ; \ x y -- offset ;
- getrow 9 / ;
- getcol 9 mod ;
- getbox dup getrow 3 / 3 * swap getcol 3 / + ;
\ Puts and gets numbers from/to grid only
- setnumber sudokugrid + c! ; \ n position --
- getnumber sudokugrid + c@ ;
- cleargrid sudokugrid 81 bounds do 0 i c! loop ;
\ -------------- \ Set related: sets are sudoku_row, sudoku_col, sudoku_box
\ ie x y -- ; adds x into bitmap y
- addbits_row cells sudoku_row + dup @ rot 1 swap lshift or swap ! ;
- addbits_col cells sudoku_col + dup @ rot 1 swap lshift or swap ! ;
- addbits_box cells sudoku_box + dup @ rot 1 swap lshift or swap ! ;
\ ie x y -- ; remove number x from bitmap y
- removebits_row cells sudoku_row + dup @ rot 1 swap lshift invert and swap ! ;
- removebits_col cells sudoku_col + dup @ rot 1 swap lshift invert and swap ! ;
- removebits_box cells sudoku_box + dup @ rot 1 swap lshift invert and swap ! ;
\ clears all bitsmaps to 0
- clearbitmaps 9 0 do i cells
0 over sudoku_row + ! 0 over sudoku_col + ! 0 swap sudoku_box + ! loop ;
\ Adds number to grid and sets
- addnumber \ number position --
2dup setnumber 2dup getrow addbits_row 2dup getcol addbits_col getbox addbits_box
\ Remove number from grid, and sets
- removenumber \ position --
dup getnumber swap 2dup getrow removebits_row 2dup getcol removebits_col 2dup getbox removebits_box nip 0 swap setnumber
\ gets bitmap at position, ie \ position -- bitmap
- getrow_bits getrow cells sudoku_row + @ ;
- getcol_bits getcol cells sudoku_col + @ ;
- getbox_bits getbox cells sudoku_box + @ ;
\ position -- composite bitmap (or'ed)
- getbits
dup getrow_bits over getcol_bits rot getbox_bits or or
\ algorithm from c.l.f circa 1995 ? Will Baden
- countbits ( number -- bits )
[HEX] DUP 55555555 AND SWAP 1 RSHIFT 55555555 AND + DUP 33333333 AND SWAP 2 RSHIFT 33333333 AND + DUP 0F0F0F0F AND SWAP 4 RSHIFT 0F0F0F0F AND + [DECIMAL] 255 MOD
\ Try tests a number in a said position of grid \ Returns true if it's possible, else false.
- try \ number position -- true/false
getbits 1 rot lshift and 0=
\ --------------
- parsegrid \ Parses Grid to fill sets.. Run before solver.
sudokugrid \ to ensure all numbers are parsed into sets/bitmaps 81 0 do dup i + c@ dup if dup i try if i addnumber else unloop drop drop FALSE exit then else drop then loop drop TRUE
\ Morespaces? manually checks for spaces ... \ Obviously this can be optimised to a count var, done initially \ Any additions/subtractions made to the grid could decrement \ a 'spaces' variable.
- morespaces?
0 sudokugrid 81 bounds do i c@ 0= if 1+ then loop ;
- findnextmove \ -- n ; n = index next item, if -1 finished.
-1 10 \ index prev_possibilities -- \ err... yeah... local variables, kind of...
81 0 do i sudokugrid + c@ 0= IF i getbits countbits 9 swap -
\ get bitmap and see how many possibilities \ stack diagram: \ index prev_possibilities new_possiblities --
2dup > if \ if new_possibilities < prev_possibilities... nip nip i swap \ new_index new_possibilies --
else \ else prev_possibilities < new possibilities, so:
drop \ new_index new_possibilies --
then THEN loop drop
\ findnextmove returns index of best next guess OR returns -1 \ if no more guesses. You then have to check to see if there are \ spaces left on the board unoccupied. If this is the case, you \ need to back up the recursion and try again.
- solver
findnextmove dup 0< if morespaces? if drop false exit else drop true exit then then
10 1 do i over try if i over addnumber recurse if drop unloop TRUE EXIT else dup removenumber then then loop
drop FALSE
\ SOLVER
- startsolving
clearbitmaps \ reparse bitmaps and reparse grid parsegrid \ just in case.. solver AND
\ --------------------- \ Display Grid \ ---------------------
\ Prints grid nicely
- .sudokugrid
CR CR sudokugrid 81 0 do dup i + c@ . i 1+ dup 3 mod 0= if dup 9 mod 0= if CR dup 27 mod 0= if dup 81 < if ." ------+-------+------" CR then then else ." | " then then drop loop drop CR
\ --------------------- \ Higher Level Words \ ---------------------
- checkifoccupied ( offset -- t/f)
sudokugrid + c@
- add ( n x y --)
xy 2dup dup checkifoccupied if dup removenumber then try if addnumber .sudokugrid else CR ." Not a valid move. " CR 2drop then
- rm
xy removenumber .sudokugrid
- clearit
cleargrid clearbitmaps .sudokugrid
- solveit
CR startsolving if ." Solution found!" CR .sudokugrid else ." No solution found!" CR CR then
- showit .sudokugrid ;
\ Print help menu
- help
CR ." Type clearit ; to clear grid " CR ." 1-9 x y add ; to add 1-9 to grid at x y (0 based) " CR ." x y rm ; to remove number at x y " CR ." showit ; redisplay grid " CR ." solveit ; to solve " CR ." help ; for help " CR CR
\ --------------------- \ Execution starts here \ ---------------------
- godoit
clearbitmaps parsegrid if CR ." Grid valid!" else CR ." Warning: grid invalid!" then .sudokugrid help
\ ------------- \ 4tH interface \ -------------
- read-sudoku
input 1 arg-open 0 begin dup 9 < while refill while 0 parse >grid repeat drop close
- bye quit ;
create wordlist \ dictionary
," clearit" ' clearit , ," add" ' add , ," rm" ' rm , ," showit" ' showit , ," solveit" ' solveit , ," quit" ' bye , ," exit" ' bye , ," bye" ' bye , ," q" ' bye , ," help" ' help , NULL ,
wordlist to dictionary
- noname ." Unknown command '" type ." '" cr ; is NotFound
\ sudoku interpreter
- sudoku
argn 1 > if read-sudoku then godoit begin ." OK" cr refill drop ['] interpret catch if ." Error" cr then again
sudoku</lang>
Fortran
This implementation uses a brute force method. The subroutine solve
recursively checks valid entries using the rules defined in the function is_safe
. When solve
is called beyond the end of the sudoku, we know that all the currently entered values are valid. Then the result is displayed.
<lang fortran>program sudoku
implicit none integer, dimension (9, 9) :: grid integer, dimension (9, 9) :: grid_solved grid = reshape ((/ & & 0, 0, 3, 0, 2, 0, 6, 0, 0, & & 9, 0, 0, 3, 0, 5, 0, 0, 1, & & 0, 0, 1, 8, 0, 6, 4, 0, 0, & & 0, 0, 8, 1, 0, 2, 9, 0, 0, & & 7, 0, 0, 0, 0, 0, 0, 0, 8, & & 0, 0, 6, 7, 0, 8, 2, 0, 0, & & 0, 0, 2, 6, 0, 9, 5, 0, 0, & & 8, 0, 0, 2, 0, 3, 0, 0, 9, & & 0, 0, 5, 0, 1, 0, 3, 0, 0/), & & shape = (/9, 9/), & & order = (/2, 1/)) call pretty_print (grid) call solve (1, 1) write (*, *) call pretty_print (grid_solved)
contains
recursive subroutine solve (i, j) implicit none integer, intent (in) :: i integer, intent (in) :: j integer :: n integer :: n_tmp if (i > 9) then grid_solved = grid else do n = 1, 9 if (is_safe (i, j, n)) then n_tmp = grid (i, j) grid (i, j) = n if (j == 9) then call solve (i + 1, 1) else call solve (i, j + 1) end if grid (i, j) = n_tmp end if end do end if end subroutine solve
function is_safe (i, j, n) result (res) implicit none integer, intent (in) :: i integer, intent (in) :: j integer, intent (in) :: n logical :: res integer :: i_min integer :: j_min if (grid (i, j) == n) then res = .true. return end if if (grid (i, j) /= 0) then res = .false. return end if if (any (grid (i, :) == n)) then res = .false. return end if if (any (grid (:, j) == n)) then res = .false. return end if i_min = 1 + 3 * ((i - 1) / 3) j_min = 1 + 3 * ((j - 1) / 3) if (any (grid (i_min : i_min + 2, j_min : j_min + 2) == n)) then res = .false. return end if res = .true. end function is_safe
subroutine pretty_print (grid) implicit none integer, dimension (9, 9), intent (in) :: grid integer :: i integer :: j character (*), parameter :: bar = '+-----+-----+-----+' character (*), parameter :: fmt = '(3 ("|", i0, 1x, i0, 1x, i0), "|")' write (*, '(a)') bar do j = 0, 6, 3 do i = j + 1, j + 3 write (*, fmt) grid (i, :) end do write (*, '(a)') bar end do end subroutine pretty_print
end program sudoku</lang> Output:
+-----+-----+-----+ |0 0 3|0 2 0|6 0 0| |9 0 0|3 0 5|0 0 1| |0 0 1|8 0 6|4 0 0| +-----+-----+-----+ |0 0 8|1 0 2|9 0 0| |7 0 0|0 0 0|0 0 8| |0 0 6|7 0 8|2 0 0| +-----+-----+-----+ |0 0 2|6 0 9|5 0 0| |8 0 0|2 0 3|0 0 9| |0 0 5|0 1 0|3 0 0| +-----+-----+-----+ +-----+-----+-----+ |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| +-----+-----+-----+
Haskell
Visit the Haskell wiki Sudoku
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>
Oz
Using built-in constraint propagation and search.
<lang oz>declare
%% a puzzle is a function that returns an initial board configuration fun {Puzzle1} %% a board is a list of 9 rows [[4 _ _ _ _ _ _ 6 _] [5 _ _ _ 8 _ 9 _ _] [3 _ _ _ _ 1 _ _ _] [_ 2 _ 7 _ _ _ _ 1] [_ 9 _ _ _ _ _ 4 _] [8 _ _ _ _ 3 _ 5 _] [_ _ _ 2 _ _ _ _ 7] [_ _ 6 _ 5 _ _ _ 8] [_ 1 _ _ _ _ _ _ 6]] end
%% Returns a list of solutions for the given puzzle. fun {Solve Puzzle} {SearchAll {GetScript Puzzle}} end
%% Creates a solver script for a puzzle. fun {GetScript Puzzle} proc {$ Board} %% Every row is a list of nine finite domain vars %% with the domain 1..9. Board = {MapRange fun {$ _} {FD.list 9 1#9} end} %% Post initial configuration. Board = {Puzzle} %% The core constraints: {ForAll {Rows Board} FD.distinct} {ForAll {Columns Board} FD.distinct} {ForAll {Boxes Board} FD.distinct}
%% Search if necessary. {FD.distribute ff {Flatten Board}} end end %% Returns the board as a list of rows. fun {Rows Board} Board %% This is already the representation we have chosen. end %% Returns the board as a list of columns. fun {Columns Board} {MapRange fun {$ I} {Column Board I} end} end %% Returns the board as a list of boxes (sub-grids). fun {Boxes Board} {MapRange fun {$ I} {Box Board I} end} end %% Helper function: map the range 1..9 to something. fun {MapRange F} {Map [1 2 3 4 5 6 7 8 9] F} end %% Returns a column of the board as a list of fields. fun {Column Board Index} {Map Board fun {$ Row} {Nth Row Index} end } end %% Returns a box of the board as a list of fields. fun {Box Board Index} Index0 = Index-1 Fields = {Flatten Board} Start = (Index0 div 3) * 27 + (Index0 mod 3)*3 in {Flatten for I in 0..2 collect:C do {C {List.take {List.drop Fields Start+I*9} 3}} end } end
in
{Inspect {Solve Puzzle1}.1}</lang>
PicoLisp
<lang PicoLisp>(load "lib/simul.l")
- Fields/Board ###
- val lst
(setq
*Board (grid 9 9) *Fields (apply append *Board) )
- Init values to zero (empty)
(for L *Board
(for This L (=: val 0) ) )
- Build lookup lists
(for (X . L) *Board
(for (Y . This) L (=: lst (make (let A (* 3 (/ (dec X) 3)) (do 3 (inc 'A) (let B (* 3 (/ (dec Y) 3)) (do 3 (inc 'B) (unless (and (= A X) (= B Y)) (link (prop (get *Board A B) 'val) ) ) ) ) ) ) (for Dir '(`west `east `south `north) (for (This (Dir This) This (Dir This)) (unless (memq (:: val) (made)) (link (:: val)) ) ) ) ) ) ) )
- Cut connections (for display only)
(for (X . L) *Board
(for (Y . This) L (when (member X (3 6)) (con (car (val This))) ) (when (member Y (4 7)) (set (cdr (val This))) ) ) )
- Display board
(de display ()
(disp *Board 0 '((This) (if (=0 (: val)) " " (pack " " (: val) " ") ) ) ) )
- Initialize board
(de main (Lst)
(for (Y . L) Lst (for (X . N) L (put *Board X (- 10 Y) 'val N) ) ) (display) )
- Find solution
(de go ()
(unless (recur (*Fields) (with (car *Fields) (if (=0 (: val)) (loop (NIL (or (assoc (inc (:: val)) (: lst)) (recurse (cdr *Fields)) ) ) (T (= 9 (: val)) (=: val 0)) ) (recurse (cdr *Fields)) ) ) ) (display) ) )
(main
(quote (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) ) )</lang>
Output:
+---+---+---+---+---+---+---+---+---+ 9 | 5 3 | 7 | | + + + + + + + + + + 8 | 6 | 1 9 5 | | + + + + + + + + + + 7 | 9 8 | | 6 | +---+---+---+---+---+---+---+---+---+ 6 | 8 | 6 | 3 | + + + + + + + + + + 5 | 4 | 8 3 | 1 | + + + + + + + + + + 4 | 7 | 2 | 6 | +---+---+---+---+---+---+---+---+---+ 3 | 6 | | 2 8 | + + + + + + + + + + 2 | | 4 1 9 | 5 | + + + + + + + + + + 1 | | 8 | 7 9 | +---+---+---+---+---+---+---+---+---+ a b c d e f g h i
<lang>(go)</lang> Output:
+---+---+---+---+---+---+---+---+---+ 9 | 5 3 4 | 6 7 8 | 9 1 2 | + + + + + + + + + + 8 | 6 7 2 | 1 9 5 | 3 4 8 | + + + + + + + + + + 7 | 1 9 8 | 3 4 2 | 5 6 7 | +---+---+---+---+---+---+---+---+---+ 6 | 8 5 9 | 7 6 1 | 4 2 3 | + + + + + + + + + + 5 | 4 2 6 | 8 5 3 | 7 9 1 | + + + + + + + + + + 4 | 7 1 3 | 9 2 4 | 8 5 6 | +---+---+---+---+---+---+---+---+---+ 3 | 9 6 1 | 5 3 7 | 2 8 4 | + + + + + + + + + + 2 | 2 8 7 | 4 1 9 | 6 3 5 | + + + + + + + + + + 1 | 3 4 5 | 2 8 6 | 1 7 9 | +---+---+---+---+---+---+---+---+---+ a b c d e f g h i
Python
See Solving Sudoku puzzles with Python for GPL'd solvers of increasing complexity of algorithm.
Ruby
Example of a back-tracking solver, from wp:Algorithmics of sudoku
<lang ruby>def read_matrix(fh)
matrix = [] (0..8).each { |i| l = fh.readline matrix[i] = [] (0..8).each { |j| matrix[i][j] = l[j..j].to_i } } matrix
end
def permissible(matrix, i, j)
ok = [true] * 9 # Same as another in the column isn't permissible... (0..8).each { |i2| next if matrix[i2][j] == 0 ok[matrix[i2][j] - 1] = false } # Same as another in the row isn't permissible... (0..8).each { |j2| next if matrix[i][j2] == 0 ok[matrix[i][j2] - 1] = false } # Same as another in the 3x3 block isn't permissible... igroup = (i / 3) * 3 jgroup = (j / 3) * 3 (igroup..(igroup + 2)).each { |i2| (jgroup..(jgroup + 2)).each { |j2| next if matrix[i2][j2] == 0 ok[matrix[i2][j2] - 1] = false } } # Convert to the array format... (1..9).select { |i2| ok[i2-1] }
end
def deep_copy_sudoku(matrix)
matrix.collect { |row| row.dup }
end
def solve_sudoku(matrix)
loop do options = [] (0..8).each { |i| (0..8).each { |j| next if matrix[i][j] != 0 p = permissible(matrix, i, j) # If nothing is permissible, there is no solution at this level. return nil if p.length == 0 options.push({:i => i, :j => j, :permissible => p}) } } # If the matrix is complete, we have a solution... return matrix if options.length == 0 omin = options.min_by { |x| x[:permissible].length } # If there is an option with only one solution, set it and re-check permissibility if omin[:permissible].length == 1 matrix[omin[:i]][omin[:j]] = omin[:permissible][0] next end # We have two or more choices. We need to search both... omin[:permissible].each { |v| mtmp = deep_copy_sudoku(matrix) mtmp[omin[:i]][omin[:j]] = v ret = solve_sudoku(mtmp) return ret if ret } # We did an exhaustive search on this branch and nothing worked out. return nil end
end
def print_matrix(matrix)
if not matrix puts "Impossible" return end border = "+-----+-----+-----+" (0..8).each { |i| puts border if i%3 == 0 (0..8).each { |j| print(j%3 == 0 ? "|" : " ") print(matrix[i][j] == 0 ? "." : matrix[i][j]) } print "|\n" } puts border
end
matrix = read_matrix(DATA) print_matrix(matrix) puts print_matrix(solve_sudoku(matrix))
__END__ 394__267_ ___3__4__ 5__69__2_ _45___9__ 6_______7 __7___58_ _1__67__8 __9__8___ _264__735</lang>
output
+-----+-----+-----+ |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| +-----+-----+-----+ +-----+-----+-----+ |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| +-----+-----+-----+
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