Implement a Non-Guessing Sudoku Solver

Question

Implement the shortest Sudoku solver.

Sudoku Puzzle:

 | 1 2 3 | 4 5 6 | 7 8 9
-+-----------------------
A|   3   |     1 |
B|     6 |       |   5
C| 5     |       | 9 8 3
-+-----------------------
D|   8   |     6 | 3   2
E|       |   5   |
F| 9   3 | 8     |   6
-+-----------------------
G| 7 1 4 |       |     9
H|   2   |       | 8
I|       | 4     |   3

Answer:

 | 1 2 3 | 4 5 6 | 7 8 9
-+-----------------------
A| 8 3 2 | 5 9 1 | 6 7 4
B| 4 9 6 | 3 8 7 | 2 5 1
C| 5 7 1 | 2 6 4 | 9 8 3
-+-----------------------
D| 1 8 5 | 7 4 6 | 3 9 2
E| 2 6 7 | 9 5 3 | 4 1 8
F| 9 4 3 | 8 1 2 | 7 6 5
-+-----------------------
G| 7 1 4 | 6 3 8 | 5 2 9
H| 3 2 9 | 1 7 5 | 8 4 6
I| 6 5 8 | 4 2 9 | 1 3 7

Rules:

1. Assume all mazes are solvable by logic only.
2. All input will be 81 characters long. Missing characters will be 0.
3. Output the solution as a single string.
4. The "grid" may be stored internally however you wish.
5. The solution must use a non-guessing solution. (see Sudoku Solver)

Example I/O:

>sudoku.py "030001000006000050500000983080006302000050000903800060714000009020000800000400030"
832591674496387251571264983185746392267953418943812765714638529329175846658429137

Answer 1

RUBY (449 436 chars)

I=*(0..8)
b=$*[0].split('').map{|v|v<'1'?I.map{|d|d+1}:[v.to_i]};f=b.map{|c|!c[1]}
[[z=I.map{|v|v%3+v/3*9},z.map{|v|v*3}],[x=I.map{|v|v*9},I],[I,x]
].map{|s,t|t.map{|i|d=[a=0]*10;s.map{|j|c=b[i+j];c.map{|v|d[v]+=1if !f[i+j]}
v,r=*c;s.map{|k|b[i+k].delete(v)if j!=k}if !r 
s[(a+=1)..8].map{|k|s.map{|l|b[i+l]-=c if l!=k&&l!=j}if c.size==2&&c==b[i+k]}}
v=d.index 1;f[i+k=s.find{|j|b[i+j].index v}]=b[i+k]=[v]if v}}while f.index(!1)
p b*''

Example:

C:\golf>soduku2.rb 030001000006000050500000983080006302000050000903800060714000009020000800000400030
"832591674496387251571264983185746392267953418943812765714638529329175846658429137"

quick explanation:
Board b is an array of 81 arrays holding all the possible values for each cell. The array on line three holds [offset,start_index] for each group (boxes,rows,columns). Three tasks are performed while iterating through the groups.

1. The value of any cell of size 1 is removed from the rest of the group.
2. If any pair of cells contain the same 2 values, these values are removed from the rest of the group.
3. The count of each value is stored in d - if there is only 1 instance of a value, we set the containing cell to that value, and mark the cell fixed in f

Repeat until all cells are fixed.

Answer 2

Prolog - 493 Characters

:-use_module(library(clpfd)).
a(X):-all_distinct(X).
b([],[],[]).
b([A,B,C|X],[D,E,F|Y],[G,H,I|Z]):-a([A,B,C,D,E,F,G,H,I]),b(X,Y,Z).
c([A,B,C,D,E,F,G,H,I|X])-->[[A,B,C,D,E,F,G,H,I]],c(X).
c([])-->[].
l(X,Y):-length(X,Y).
m(X,Y):-maplist(X,Y).
n(L,M):-l(M,L).
o(48,_).
o(I,O):-O is I-48.
:-l(L,81),see(user),m(get,L),seen,maplist(o,L,M),phrase(c(M),R),l(R,9),m(n(9),R),append(R,V),V ins 1..9,m(a,R),transpose(R,X),m(a,X),R=[A,B,C,D,E,F,G,H,I],b(A,B,C),b(D,E,F),b(G,H,I),flatten(R,O),m(write,O).

Output:

Inputting: 000000000000003085001020000000507000004000100090000000500000073002010000000040009 Outputs: 987654321246173985351928746128537694634892157795461832519286473472319568863745219

Inputting: 030001000006000050500000983080006302000050000903800060714000009020000800000400030 Outputs: 832591674496387251571264983185746392267953418943812765714638529329175846658429137