The objective of Sudoku is to ll a 99 grid with the numbers 1-9 so that each column, row, and 33 sub-grid (or box) contains one of each digit. You may try out the game here: sudoku.com. Sudoku has 81 variables, i.e. 81 tiles. The variables are named by row and column, and are valued from 1 to 9 subject to the constraints that no two cells in the same row, column, or box may be the same.

Frame your problem in terms of variables, domains, and constraints. We suggest representing a Sudoku board with a Python dictionary, where each key is a variable name based on location, and value of the tile placed there. Using variable names Al A9 I1 I9, the board above has: sudoku_dict[B1] = 9, and sudoku_dict[E9] = 8.

We give value zero to a tile that has not yet been filled.

Your program will be executed as follows:

$ python driver_3.py <input_string>

In the starter zip, sudokus_start.txt, contains hundreds of sample unsolved Sudoku boards, and sudokus_finish.txt the corresponding solutions. Each board is represented as a single line of text, starting from the top-left corner of the board, and listed left-to-right, top-to-bottom.

The first board in sudokus_start.txt is represented as the string:

003020600900305001001806400008102900700000008006708200002609500800203009005010300

Which is equivalent to:

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

Your program will generate output.txt, containing a single line of text representing the finished Sudoku board. E.g.:

483921657967345821251876493548132976729564138136798245372689514814253769695417382

Test your program using sudokus_finish.txt, which contains the solved versions of all of the same puzzles.

Besides your driver (and any other python code dependency), submit a README.txt with your results and observations, including the:

• number AND line numbers of boards you could solve from txt ,
• running time, and
• any other relevant information.

III. Backtracking Algorithm

Implement backtracking search using the minimum remaining value heuristic. Pick your own order of values to try for each variable, and apply forward checking to reduce variables domains.

• Test your program on txt.
• Report the puzzles you can solve now, running time, observations.

IV. Important Information

1. Test-Run Your Code

Test, test, test. Make sure you produce an output file with the exact format of the example given.

3. Time Limit

No brute-force! Your program should solve puzzles in well under a minute per board. Programs with much longer running times will be killed.

4. Just for fun

Try your code on the worlds hardest Sudokus! Theres nothing to submit here, just for fun. For example:

Sudoku:

800000000003600000070090200050007000000045700000100030001000068008500010090000400

Solution:

812753649943682175675491283154237896369845721287169534521974368438526917796318452