使用Backtracking算法，解决Sudoku问题。
Introduction
The objective of Sudoku is to ll a 9x9 grid with the numbers 1-9 so that each column, row, and 3x3 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 A1…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.
What To Submit
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 sudokus_start.txt ,
- running time, and
- any other relevant information.
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 sudokus_start.txt .
- Report the puzzles you can solve now, running time, observations.
Important Information
- Test-Run Your Code
Test, test, test. Make sure you produce an output file with the exact format of the example given. - Grading Submissions
We test your final program on 20 boards . Each board is worth 5 points if solved, and zero otherwise. These boards are similar to those in your starter zip, so if you solve all those, you’ll get full credit. - 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. - Just for fun
Try your code on the world’s hardest Sudokus! There’s nothing to submit here, just for fun.
For example:
Sudoku:
800000000003600000070090200050007000000045700000100030001000068008500010090000400
Solution:
81275364994368217567549128315423789636984572128716953452197436843852691779631845