In this assignment, you will be implementing a backtracking algorithm to solve Sudoku puzzles. If you arent familiar (or even if you are and need a refresher), have a look at this site.

Starting point

Download and extract these materials. Contained are:

Sudoku.java , the file you will modify.

5 _.su files, which are plain text files containing Sudoku puzzles to solve.

Since theyre plain text files (like java files), you can open them in your text/code editor.

Sudoku.java contains the following:

a _main method which can accept some command-line arguments. the readBoard method, which reads a board from a file. main calls this.

Unsolved (empty) cells contain 0s.

the printBoard method, which prints the board to the console, which will be very helpful. the solve backtracking template method.

and finally, 8 skeleton methods for you to fill out.

you know, cause Halloween. _💀

Testing

We will be testing your code on the command line. You are welcome to use an IDE, but before submitting, please test that your Java files can be compiled and run on the command line without it.

We should be able to run your program like so:

to run all the test methods, or:

to load and solve a Sudoku board file.

The _main we gave you handles this command-line interface. But right now, nothing happens 🙂

Your task

This is a tough project. As such, 60% of the grade is for correctness, and 40% is for the thoroughness of your testing methods.

You will implement four methods to solve the problem: isFullSolution , reject , extend , and next .

To complement those four, there are four testing methods:

testIsFullSolution , testReject , testExtend , and testNext . Each of these should make several tests of the corresponding solving methods.

The puzzle-solving algorithm

By implementing the four solving methods, you will be constructing a backtracking solver program. Important points:

You must not change any of the original numbers already on the board. You must implement all the Sudoku rules: each row, column, and 33 square may only contain each number once.

You only need to find one solution, not all solutions. Once you find a solution, you can stop.

If a board is not solvable, your program must say so.

The puzzle-solving methods

These methods make up the four parts of the backtracking template. These methods are not recursive! Only the _solve method is, and we already wrote that for you 😉

boolean isFullSolution(int[][] board)

This takes a board as a 2D array, and returns _true if it is complete (no empty cells) and satisfies all the rules.

If there are any empty cells, or if there are any rule violations, it returns false.

boolean reject(int[][] board)

This takes a partial solution, and returns _true if it is impossible to continue with this board.

For example, if there are two 3s on one row, there is no reason to keep solving this board. int[][] extend(int[][] board)

This takes a partial solution, and constructs a new partial solution. When I say new I mean use _new to allocate a new 2D array!

What I mean by constructs a new partial solution is it places a number into a previously-empty cell.

If there are no more possible cells to place a number in, it should return null.

int[][] next(int[][] board)

The partner to extend . This takes a partial solution, and constructs another new partial solution.

It will change the most-recently-placed number to the next possible option.

So if the most-recently-placed number was a 1, this would change it to a 2

or a 2 to a 3, or a 3 to a 4, and so on.

If there are no options for the most-recently-placed number, it should return null.

Do not write all the methods at once. Start with isFullSolution and reject . Test them extensively with your testing methods (by running your program with java Sudoku -t ).

The testing methods

Re-read starting at Chapter 2.16 to review the concepts behind writing test methods. Write your testing methods at the same time you write the solving methods. Have a look at this 8-Queens example to see some example testing methods.

For each of the testing methods, try to follow these guidelines:

Come up with a variety of partial solutions that will test all possible paths through your solving method.

Call the method with those partial solutions.

Check that the method actually returns what you expect it to return. Print out the test cases and results, so that you can easily see if things are looking right.

Include enough test cases that you are convinced that your solving method is working properly.

You can make new board files following the guidelines below, and then use readBoard to load them for testing.

For example, if I were testing the reject method, I would give it

a board with two of the same number in the same row. a board with two of the same number in the same column.

a board with two of the same number in a 33 square.

(probably a few versions of that, to be thorough.) the boards we gave you ( 1-trivial.su etc.) to make sure it doesnt reject those. a solved board (look online for one) to make sure it doesnt reject that.

Example boards

Weve included 5 example boards (the _.su files). If you open them in your text editor, you will see they look something like this:

There are 9 rows, and each has 9 columns. Any non-number character is treated as an empty (unsolved) cell.

You can open one of the existing files and File > Save As to make your own boards. Make a bunch! Its fine!

Sudoku.java

Any extra boards besides the ones we gave you

And if anything is wrong/not working, a plain text (.txt) file with notes to the grader about what is not working.

Submit to the Box folder at this link. Drag your zip file into your browser to upload. If you can see your file, you uploaded it correctly!

You can also re-upload if you made a mistake and need to fix it.

2016-2018 Jarrett Billingsley