# Homework5: Sudoku solution

INTRODUCTION: Sudoku is just a puzzle, but the backtracking
technique for solving it is used in many important application domains.
To solve a Suduku without backtracking, you could generate every
possible solution, then evaluate all of them and collect the legal ones.
But there are 9^81 ways to fill in a Sudoku grid. 9^81 is ~= 2*10^77. If
you could evaluate a billion grids per second, it would take 2*10^68
seconds. The universe is less than 10^18 seconds old. For this
homework, you will learn the power of backtracking by writing a
Sudoku solver that finds answers in just a few seconds.
The puzzle on page 1, and all puzzles that appear in the code, are
SUDOKU Rules: A puzzle looks like the one on the previous page: a 9x9
grid with some numbers filled in. The challenge is to fill in each empty
space with a digit 1 through 9, so that no digit is repeated in any row,
column or “block”. “Block” is my name for the nine 3x3 blocks outlined
in thicker black lines in the picture.
new Java project containing package “sudoku”. Import the 4 starter files
Solver.java, and TestGridSupplier.java. You won't need to change
Evaluation.java or TestGridSupplier.java. Your assignment is to finish
Grid.java and Solver.java.
Grid: This class models a Sudoku puzzle that is unsolved, partially
solved, or completely solved. The class has a 9x9 array of ints, called
“values”. If a Sudoku square is empty, the corresponding cell in “values”
is zero; otherwise the cell in “values” contains the number in the Sudoku
square. The starter class has a ctor and a toString() method that you
should not change. It also has 4 empty methods that you need to write:
next9Grids(), isLegal(), isFull(), and equals(). Do not change their
names, arg lists, or return types. The comments on the unfinished
methods tell you all you need to know about what they should do. It’s ok
to add more methods to this class.
You don’t need to provide this class with hashCode() or compareTo()
methods. The equals() method is just so that you can compare your
puzzle solutions to solutions in TestGridSupplier. (That is, you won’t be
collecting Grid instances into a hash set a tree set.)
Solver: Most of this class has already been written. Complete the
solveRecurse() method using the backtracking technique you saw in
lecture and lab. Also complete the evaluate() method. The main()
method is for you to use while testing your code with the puzzles and
solutions in TestGridSupplier.
Evaluation: You saw this enum in lecture and lab. It contains 3 values
that represent the 3 possible outcomes of the evaluate() method of the
Grid class. Look at the source code. Sometimes enums can be
complicated, but this one is not. You might need to write a very simple
enum for the next midterm.
TestGridSupplier: This class contains static methods that return Grid
instances. Some of them are puzzles, some are solutions, and some are
for testing your code. Extra credit: are they useful? Comment on Piazza
for participation points.