Shirokuro Solver
CS491 Project
Alexandre Lomovtsev
Supervised by Professor Russell Abbott
2009
Goals of this project
•
Develop a strategy for solving Shirokuro puzzles.
•
Create the solver-program by means of the
Constraint Programming (CP).
What is “Shirokuro”?
“Shirokuro is a single-played game ” (in Japanese means
"white-and-black“). The goal of the game is to fill in every
empty grid space with either a white circle or a black
circle in such a way that:
(1) no two-by-two regions of the grid contains four circles of
the same color;
(2) every white circle is connected to every other white circle
through a chain of only white circles that runs horizontally
and/or vertically;
(3) every black circle is connected to every other black circle
through a chain of only black circles that runs horizontally
and/or vertically.
Shirokuro example
Constraint Programming
What is CP?
“Constraint programming represents one of the closest
approaches computer science has yet made to the Holy
Grail of programming: the user states the problem, the
computer solves it.”
Eugene C. Freuder, Constraints, April 1997
How does it work?
Step1 – stating constraints about the problem variables
Step2 – finding solution satisfying all the constraints
Tools
►
Programming Language
 Java 6 Standard Edition
►
Development Tool
 Eclipse (Version: 3.4.0)
►
Additional Resources
 Choco - constraint programming system
Why use Choco?
Choco is an open source Java library developed for the
constraint programming.
Choco was successfully used in solving a well known
puzzles as Sudoku, Magic square, Queens problem, and
many other.
Choco can be used as a black box that accepts a
problem and returns a solution.
Choco is extensible.
Choco: creating Model
Model = Variables + Constraints
Variables in Choco can have different types:
• integer,
• real,
• set.
Variable properties:
• name,
• domain,
• options.
Constraints – specify conditions to be held on variables
to the model.
Shirokuro’s Model (1)
Variables
• Model contains N*N variables, where N is the field size;
• Variables’ domains:
{0,1} for empty cells,
{0,0} and {1,1} for cells containing white and black
circles, respectfully.
Shirokuro’s Model (2)
Constraints: no single cells
Shirokuro’s Model (3)
Constraints: no 2x2 clusters of the same color circles
Shirokuro’s Model (4)
Constraints: no “diamond” clusters
Shirokuro’s Model (4)
Constraints: no alternating colors along the perimeter
Puzzle Solving Strategy (1)
 Build the perimeter and fill in the “obvious” cells
Puzzle Solving Strategy (2)
 Create a Model and Read a Model to the Solver
 Verify solutions found by the Solver
“Solution 1” contains a group of isolated
dots and will not be accepted by verifying
method.
DEMO
Advanced Constraints
No isolation by forming a loop or an arch.
Connectivity constraint vs. no-single-cell
constraint.
This constraints are not implemented yet.
Plans for the future
 Develop an advanced constraint for
preventing formation of isolated groups.
 Modify algorithm for an arbitrary size and
shape of the field.
 Improve functionality of the GUI with the
following operations:
• Save desired puzzles on the disk,
• Load previously saved puzzles,
• Browse a list of solutions,
• Browse saved puzzles.
Thank you