Constraint programming is a style of programming where relations between variables are stated in the form of constraints. Constraints differ from the common primitives of other programming languages in that they do not specify a step or sequence of steps to execute but rather the properties of a solution to be found. If you want use a constraint-specific programming language, you should consider something like Prolog. If however you like Groovy but want to apply a touch of constraint style magic to your code, read on to learn about Gecode/J and Choco.
Gecode/J is a Java interface for the Gecode C++ constraint programming library. Let's have a look at making the Money example from the Gecode/J library a bit Groovier. If you haven't seen the example before, it involves solving the following puzzle:
How can I replace the letters in the puzzle with numbers so that the numbers add up in the expected way. See here for further details.
A little helper library
First we create a little helper library to make our Groovy code a little cleaner:
A Groovy Solution
Here is how we could code the solution.
It relies on the same
Options class used in the original example.
Running this code (we used the latest HEAD version of Groovy on Java 6 with the following JVM argument,
Running the program with the
-gui command line argument yields the following GUI display:
It would be fun to take the example a little further with a proper DSL to define the constraints.
Choco is a java library for constraint satisfaction problems (CSP), constraint programming (CP) and explanation-based constraint solving (e-CP). It is built on a event-based propagation mechanism with backtrackable structures. It's a great alternative to Gecode/J especially if you want a Java only solution.
Choco Magic Squares
And has this output:
We can have a little more fun with this example. First let's make the diagonals also add up:
Now, let's also make the left kite (defined as below):
Also add up to the magic square value:
Finally, let's make the middle columns in the bottom row equal to '1514':
Let's see what solutions we now have:
Which yields the following results:
The third solution in this list matches the famous Albrecht Dürer engraving.
This engraving has the following properties (from wikipedia):
The order-4 magic square in Albrecht Dürer's engraving Melancholia I is believed to be the first seen in European art. The sum 34 can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, the corner squares, the four outer numbers clockwise from the corners (3+8+14+9) and likewise the four counter-clockwise (the locations of four queens in the two solutions of the 8 queens puzzle), the two sets of four symmetrical numbers (2+8+9+15 and 3+5+12+14) and the sum of the middle two entries of the two outer columns and rows (e.g. 5+9+8+12), as well as several kite-shaped quartets, e.g. 3+5+11+15; the two numbers in the middle of the bottom row give the date of the engraving: 1514.