彩色的正方形拼图与Numberjack

Question

I'm going crazy with this problem that I have to solve with Numberjack, that is a library in python for CSP. We have nxm squares with colored sides. These squares must be arranged in anxm grid in such a way that the squares' adjacent sides are of the same color. The square can be rotated and shifted. An example:

I thought about using 4 matrix (one for nord, one for sud, one for west and one for east side ) and a number for a color. Nord(i,j), West(i,j), East(i,j), Sud(i,j) describe the square i,j on the grid. Which constraints i have to consider?

Answer 1

As this sounds like homework, let me just outline one model that works:

Describe each given type of tile as a quintuple (Type,N,E,S,W) , where Type is an identifier for this type of tile, and N,E,S,W are the colours on the north, east, south and west side. For each type of tile, have four such tuples for the different rotations.

Represent the grid with nxm similar tuples (Type,N,E,S,W) , where Type ranges over the tile type identifiers, and N,E,S,W over the colours.

You then need three types of constraints, all of which should be easily representable in Numberjack (and other finite-domain style solvers):

• every grid tuple matches one of the tile descriptor tuples
• adjacent colours match
• the grid contains the right number of tiles of each type