Visual info on splits

examples/split_problems.md

@@ -0,0 +1,86 @@
+To make computation more tractable, a tiling problem can be split into two or more sub-problems. Each solution to the original problem is also the solution to exactly one of the sub-problems.
+
+```
+>>> from polyomino.board import Chessboard
+>>> from polyomino.constant import TETROMINOS, ALL_PENTOMINOS
+
+```
+
+First a problem which involves no repeated tiles. It can be solved without splitting, but let us look at how splitting works:
+```
+>>> problem = Chessboard().tile_with(ALL_PENTOMINOS + [TETROMINOS['Square']])
+>>> subproblems = problem.split(at_least=2)
+>>> len(subproblems)
+3
+>>> example = subproblems[0]
+>>> example
+<polyomino.problem.TilingSubProblem object at ...>
+>>> print(example.display())
++-+-+-+-+-+-+-+-+
+| |         |   |
++ +-+-+-+-+-+   +
+|     |     |   |
++-+ +-+ +-+-+-+-+
+| | |   | |     |
++ +-+-+-+ +-+-+ +
+|       |     | |
++-+-+-+-+-+-+ + +
+|   |       | | |
++-+ +-+-+ +-+-+-+
+| |   | | | |   |
++ +-+ + +-+ +-+ +
+|   | | |     | |
++   +-+ +-+ +-+ +
+|   |     | |   |
++-+-+-+-+-+-+-+-+
+>>> sub_solution = example.solve()
+>>> sub_solution
+<polyomino.solution.Solution object at ...>
+>>> example.is_solution(sub_solution.array)
+True
+>>> sub_solution.tiling
+[[(0, 0), (1, 1), (1, 0), (2, 0)], [(0, 3), (1, 2), (0, 2), (0, 1)], [(3, 3), (2, 2), (2, 3), (1, 3)], [(3, 0), (2, 1), (3, 1), (3, 2)]]
+>>> sub_solution.display()
++-+-+-+-+-+-+-+-+
+| |         |   |
++ +-+-+-+-+-+   +
+|     |     |   |
++-+ +-+ +-+-+-+-+
+| | |   | |     |
++ +-+-+-+ +-+-+ +
+|       |     | |
++-+-+-+-+-+-+ + +
+|   |       | | |
++-+ +-+-+ +-+-+-+
+| |   | | | |   |
++ +-+ + +-+ +-+ +
+|   | | |     | |
++   +-+ +-+ +-+ +
+|   |     | |   |
++-+-+-+-+-+-+-+-+
+>>> solution = example.original_solution(sub_solution)
+>>> solution
+<polyomino.solution.Solution object at ...>
+>>> problem.is_solution(solution.array)
+True
+>>> solution.tiling
+[[(0, 0), (1, 1), (1, 0), (2, 0)], [(0, 3), (1, 2), (0, 2), (0, 1)], [(3, 3), (2, 2), (2, 3), (1, 3)], [(3, 0), (2, 1), (3, 1), (3, 2)]]
+>>> solution.display()
++-+-+-+-+-+-+-+-+
+| |         |   |
++ +-+-+-+-+-+   +
+|     |     |   |
++-+ +-+ +-+-+-+-+
+| | |   | |     |
++ +-+-+-+ +-+-+ +
+|       |     | |
++-+-+-+-+-+-+ + +
+|   |       | | |
++-+ +-+-+ +-+-+-+
+| |   | | | |   |
++ +-+ + +-+ +-+ +
+|   | | |     | |
++   +-+ +-+ +-+ +
+|   |     | |   |
++-+-+-+-+-+-+-+-+
+```

polyomino/problem.py

@@ -1,6 +1,7 @@
 import numpy as np
 
 from exact_cover import get_exact_cover
+from exact_cover.helpers import split_problem
 
 from .error import CantPlaceSinglePiece
 from .solution import Solution
@@ -76,6 +77,14 @@ def output_array(self, filename):
     def set_name(self, name):
         self._name = name
 
+    def split(self, at_least=1):
+        arrays = split_problem(self.array, at_least)
+        for array in arrays:
+            problem = TilingProblem(self.board, self.tileset)
+            problem.array = array
+            problem.key = self.key
+            yield problem
+
     @property
     def size(self):
         self.make_problem()

pyproject.toml

@@ -8,7 +8,7 @@ license = "MIT"
 
 [tool.poetry.dependencies]
 python = "^3.7.1"
-exact-cover = "0.4.3"
+exact-cover = "0.8.0"
 numpy = "^1.20"
 pretty-poly = "0.2.0"