From 313f93dbc5a3431ef92628e37791d4c4f289da20 Mon Sep 17 00:00:00 2001
From: Jack Grahl <jack.grahl@gmail.com>
Date: Tue, 6 Jul 2021 23:54:45 +0100
Subject: [PATCH] Add lots of things that we expect to do in doctst.

---
 examples/split_problems.md | 86 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 86 insertions(+)
 create mode 100644 examples/split_problems.md

diff --git a/examples/split_problems.md b/examples/split_problems.md
new file mode 100644
index 0000000..d4a4a46
--- /dev/null
+++ b/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()
++-+-+-+-+-+-+-+-+
+| |         |   |
++ +-+-+-+-+-+   +
+|     |     |   |
++-+ +-+ +-+-+-+-+
+| | |   | |     |
++ +-+-+-+ +-+-+ +
+|       |     | |
++-+-+-+-+-+-+ + +
+|   |       | | |
++-+ +-+-+ +-+-+-+
+| |   | | | |   |
++ +-+ + +-+ +-+ +
+|   | | |     | |
++   +-+ +-+ +-+ +
+|   |     | |   |
++-+-+-+-+-+-+-+-+
+```