From 23c719da5bc1018e8a5bbca65c52ee80d400975c Mon Sep 17 00:00:00 2001
From: Jack Grahl <jack.grahl@gmail.com>
Date: Tue, 1 Nov 2022 23:11:47 +0000
Subject: [PATCH] Add a way of calculating order.

---
 polyomino/order.py  | 31 ++++++++++++++++++++++++++
 tests/test_order.py | 54 +++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 85 insertions(+)
 create mode 100644 polyomino/order.py
 create mode 100644 tests/test_order.py

diff --git a/polyomino/order.py b/polyomino/order.py
new file mode 100644
index 0000000..7aaf4bc
--- /dev/null
+++ b/polyomino/order.py
@@ -0,0 +1,31 @@
+from polyomino.board import Rectangle
+from polyomino.error import CantPlaceSinglePiece
+
+
+def rectangles(size):
+    """
+        >>> list(rectangles(20):
+        [(1, 20), (2, 10), (4, 5)]
+        >>> list(rectangles(16):
+        [(1, 16), (2, 8), (4, 6)]
+    """
+    for i in range(1, size):
+        if size % i == 0:
+            yield i, size // i
+
+
+def has_order_greater_than(tile, k):
+    n = len(tile)
+
+    for i in range(1, k + 1):
+        for x, y in rectangles(n * i):
+            board = Rectangle(x, y)
+            problem = board.tile_with_many(tile)
+            try:
+                solution = problem.solve()
+                if solution:
+                    return False, i, solution.tiling
+            except CantPlaceSinglePiece:
+                pass
+
+    return True, None, None
diff --git a/tests/test_order.py b/tests/test_order.py
new file mode 100644
index 0000000..15a55d2
--- /dev/null
+++ b/tests/test_order.py
@@ -0,0 +1,54 @@
+from polyomino.order import has_order_greater_than
+
+
+def test_rectangle():
+    tile = [(0, 0), (0, 1), (0, 2)]
+
+    predicate, n, tiling = has_order_greater_than(tile, 1)
+    assert not predicate
+    assert n == 1
+    assert tiling == [tile]
+
+    predicate, n, tiling = has_order_greater_than(tile, 2)
+    assert not predicate
+    assert n == 1
+    assert tiling == [tile]
+
+    predicate, n, tiling = has_order_greater_than(tile, 3)
+    assert not predicate
+    assert n == 1
+    assert tiling == [tile]
+
+
+def test_t_tetromino():
+    tile = [(0, 0), (0, 1), (0, 2), (1, 1)]
+
+    predicate, n, tiling = has_order_greater_than(tile, 1)
+    assert predicate
+    assert n is None
+    assert tiling is None
+
+    predicate, n, tiling = has_order_greater_than(tile, 2)
+    assert predicate
+    assert n is None
+    assert tiling is None
+
+    predicate, n, tiling = has_order_greater_than(tile, 3)
+    assert predicate
+    assert n is None
+    assert tiling is None
+
+    predicate, n, tiling = has_order_greater_than(tile, 4)
+    assert not predicate
+    assert n == 4
+    assert len(tiling) == 4
+
+    predicate, n, tiling = has_order_greater_than(tile, 5)
+    assert not predicate
+    assert n == 4
+    assert len(tiling) == 4
+
+    predicate, n, tiling = has_order_greater_than(tile, 6)
+    assert not predicate
+    assert n == 4
+    assert len(tiling) == 4