Add a way of calculating order.

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

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