Merge pull request #73 from parmentelat/all_solutions

test solution_count on small_trimino problem

tests/bruteforce.py

@@ -0,0 +1,23 @@
+"""
+bruteforce algorithm to compute the expected solutions
+and help write tests
+"""
+
+from itertools import chain, combinations
+
+import numpy as np
+
+# from the itertools module documentation
+def powerset(iterable):
+    "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
+    s = list(iterable)
+    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
+
+
+def bruteforce(data):
+    """
+    Brute-force generator of all exact cover solutions
+    """
+    for subset in powerset(range(data.shape[0])):
+        if np.all(data[list(subset)].sum(axis=0) == 1):
+            yield subset

tests/problems.py

@@ -0,0 +1,126 @@
+import numpy as np
+
+from exact_cover.io import DTYPE_FOR_ARRAY
+
+# one specific problem that I had trouble with
+# originally based on solving the trivial problem
+# of arranging 2 identical triminos on a 3x3 board
+
+#    +--+
+#    |  |
+# +--+--+
+# |  |  |
+# +--+--+
+
+# +--+--+--+
+# |xx|  |xx|
+# +--+--+--+
+# |  |  |  |
+# +--+--+--+
+# |xx|  |  |
+# +--+--+--+
+
+# this problem has 2 solutions
+# (5, 13) and (6, 12)
+def small_trimino_problem():
+    to_cover = [
+        [1, 0, 0, 1, 1, 0, 1, 0],
+        [1, 0, 0, 0, 1, 1, 0, 1],
+        [1, 0, 0, 0, 1, 1, 1, 0],
+        [1, 0, 1, 0, 1, 1, 0, 0],
+        [1, 0, 0, 0, 1, 0, 1, 1],
+        [1, 0, 1, 1, 1, 0, 0, 0],  # <- 5
+        [1, 0, 0, 0, 0, 1, 1, 1],  # <- 6
+        [0, 1, 0, 1, 1, 0, 1, 0],
+        [0, 1, 0, 0, 1, 1, 0, 1],
+        [0, 1, 0, 0, 1, 1, 1, 0],
+        [0, 1, 1, 0, 1, 1, 0, 0],
+        [0, 1, 0, 0, 1, 0, 1, 1],
+        [0, 1, 1, 1, 1, 0, 0, 0],  # <- 12
+        [0, 1, 0, 0, 0, 1, 1, 1],  # <- 13
+    ]
+    return dict(
+        data=np.array(to_cover, dtype=DTYPE_FOR_ARRAY),
+        solution1=[5, 13],
+        solution_count=2,
+    )
+
+def small_trimino_problem_from_file():
+    return dict(
+        data=np.load("tests/files/small_trimino_problem.npy"),
+        solution1=[5, 13],
+        solution_count=2,
+    )
+
+# https://en.wikipedia.org/wiki/Exact_cover#Detailed_example
+def detailed_wikipedia_problem():
+    sets = [
+        {1, 4, 7},
+        {1, 4},         # <- 1
+        {4, 5, 7},
+        {3, 5, 6},      # <- 3
+        {2, 3, 6, 7},
+        {2, 7},         # <- 5
+    ]
+    return dict(
+        data=np.array(
+            [[1 if i in s else 0 for i in range(1, 8)] for s in sets],
+            dtype=DTYPE_FOR_ARRAY),
+        solution1=[1, 3, 5],
+        solution_count=1,
+    )
+
+def bruteforce_problem1():
+    to_cover = [
+        [1, 0, 0, 1, 0, 0, 1, 0], # <- sol1
+        [0, 1, 0, 0, 1, 0, 0, 1], # <- sol1
+        [0, 0, 1, 0, 0, 1, 0, 0], # <- sol1
+        [0, 0, 0, 1, 0, 0, 0, 0], # <- sol2
+        [1, 0, 1, 0, 1, 0, 0, 1], # <- sol2
+        [0, 1, 0, 0, 0, 1, 1, 0], # <- sol2
+
+    ]
+    return dict(
+        data=np.array(to_cover, dtype=DTYPE_FOR_ARRAY),
+        solution1=[0, 1, 2],
+        solution_count=2,
+    )
+
+def bruteforce_problem2():
+    to_cover = [
+        [1, 0, 0, 1, 0, 0, 1, 0], # <- sol1
+        [0, 1, 0, 0, 1, 0, 0, 1], # <- sol1
+        [0, 0, 1, 0, 0, 1, 0, 0], # <- sol1
+        [0, 0, 0, 1, 0, 0, 0, 0], # <- sol2
+        [1, 0, 1, 0, 1, 0, 0, 1], # <- sol2
+        [0, 1, 0, 0, 0, 1, 1, 0], # <- sol2
+        [1, 0, 0, 1, 0, 0, 1, 0], # <- sol1
+        [0, 1, 0, 0, 1, 0, 0, 1], # <- sol1
+        [0, 0, 1, 0, 0, 1, 0, 0], # <- sol1
+    ]
+    return dict(
+        data=np.array(to_cover, dtype=DTYPE_FOR_ARRAY),
+        solution1=[0, 1, 2],
+        solution_count=9,
+    )
+
+def bruteforce_problem3():
+    to_cover = [
+        [1, 0, 0, 1, 0, 0, 1, 0], # <- sol1
+        [0, 1, 0, 0, 1, 0, 0, 1], # <- sol1
+        [0, 0, 1, 0, 0, 1, 0, 0], # <- sol1
+        [0, 0, 0, 1, 0, 0, 0, 0], # <- sol2
+        [1, 0, 1, 0, 1, 0, 0, 1], # <- sol2
+        [0, 1, 0, 0, 0, 1, 1, 0], # <- sol2
+        [1, 0, 0, 1, 0, 0, 1, 0], # <- sol1
+        [0, 1, 0, 0, 1, 0, 0, 1], # <- sol1
+        [0, 0, 1, 0, 0, 1, 0, 0], # <- sol1
+        [0, 0, 0, 1, 0, 0, 0, 0], # <- sol2
+        [1, 0, 1, 0, 1, 0, 0, 1], # <- sol2
+        [0, 1, 0, 0, 0, 1, 1, 0], # <- sol2
+    ]
+    return dict(
+        data=np.array(to_cover, dtype=DTYPE_FOR_ARRAY),
+        solution1=[0, 1, 2],
+        solution_count=16,
+    )

tests/test_solution_count.py

@@ -3,6 +3,9 @@
 from exact_cover_impl import get_solution_count
 from exact_cover.io import DTYPE_FOR_ARRAY
 
+from .problems import small_trimino_problem
+from .problems import detailed_wikipedia_problem
+from .problems import bruteforce_problem1
 
 def test_solution_count():
     data = np.array([[1, 0, 0], [0, 1, 0], [0, 1, 1], [0, 0, 1]], dtype=DTYPE_FOR_ARRAY)
@@ -20,3 +23,33 @@ def test_solution_count_no_solutions():
     data = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 0]], dtype=DTYPE_FOR_ARRAY)
     result = get_solution_count(data)
     assert result == 0
+
+def test_small_trimino_problem():
+    problem = small_trimino_problem()
+    data = problem['data']
+    result = get_solution_count(data)
+    assert result == problem['solution_count']
+
+def test_detailed_wikipedia_problem():
+    problem = detailed_wikipedia_problem()
+    data = problem['data']
+    result = get_solution_count(data)
+    assert result == problem['solution_count']
+
+def test_bruteforce_problem1():
+    problem = bruteforce_problem1()
+    data = problem['data']
+    result = get_solution_count(data)
+    assert result == problem['solution_count']
+
+def test_bruteforce_problem2():
+    problem = bruteforce_problem2()
+    data = problem['data']
+    result = get_solution_count(data)
+    assert result == problem['solution_count']
+
+def test_bruteforce_problem3():
+    problem = bruteforce_problem3()
+    data = problem['data']
+    result = get_solution_count(data)
+    assert result == problem['solution_count']

tests/test_trimino_based.py

@@ -3,60 +3,19 @@
 
 from exact_cover import get_exact_cover
 from exact_cover.error import NoSolution
-from exact_cover.io import DTYPE_FOR_ARRAY
 
-# from exact_cover.helpers import is_solution
+from .problems import (
+    # the exact cover matrix built manually
+    small_trimino_problem,
+    # the same store in a file
+    small_trimino_problem_from_file)
 
-DTYPE = dict(dtype=DTYPE_FOR_ARRAY)
 
-# from exact_cover.io import load_problem
-
-# from tests.config import GLOBAL_CONFIG
-
-
-# one specific problem that I had trouble with
-# originally based on solving the trivial problem
-# of arranging 2 identical triminos on a 3x3 board
-
-#    +--+
-#    |  |
-# +--+--+
-# |  |  |
-# +--+--+
-
-# +--+--+--+
-# |xx|  |xx|
-# +--+--+--+
-# |  |  |  |
-# +--+--+--+
-# |xx|  |  |
-# +--+--+--+
-
-
-# the exact cover matrix built manually
 def input1():
-    to_cover = [
-        [1, 0, 0, 1, 1, 0, 1, 0],
-        [1, 0, 0, 0, 1, 1, 0, 1],
-        [1, 0, 0, 0, 1, 1, 1, 0],
-        [1, 0, 1, 0, 1, 1, 0, 0],
-        [1, 0, 0, 0, 1, 0, 1, 1],
-        [1, 0, 1, 1, 1, 0, 0, 0],  # <- 5
-        [1, 0, 0, 0, 0, 1, 1, 1],
-        [0, 1, 0, 1, 1, 0, 1, 0],
-        [0, 1, 0, 0, 1, 1, 0, 1],
-        [0, 1, 0, 0, 1, 1, 1, 0],
-        [0, 1, 1, 0, 1, 1, 0, 0],
-        [0, 1, 0, 0, 1, 0, 1, 1],
-        [0, 1, 1, 1, 1, 0, 0, 0],
-        [0, 1, 0, 0, 0, 1, 1, 1],  # <- 13
-    ]
-    return np.array(to_cover, **DTYPE)
-
+    return small_trimino_problem()['data']
 
 def input2():
-    return np.load("tests/files/small_trimino_problem.npy")
-
+    return small_trimino_problem_from_file()['data']
 
 def test_inputs_are_equal():
     m1 = input1()
@@ -77,8 +36,10 @@ def run_on_input(array, expected):
 
 
 def test_input1():
-    run_on_input(input1(), [5, 13])
+    expected = small_trimino_problem()['solution1']
+    run_on_input(input1(), expected)
 
 
 def test_input2():
-    run_on_input(input2(), [5, 13])
+    expected = small_trimino_problem_from_file()['solution1']
+    run_on_input(input2(), expected)