def tests(grid):
print(grid.unicode())
stats = Maze_Statistics(grid)
v = stats.size()
p, w, e = stats.Euler_edge_counts()
k, _ = Helper.find_components(grid)
print("%s: %d cells" % (stats.name, v) + \
", %d passages, %d walls, %d edges" % (p//2, w//2, e//2) + \
", %d maze components" % k)
degseq = stats.degree_counts()
print(" Degree sequence: " + sorted_degrees(degseq))
# The maze is a tree if and only if both of the following
# are true:
# (a) the maze is passage-connected, and
# (b) the number of passages is one less than the number
# of cells.
assert v is 35, "Vertex count error (got %s, expected v=5x7=35)" % v
assert p is 68, "Passage count error (got %s, expected p=v-1=34)" % (p //
2)
assert e is 126, "Edge count error (got %s, expected e=63)" % (e // 2)
assert w is 58, "Wall count error (got %s, expected w=e-p=29)" % (w // 2)
assert k is 1, "The maze is disconnected (got k=%d, expected k=1)" % k
def components(self, maze, v, e):
"""component count and characteristic"""
k, _ = Helper.find_components(maze)
key = 'k'
if key not in self.legend:
self.make_key(key, "Number of components (k)")
self.make_moments(key, k)
chi = v - e - k
key = 'chi'
if key not in self.legend:
self.make_key(key, "Maze characteristic (v-e-k)")
self.make_moments(key, chi)
return k
def check_maze(grid):
"""check that the maze is perfect
We want the maze to be a spanning tree of the grid. If v is the
number of vertices, e the number of edges, and k the number of
components, we want to satisfy both the following conditions:
(1) k = 1 (the maze is connected)
(2) v = e + 1 (every edge is a bridge, given k=1)
Since edges are counted in the manner of Euler, we count each edge
twice.
Note: Loops are not counted here with multiplicity, but the
assertion will fail (as it should) if any loops occur.
"""
m, n = grid.rows, grid.cols
v = m * n # number of vertices
e = 0 # number of arcs (2e)
for cell in grid.each():
e += len(cell.arcs) # Euler counting
k, _ = Helper.find_components(grid)
# note: e is twice the number of edges
assert e + 2 == 2 * v and k == 1, \
"v=%d, 2*e=%d, k=%d - not a tree" % (v, e, k)
