def count_em(n):
vertices, edges = make_grid(n)
corner_root = (0, ) * 2
vertex_order = order_vertices(vertices, edges, root = corner_root)
edge_order = order_edges(vertices, edges, vertex_order)
frontiers = make_frontiers(vertex_order, edge_order)
beads = make_connectedness_tree(
vertex_order,
edge_order,
frontiers,
)
beads = reduce_beads(beads, verbose = False)
count = bdd_count_solutions({'s' : len(beads), 'dag' : beads})
print count * 2
def make_bdd(vertices, edges, root):
vertex_order = order_vertices(vertices, edges, root)
edge_order = order_edges(vertices, edges, vertex_order)
frontiers = make_frontiers(vertex_order, edge_order)
print 'begin horrific connectedness tree construction procedure'
beads = make_connectedness_tree(
vertex_order,
edge_order,
frontiers,
verbose = True,
)
print '\noutput (unreduced) contains %d beads\n' % len(beads)
beads = reduce_beads(beads)
print '\noutput (reduced) contains %d beads\n' % len(beads)
return beads, edge_order, vertex_order
def main():
# trying anything above n = 5 may prove a bit foolish
n = 5
print 'making a %d by %d grid' % (n, n)
vertices, edges = make_grid(n)
# experiment: trying to fix roots
central_root = (n/2, ) * 2 # this seems to work poorly
corner_root = (0, ) * 2
vertex_order = order_vertices(vertices, edges, root = corner_root)
edge_order = order_edges(vertices, edges, vertex_order)
frontiers = make_frontiers(vertex_order, edge_order)
print 'begin horrific connectedness tree construction procedure'
beads = make_connectedness_tree(
vertex_order,
edge_order,
frontiers,
verbose = True,
)
print '\noutput (unreduced) contains %d beads\n' % len(beads)
beads = reduce_beads(beads)
print '\noutput (reduced) contains %d beads\n' % len(beads)
plots_across = 5
plots_down = 5
n_plots = plots_across * plots_down
subplot_margin = -1
subplot_width = 2 * n + 1
subplot_height = 2 * n + 1
plot_width = (
plots_across * subplot_width + subplot_margin * (plots_across - 1)
)
plot_height = (
plots_down * subplot_height + subplot_margin * (plots_down - 1)
)
figure_bmp = numpy.ones((plot_width, plot_height), dtype = numpy.int)
def carve_edge(bmp, edge_i):
(u_i, v_i) = edge_order[edge_i]
(u_x, u_y) = vertex_order[u_i]
(v_x, v_y) = vertex_order[v_i]
bmp[2 * u_x + 1, 2 * u_y + 1] = 1
bmp[2 * v_x + 1, 2 * v_y + 1] = 1
if u_x == v_x and u_y == v_y + 1:
bmp[2 * u_x + 1, 2 * v_y + 2] = 1
elif u_x == v_x and u_y + 1 == v_y:
bmp[2 * u_x + 1, 2 * u_y + 2] = 1
elif u_x == v_x + 1 and u_y == v_y:
bmp[2 * v_x + 2, 2 * u_y + 1] = 1
elif u_x + 1 == v_x and u_y == v_y:
bmp[2 * u_x + 2, 2 * u_y + 1] = 1
for plot, soln in enumerate(gen_random_solutions(beads, how_many = n_plots)):
bmp = numpy.zeros((subplot_width, subplot_height), dtype = numpy.int)
for i, include_edge in enumerate(soln):
if include_edge:
carve_edge(bmp, i)
plot_x = plot / plots_down
plot_y = plot % plots_down
plot_xx = plot_x * (subplot_width + subplot_margin)
plot_yy = plot_y * (subplot_height + subplot_margin)
x_slice = slice(plot_xx, plot_xx + subplot_width)
y_slice = slice(plot_yy, plot_yy + subplot_height)
figure_bmp[x_slice, y_slice] = 4 * (1 - bmp)
# print soln
pylab.figure()
pylab.imshow(
figure_bmp.T,
interpolation = 'nearest',
cmap = pylab.cm.Greys,
)
pylab.xticks([])
pylab.yticks([])
pylab.imsave(
'pretties.png',
figure_bmp.T,
cmap = pylab.cm.Greys,
)
pylab.show()