def plot_graph_and_tree(G, T, time):
""" Plot a graph G and a tree T on top of it
Assumes that G has an embedding in the plane, represented as a dictionary G.pos"""
plt.clf()
nx.draw_networkx_edges(G, G.pos, alpha=.75, width=.5, style='dotted')
nx.draw_networkx_edges(T, G.pos, alpha=.5, width=2)
X = np.array(list(G.pos.values()))
plt.plot(X[:,0], X[:,1], 'bo', alpha=.5)
plt.plot([G.pos[T.root][0]], [G.pos[T.root][1]], 'bo', ms=12, mew=4, alpha=.95)
# display the most recently swapped edges
P = models.my_path_graph(T.path)
nx.draw_networkx_edges(P, G.pos, alpha=.25 + (1-time)*.5, width=4, edge_color='c')
P = models.my_path_graph([T.u_new, T.v_new])
P.add_edge(T.u_old, T.v_old)
nx.draw_networkx_edges(P, G.pos, alpha=.25 + (1-time)*.5, width=4, edge_color='y')
# find and display the current longest path
path = nx.shortest_path(T, T.root)
furthest_leaf = max(path, key=lambda l: len(path[l]))
P = models.my_path_graph(path[furthest_leaf])
if len(path[furthest_leaf]) <= T.k:
col = 'g'
else:
col = 'r'
nx.draw_networkx_edges(P, G.pos, alpha=.5, width=4, edge_color=col)
plt.text(G.pos[furthest_leaf][0], G.pos[furthest_leaf][1], '%d hops from root'%len(path[furthest_leaf]), color=col, alpha=.8, fontsize=9)
T.depth = len(path[furthest_leaf])
def hidden_image_maze(fname, style='jittery'):
""" Supported styles: jittery, smooth, sketch"""
H = models.image_grid_graph(fname) # get a subgraph of the grid corresponding to edges between black pixels
G = H.base_graph
# for every edge in H, make the corresponding edge in H have weight 0
for u,v in H.edges():
G[u][v]['weight'] = 0
# find a minimum spanning tree on G (which will include the maze solution)
T = nx.minimum_spanning_tree(G)
# find the maze solution in the spanning tree
P = models.my_path_graph(nx.shortest_path(T, (0,0), max(H.nodes())))
# generate the dual graph, including edges not crossed by the spanning tree
D = models.dual_grid(G, T)
views.add_maze_boundary(D, max(G.nodes()))
views.make_entry_and_exit(D, max(G.nodes()))
pos = views.layout_maze(D, fast=(style == 'jittery'))
views.plot_maze(D, pos, P, G.pos)
# make it stylish if requested
if style == 'sketch':
plt.figure(1)
D_pos = views.layout_maze(D, fast=True)
nx.draw_networkx_edges(D, D_pos, width=1, edge_color='k')
D_pos = views.layout_maze(D, fast=True)
nx.draw_networkx_edges(D, D_pos, width=1, edge_color='k')
# show the pixel colors loaded from the file, for "debugging"
plt.figure(2)
for v in G:
plt.plot([G.pos[v][0]], [G.pos[v][1]], '.', alpha=.5, color=G.node[v]['color'])
def plot_graph_and_tree(G, T, time):
""" Plot a graph G and a tree T on top of it
Assumes that G has an embedding in the plane, represented as a dictionary G.pos"""
plt.clf()
nx.draw_networkx_edges(G, G.pos, alpha=.75, width=.5, style='dotted')
nx.draw_networkx_edges(T, G.pos, alpha=.5, width=2)
X = np.array(list(G.pos.values()))
plt.plot(X[:, 0], X[:, 1], 'bo', alpha=.5)
plt.plot([G.pos[T.root][0]], [G.pos[T.root][1]],
'bo',
ms=12,
mew=4,
alpha=.95)
# display the most recently swapped edges
P = models.my_path_graph(T.path)
nx.draw_networkx_edges(P,
G.pos,
alpha=.25 + (1 - time) * .5,
width=4,
edge_color='c')
P = models.my_path_graph([T.u_new, T.v_new])
P.add_edge(T.u_old, T.v_old)
nx.draw_networkx_edges(P,
G.pos,
alpha=.25 + (1 - time) * .5,
width=4,
edge_color='y')
# find and display the current longest path
path = nx.shortest_path(T, T.root)
furthest_leaf = max(path, key=lambda l: len(path[l]))
P = models.my_path_graph(path[furthest_leaf])
if len(path[furthest_leaf]) <= T.k:
col = 'g'
else:
col = 'r'
nx.draw_networkx_edges(P, G.pos, alpha=.5, width=4, edge_color=col)
plt.text(G.pos[furthest_leaf][0],
G.pos[furthest_leaf][1],
'%d hops from root' % len(path[furthest_leaf]),
color=col,
alpha=.8,
fontsize=9)
T.depth = len(path[furthest_leaf])
def random_maze(n=25):
G = models.my_grid_graph([n,n])
T = nx.minimum_spanning_tree(G)
P = models.my_path_graph(nx.shortest_path(T, (0,0), (n-1, n-1)))
D = models.dual_grid(G, T)
views.add_maze_boundary(D, [n, n])
views.make_entry_and_exit(D, [n, n])
pos = views.layout_maze(D, fast=True)
views.plot_maze(D, pos, P, G.pos)
def random_maze(n=25):
G = models.my_grid_graph([n, n])
T = nx.minimum_spanning_tree(G)
P = models.my_path_graph(nx.shortest_path(T, (0, 0), (n - 1, n - 1)))
D = models.dual_grid(G, T)
views.add_maze_boundary(D, [n, n])
views.make_entry_and_exit(D, [n, n])
pos = views.layout_maze(D, fast=True)
views.plot_maze(D, pos, P, G.pos)
def test_graph_utils(self):
P = model.my_path_graph(model.nx.shortest_path(self.G, (0,0), (4,4)))
H = model.image_grid_graph('test.png')
d = model.dual_grid_edge((0,0), (0,1))
assert d == ((-0.5, 0.5), (0.5, 0.5)), 'dual of integer lattice should be offset by .5s'
D = model.dual_grid(H.base_graph, H)
graphics.add_maze_boundary(D, [5,5])
graphics.make_entry_and_exit(D, [5,5])
HH = graphics.split_edges(H)
def test_graph_utils(self):
P = model.my_path_graph(model.nx.shortest_path(self.G, (0, 0), (4, 4)))
H = model.image_grid_graph('test.png')
d = model.dual_grid_edge((0, 0), (0, 1))
assert d == ((-0.5, 0.5),
(0.5,
0.5)), 'dual of integer lattice should be offset by .5s'
D = model.dual_grid(H.base_graph, H)
graphics.add_maze_boundary(D, [5, 5])
graphics.make_entry_and_exit(D, [5, 5])
HH = graphics.split_edges(H)
def border_maze(fname='test.png', fast=True):
G = models.image_grid_graph(
fname, colors=set([(255, 255, 255, 255), (0, 0, 0, 255)])
) # get a subgraph of the grid corresponding to edges between black and white
H = models.image_grid_graph(
fname, colors=set([(0, 0, 0, 255)])
) # get a subgraph of the grid corresponding to edges between black pixels
# for every edge in H, make the corresponding edge in G have weight 0
for u, v in G.edges():
G[u][v]['weight'] = (H.has_edge(u, v)
and .1) or (1. + G.base_graph[u][v]['weight'])
# find a minimum spanning tree on G (which will include the maze solution)
T = nx.minimum_spanning_tree(G)
# add border edges to G
B = models.image_grid_graph(fname,
colors=set([(255, 255, 255, 255),
(0, 0, 0, 255), (255, 0, 0, 255)]))
for u, v in B.edges():
if not G.has_edge(u, v):
G.add_edge(u, v)
# find the maze solution in the spanning tree
for u, v in G.edges():
if len(G[u]) < 4 and len(G[v]) < 4:
G[u][v]['weight'] = 1
else:
G[u][v]['weight'] = 1e6
for u, v in T.edges():
G[u][v]['weight'] = 0
P = models.my_path_graph(
nx.shortest_path(G, (0, 0), max(G.nodes()), weight='weight'))
G_pos = G.base_graph.pos
# generate the dual graph, including edges not crossed by the spanning tree
D = models.dual_grid(G, T)
D = views.split_edges(D)
pos = views.layout_maze(D, fast=fast)
views.plot_maze(D, pos, P, G_pos)
# show the pixel colors loaded from the file, for "debugging"
plt.figure(2)
for v in G:
plt.plot([G_pos[v][0]], [G_pos[v][1]],
'.',
alpha=.5,
color=G.base_graph.node[v]['color'])
return dict(G=G, H=H, T=T, P=P, B=B)
def border_maze(fname='test.png', fast=True):
G = models.image_grid_graph(fname, colors=set([(255,255,255,255), (0,0,0,255)])) # get a subgraph of the grid corresponding to edges between black and white
H = models.image_grid_graph(fname, colors=set([(0,0,0,255)])) # get a subgraph of the grid corresponding to edges between black pixels
# for every edge in H, make the corresponding edge in G have weight 0
for u,v in G.edges():
G[u][v]['weight'] = (H.has_edge(u,v) and .1) or (1.+G.base_graph[u][v]['weight'])
# find a minimum spanning tree on G (which will include the maze solution)
T = nx.minimum_spanning_tree(G)
# add border edges to G
B = models.image_grid_graph(fname, colors=set([(255,255,255,255), (0,0,0,255), (255,0,0,255)]))
for u,v in B.edges():
if not G.has_edge(u, v):
G.add_edge(u, v)
# find the maze solution in the spanning tree
for u,v in G.edges():
if len(G[u]) < 4 and len(G[v]) < 4:
G[u][v]['weight'] = 1
else:
G[u][v]['weight'] = 1e6
for u,v in T.edges():
G[u][v]['weight'] = 0
P = models.my_path_graph(nx.shortest_path(G, (0,0), max(G.nodes()), weight='weight'))
G_pos = G.base_graph.pos
# generate the dual graph, including edges not crossed by the spanning tree
D = models.dual_grid(G, T)
D = views.split_edges(D)
pos = views.layout_maze(D, fast=fast)
views.plot_maze(D, pos, P, G_pos)
# show the pixel colors loaded from the file, for "debugging"
plt.figure(2)
for v in G:
plt.plot([G_pos[v][0]], [G_pos[v][1]], '.', alpha=.5, color=G.base_graph.node[v]['color'])
return dict(G=G, H=H, T=T, P=P, B=B)
def hidden_image_maze(fname, style='jittery'):
""" Supported styles: jittery, smooth, sketch"""
H = models.image_grid_graph(
fname
) # get a subgraph of the grid corresponding to edges between black pixels
G = H.base_graph
# for every edge in H, make the corresponding edge in H have weight 0
for u, v in H.edges():
G[u][v]['weight'] = 0
# find a minimum spanning tree on G (which will include the maze solution)
T = nx.minimum_spanning_tree(G)
# find the maze solution in the spanning tree
P = models.my_path_graph(nx.shortest_path(T, (0, 0), max(H.nodes())))
# generate the dual graph, including edges not crossed by the spanning tree
D = models.dual_grid(G, T)
views.add_maze_boundary(D, max(G.nodes()))
views.make_entry_and_exit(D, max(G.nodes()))
pos = views.layout_maze(D, fast=(style == 'jittery'))
views.plot_maze(D, pos, P, G.pos)
# make it stylish if requested
if style == 'sketch':
plt.figure(1)
D_pos = views.layout_maze(D, fast=True)
nx.draw_networkx_edges(D, D_pos, width=1, edge_color='k')
D_pos = views.layout_maze(D, fast=True)
nx.draw_networkx_edges(D, D_pos, width=1, edge_color='k')
# show the pixel colors loaded from the file, for "debugging"
plt.figure(2)
for v in G:
plt.plot([G.pos[v][0]], [G.pos[v][1]],
'.',
alpha=.5,
color=G.node[v]['color'])
def ld_maze(n=25):
""" having many low-degree vertices makes for hard mazes
unfortunately, finding them is slow"""
# start with an nxn square grid
G = models.my_grid_graph([n,n])
# make a pymc model of a low-degree spanning tree on this
T = models.LDST(G, beta=10)
mod_mc = mc.MCMC([T])
mod_mc.use_step_method(models.STMetropolis, T)
mod_mc.sample(100, burn=99)
T = T.value
P = models.my_path_graph(nx.shortest_path(T, (0,0), (n-1, n-1)))
D = models.dual_grid(G, T)
views.add_maze_boundary(D, [n,n])
views.make_entry_and_exit(D, [n,n])
D = views.split_edges(D)
D = views.split_edges(D)
D_pos = views.layout_maze(D, fast=False)
views.plot_maze(D, D_pos, P, G.pos)
def ld_maze(n=25):
""" having many low-degree vertices makes for hard mazes
unfortunately, finding them is slow"""
# start with an nxn square grid
G = models.my_grid_graph([n, n])
# make a pymc model of a low-degree spanning tree on this
T = models.LDST(G, beta=10)
mod_mc = mc.MCMC([T])
mod_mc.use_step_method(models.STMetropolis, T)
mod_mc.sample(100, burn=99)
T = T.value
P = models.my_path_graph(nx.shortest_path(T, (0, 0), (n - 1, n - 1)))
D = models.dual_grid(G, T)
views.add_maze_boundary(D, [n, n])
views.make_entry_and_exit(D, [n, n])
D = views.split_edges(D)
D = views.split_edges(D)
D_pos = views.layout_maze(D, fast=False)
views.plot_maze(D, D_pos, P, G.pos)