def is_bipartite(graph):
"""Runs breadth-first search through a graph to determine if a graph
is bipartite. Uses 2-color test:
https://en.wikipedia.org/wiki/Bipartite_graph#Testing_bipartiteness
Objectives:
O(m + n) running time (linear)
Args:
graph: the given graph, with nodes encoded as strings.
Returns:
True if a graph is bipartite, False otherwise.
>>> g = graph(kind='undirected')
>>> g.add_vertex('A')
>>> g.add_vertex('B')
>>> g.add_vertex('C')
>>> g.add_vertex('D')
>>> g.add_edge('A', 'B')
>>> g.add_edge('A', 'C')
>>> g.add_edge('B', 'D')
>>> g.add_edge('C', 'D')
>>> is_bipartite(g)
True
>>> g.add_vertex('E')
>>> g.add_edge('B', 'E')
>>> g.add_edge('D', 'E')
>>> is_bipartite(g)
False
"""
V = set(graph.vertices.keys())
explored = {node: 0 for node in V}
q = queue()
color = {}
curr_color = 0
s = V.pop()
explored[s] = 1
color[s] = curr_color
q.push(s)
while q.size:
node = q.pop()
curr_color = 0 if color[node] else 1
for neighbor in graph.vertices[node]:
if not explored[neighbor]:
explored[neighbor] = 1
color[neighbor] = curr_color
q.push(neighbor)
elif color[neighbor] == color[node]:
return False
return True
def bfs(graph, root):
"""Runs breadth-first search through a graph, starting at a given root.
Objectives:
O(m + n) running time (linear)
Args:
graph: the given graph, with nodes encoded as strings.
root: the node from which to start the search.
Returns:
A dictionary containing the parent-child relationships of the bfs tree.
>>> g = graph(kind='undirected')
>>> g.add_vertex('A')
>>> g.add_vertex('B')
>>> g.add_vertex('C')
>>> g.add_vertex('D')
>>> g.add_vertex('E')
>>> g.add_edge('A', 'B')
>>> g.add_edge('A', 'C')
>>> g.add_edge('B', 'D')
>>> g.add_edge('C', 'D')
>>> g.add_edge('B', 'E')
>>> g.add_edge('D', 'E')
>>> prev, dist = bfs(g, 'A')
>>> prev['A']
>>> prev['D']
'C'
>>> prev['E']
'B'
>>> dist['C']
1
>>> dist['E']
2
"""
V = set(graph.vertices.keys()) - {root}
explored = {node: 0 for node in V}
q = queue()
prev = {root: None}
dist = {root: 0}
explored[root] = 1
q.push(root)
while q.size:
node = q.pop()
for neighbor in graph.vertices[node]:
if not explored[neighbor]:
explored[neighbor] = 1
prev[neighbor] = node
dist[neighbor] = dist[node] + 1
q.push(neighbor)
return prev, dist
def bfs(graph, root):
"""Runs breadth-first search through a graph, starting at a given root.
Objectives:
O(m + n) running time (linear)
Args:
graph: the given graph, with nodes encoded as strings.
root: the node from which to start the search.
Returns:
A dictionary containing the parent-child relationships of the bfs tree.
>>> g = graph(kind='undirected')
>>> g.add_vertex('A')
>>> g.add_vertex('B')
>>> g.add_vertex('C')
>>> g.add_vertex('D')
>>> g.add_vertex('E')
>>> g.add_edge('A', 'B')
>>> g.add_edge('A', 'C')
>>> g.add_edge('B', 'D')
>>> g.add_edge('C', 'D')
>>> g.add_edge('B', 'E')
>>> g.add_edge('D', 'E')
>>> prev, dist = bfs(g, 'A')
>>> prev['A']
>>> prev['D']
'C'
>>> prev['E']
'B'
>>> dist['C']
1
>>> dist['E']
2
"""
V = set(graph.vertices.keys()) - {root}
explored = {node: 0 for node in V}
q = queue()
prev = {root: None}
dist = {root: 0}
explored[root] = 1
q.push(root)
while q.size:
node = q.pop()
for neighbor in graph.vertices[node]:
if not explored[neighbor]:
explored[neighbor] = 1
prev[neighbor] = node
dist[neighbor] = dist[node] + 1
q.push(neighbor)
return prev, dist
def run():
print "queue TEST STARTING"
q = queue()
i = 0
LIMIT = 1000
for j in xrange(0, LIMIT + 1):
q.push(j)
for j in xrange(0, LIMIT + 1):
x = q.pop()
assert x == j
assert q.empty()
print "queue TEST COMPLETED"
def run():
print "queue TEST STARTING"
q = queue()
i = 0
LIMIT = 1000
for j in xrange(0,LIMIT+1):
q.push(j)
for j in xrange(0, LIMIT+1):
x = q.pop()
assert x == j
assert q.empty()
print "queue TEST COMPLETED"
def is_bipartite(graph):
"""Runs breadth-first search through a graph to determine if a graph
is bipartite. Uses 2-color test:
https://en.wikipedia.org/wiki/Bipartite_graph#Testing_bipartiteness
Objectives:
O(m + n) running time (linear)
Args:
graph: the given graph, with nodes encoded as strings.
Returns:
True if a graph is bipartite, False otherwise.
>>> g = graph(kind='undirected')
>>> g.add_vertex('A')
>>> g.add_vertex('B')
>>> g.add_vertex('C')
>>> g.add_vertex('D')
>>> g.add_edge('A', 'B')
>>> g.add_edge('A', 'C')
>>> g.add_edge('B', 'D')
>>> g.add_edge('C', 'D')
>>> is_bipartite(g)
True
>>> g.add_vertex('E')
>>> g.add_edge('B', 'E')
>>> g.add_edge('D', 'E')
>>> is_bipartite(g)
False
"""
V = set(graph.vertices.keys())
explored = {node: 0 for node in V}
q = queue()
color = {}
s = V.pop()
explored[s] = 1
color[s] = 0
q.push(s)
while q.size:
node = q.pop()
for neighbor in graph.vertices[node]:
if not explored[neighbor]:
explored[neighbor] = 1
color[neighbor] = 1 - color[node] # Opposite
q.push(neighbor)
elif color[neighbor] == color[node]:
return False
return True
def bfs(start, dest):
dist = {start: 0}
Q = queue()
Q.push(start)
while not Q.empty():
n = Q.pop()
if n == dest:
return dist[n]
for o in n.getNeighbors():
if o not in dist:
dist[o] = dist[n] + 1
Q.push(o)
assert False