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bridgeEdges.py
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231 lines (210 loc) · 7.41 KB
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# Bridge Edges v4
#
# Find the bridge edges in a graph given the
# algorithm in lecture.
# Complete the intermediate steps
# - create_rooted_spanning_tree
# - post_order
# - number_of_descendants
# - lowest_post_order
# - highest_post_order
#
# And then combine them together in
# `bridge_edges`
# So far, we've represented graphs
# as a dictionary where G[n1][n2] == 1
# meant there was an edge between n1 and n2
#
# In order to represent a spanning tree
# we need to create two classes of edges
# we'll refer to them as "green" and "red"
# for the green and red edges as specified in lecture
#
# So, for example, the graph given in lecture
# G = {'a': {'c': 1, 'b': 1},
# 'b': {'a': 1, 'd': 1},
# 'c': {'a': 1, 'd': 1},
# 'd': {'c': 1, 'b': 1, 'e': 1},
# 'e': {'d': 1, 'g': 1, 'f': 1},
# 'f': {'e': 1, 'g': 1},
# 'g': {'e': 1, 'f': 1}
# }
# would be written as a spanning tree
# S = {'a': {'c': 'green', 'b': 'green'},
# 'b': {'a': 'green', 'd': 'red'},
# 'c': {'a': 'green', 'd': 'green'},
# 'd': {'c': 'green', 'b': 'red', 'e': 'green'},
# 'e': {'d': 'green', 'g': 'green', 'f': 'green'},
# 'f': {'e': 'green', 'g': 'red'},
# 'g': {'e': 'green', 'f': 'red'}
# }
#
def create_rooted_spanning_tree(G, root):
S = {}
open = [root]
visited = [root]
for key in G.keys():
S[key] = {}
while open:
current = open.pop()
for neighbor in G[current]:
if not S[current].has_key(neighbor):
color = 'red' if neighbor in visited else 'green'
S[current][neighbor] = color
S[neighbor][current] = color
if neighbor not in visited:
visited.append(neighbor)
open.append(neighbor)
# your code here
return S
# This is just one possible solution
# There are other ways to create a
# spanning tree, and the grader will
# accept any valid result
# feel free to edit the test to
# match the solution your program produces
def test_create_rooted_spanning_tree():
G = {'a': {'c': 1, 'b': 1},
'b': {'a': 1, 'd': 1},
'c': {'a': 1, 'd': 1},
'd': {'c': 1, 'b': 1, 'e': 1},
'e': {'d': 1, 'g': 1, 'f': 1},
'f': {'e': 1, 'g': 1},
'g': {'e': 1, 'f': 1}
}
S = create_rooted_spanning_tree(G, "a")
print S
assert S == {'a': {'c': 'green', 'b': 'green'},
'b': {'a': 'green', 'd': 'red'},
'c': {'a': 'green', 'd': 'green'},
'd': {'c': 'green', 'b': 'red', 'e': 'green'},
'e': {'d': 'green', 'g': 'green', 'f': 'green'},
'g': {'e': 'green', 'f': 'red'},
'f': {'e': 'green', 'g': 'red'},
}
###########
def recGetOrder(S, order, postOrder, item, open):
open.append(item)
print item
for neighbor, value in S[item].iteritems():
if value == 'green' and open not in neighbor:
if postOrder.has_key(neighbor):
order += 1
postOrder[item] = order
else:
recGetOrder(S, order, postOrder, neighbor, open)
print open
def getLowestNode(S, startNode, open, postOrder):
for neighbor, value in S[startNode].iteritems():
if value == 'green' and not postOrder.has_key(neighbor) and neighbor not in open:
open.append(neighbor)
print open
def post_order(S, root):
# return mapping between nodes of S and the post-order value
# of that node
postOrder = {}
order = 0
open = []
recGetOrder(S, order, postOrder, root, open)
# for neighbor, value in S[root].iteritems():
# if value == 'green':
# while not postOrder.has_key(neighbor):
# (neighbor, value) = S[neighbor].iteritems()
# if value == 'green' and neighbor not in open:
# open.append(neighbor)
# if postOrder.has_key(neighbor):
# order += 1
# postOrder[item] = order
lowestNode = getLowestNode(S, root, open, postOrder)
print postOrder
return postOrder
# This is just one possible solution
# There are other ways to create a
# spanning tree, and the grader will
# accept any valid result.
# feel free to edit the test to
# match the solution your program produces
def test_post_order():
S = {'a': {'c': 'green', 'b': 'green'},
'b': {'a': 'green', 'd': 'red'},
'c': {'a': 'green', 'd': 'green'},
'd': {'c': 'green', 'b': 'red', 'e': 'green'},
'e': {'d': 'green', 'g': 'green', 'f': 'green'},
'f': {'e': 'green', 'g': 'red'},
'g': {'e': 'green', 'f': 'red'}
}
po = post_order(S, 'a')
assert po == {'a':7, 'b':1, 'c':6, 'd':5, 'e':4, 'f':2, 'g':3}
##############
def number_of_descendants(S, root):
# return mapping between nodes of S and the number of descendants
# of that node
pass
def test_number_of_descendants():
S = {'a': {'c': 'green', 'b': 'green'},
'b': {'a': 'green', 'd': 'red'},
'c': {'a': 'green', 'd': 'green'},
'd': {'c': 'green', 'b': 'red', 'e': 'green'},
'e': {'d': 'green', 'g': 'green', 'f': 'green'},
'f': {'e': 'green', 'g': 'red'},
'g': {'e': 'green', 'f': 'red'}
}
nd = number_of_descendants(S, 'a')
assert nd == {'a':7, 'b':1, 'c':5, 'd':4, 'e':3, 'f':1, 'g':1}
###############
def lowest_post_order(S, root, po):
# return a mapping of the nodes in S
# to the lowest post order value
# below that node
# (and you're allowed to follow 1 red edge)
pass
def test_lowest_post_order():
S = {'a': {'c': 'green', 'b': 'green'},
'b': {'a': 'green', 'd': 'red'},
'c': {'a': 'green', 'd': 'green'},
'd': {'c': 'green', 'b': 'red', 'e': 'green'},
'e': {'d': 'green', 'g': 'green', 'f': 'green'},
'f': {'e': 'green', 'g': 'red'},
'g': {'e': 'green', 'f': 'red'}
}
po = post_order(S, 'a')
l = lowest_post_order(S, 'a', po)
assert l == {'a':1, 'b':1, 'c':1, 'd':1, 'e':2, 'f':2, 'g':2}
################
def highest_post_order(S, root, po):
# return a mapping of the nodes in S
# to the highest post order value
# below that node
# (and you're allowed to follow 1 red edge)
pass
def test_highest_post_order():
S = {'a': {'c': 'green', 'b': 'green'},
'b': {'a': 'green', 'd': 'red'},
'c': {'a': 'green', 'd': 'green'},
'd': {'c': 'green', 'b': 'red', 'e': 'green'},
'e': {'d': 'green', 'g': 'green', 'f': 'green'},
'f': {'e': 'green', 'g': 'red'},
'g': {'e': 'green', 'f': 'red'}
}
po = post_order(S, 'a')
h = highest_post_order(S, 'a', po)
assert h == {'a':7, 'b':5, 'c':6, 'd':5, 'e':4, 'f':3, 'g':3}
#################
def bridge_edges(G, root):
# use the four functions above
# and then determine which edges in G are bridge edges
# return them as a list of tuples ie: [(n1, n2), (n4, n5)]
pass
def test_bridge_edges():
G = {'a': {'c': 1, 'b': 1},
'b': {'a': 1, 'd': 1},
'c': {'a': 1, 'd': 1},
'd': {'c': 1, 'b': 1, 'e': 1},
'e': {'d': 1, 'g': 1, 'f': 1},
'f': {'e': 1, 'g': 1},
'g': {'e': 1, 'f': 1}
}
bridges = bridge_edges(G, 'a')
assert bridges == [('d', 'e')]
#test_create_rooted_spanning_tree()
test_post_order()