def number_of_descendants(S, root):
nd = {}
for node in S:
nd[node] = 0
ancestors = create_ancestors(S, root)
for node in nd:
for a in ancestors:
if node in ancestors[a]:
nd[node] += 1
return nd
def bridge_edges(G, root):
S = create_rooted_spanning_tree(G, root)
po = post_order(S, root)
ancestors = create_ancestors(S, root)
nd = number_of_descendants(S, root)
l, h = po_low_high(S, root, po)
bridges = []
for node in S:
for n in S[node]:
if n not in ancestors[node]:
if S[node][n] == 'green':
if h[n] <= po[n]:
if l[n] > abs(nd[n] - po[n]):
bridges.append((node, n))
return bridges
def bridge_edges(G, root):
S = create_rooted_spanning_tree(G, root)
po = post_order(S, root)
ancestors = create_ancestors(S, root)
nd = number_of_descendants(S, root)
l, h = po_low_high(S, root, po)
bridges = []
for node in S:
for n in S[node]:
if n not in ancestors[node]:
if S[node][n] == 'green':
if h[n] <= po[n]:
if l[n] > abs(nd[n]-po[n]):
bridges.append((node, n))
return bridges
def po_low_high(S, root, po):
lpo, hpo = {}, {}
ancestors = create_ancestors(S, root)
reverse_po = dict(zip(po.values(), po))
for i in range(1, len(reverse_po) + 1):
n = reverse_po[i]
temp = [po[n]]
for node in S[n]:
if node not in ancestors[n]:
temp.append(po[node])
for x in S[node]:
if S[node][x] == 'red':
temp.append(po[x])
lpo[n], hpo[n] = min(temp), max(temp)
return lpo, hpo
def po_low_high(S, root, po):
lpo, hpo = {}, {}
ancestors = create_ancestors(S, root)
reverse_po = dict(zip(po.values(),po))
for i in range(1, len(reverse_po)+1):
n = reverse_po[i]
temp = [po[n]]
for node in S[n]:
if node not in ancestors[n]:
temp.append(po[node])
for x in S[node]:
if S[node][x] == 'red':
temp.append(po[x])
lpo[n], hpo[n] = min(temp), max(temp)
return lpo, hpo