"""Find the group containing p and return the position of its leader.
"""
if p._parent != p:
# overwrite pos._parent after recursion
p._parent = self.find(p._parent)
return p._parent
def union(self, p, q):
"""Merges the groups containing elements p and q."""
a = self.find(p)
b = self.find(q)
if a is not b:
if a._size > b._size:
b._parent = a
a._size += b._size
else:
a._parent = b
b._size += a._size
if __name__ == "__main__":
from graph_examples import figure_14_15 as example
graph = example()
edges = MST_PrimJarnik(graph)
for edge in edges:
print(str(edge))
print("=" * 20)
edges = MST_Kruskal(graph)
for edge in edges:
print(str(edge))
def find(self, p):
"""Find the group containing p and return the position of its leader.
"""
if p._parent != p:
# overwrite pos._parent after recursion
p._parent = self.find(p._parent)
return p._parent
def union(self, p, q):
"""Merges the groups containing elements p and q."""
a = self.find(p)
b = self.find(q)
if a is not b:
if a._size > b._size:
b._parent = a
a._size += b._size
else:
a._parent = b
b._size += a._size
if __name__ == "__main__":
from graph_examples import figure_14_15 as example
graph = example()
edges = MST_PrimJarnik(graph)
for edge in edges:
print(str(edge))
print("="*20)
edges = MST_Kruskal(graph)
for edge in edges:
print(str(edge))
discovered[
v] = e #e is the tree edge that is discovered in v
next_level.append(
v) #v will be further considered in next pass
level = next_level
def BFS_complete(g):
"""Perform BFS for entire graph and return forest as a dictionary.
Result maps each vertex v to the edge that was used to discover it.
(vertices that are roots of a BFS tree are mapped to None).
"""
forest = {}
for u in g.vertices():
if u not in forest:
forest[u] = None #u will the root of our tree
BFS(g, u, forest)
return forest
if __name__ == '__main__':
#from graph_examples import figure_14_11 as example
from graph_examples import figure_14_9_smaller as example
#from graph_examples import figure_14_12_smaller as example
g = example()
print("Number of vertices is", g.vertex_count())
print("Number of edges is", g.edge_count())
bfs = BFS_complete(g)
print("BFS", [str(v) for v in bfs])
from copy import deepcopy
def floyd_warshall(g):
"""Return a new graph that is the transitive closure of g."""
closure = deepcopy(g) # imported from copy module
verts = list(closure.vertices()) # make indexable list
n = len(verts)
for k in range(n):
for i in range(n):
# verify that edge (i,k) exists in the partial closure
if i != k and closure.get_edge(verts[i], verts[k]) is not None:
for j in range(n):
# verify that edge (k,j) exists in the partial closure
if i != j != k and closure.get_edge(verts[k], verts[j]) is not None:
# if (i,j) not yet included, add it to the closure
if closure.get_edge(verts[i], verts[j]) is None:
closure.insert_edge(verts[i], verts[j])
return closure
if __name__ == '__main__':
from graph_examples import figure_14_11 as example
g = example()
print("Number of vertices is", g.vertex_count())
print("Number of edges is", g.edge_count())
closure = floyd_warshall(g)
print("Number of edges in closure is", closure.edge_count())
