8.6. Implementation¶
Using dictionaries, it is easy to implement the adjacency list in
Python. In our implementation of the Graph abstract data type we will
create two classes (see Listing 1 and Listing 2), Graph, which holds the master list of vertices,
and Vertex, which will represent each vertex in the graph.
Each Vertex uses a dictionary to keep track of the vertices to which
it is connected, and the weight of each edge. This dictionary is called
connectedTo. The listing below shows the code for the Vertex
class. The constructor simply initializes the id, which will
typically be a string, and the connectedTo dictionary. The
addNeighbor method is used add a connection from this vertex to
another. The getConnections method returns all of the vertices in
the adjacency list, as represented by the connectedTo instance
variable. The getWeight method returns the weight of the edge from
this vertex to the vertex passed as a parameter.
Listing 1
class Vertex:
def __init__(self,key):
self.id = key
self.connectedTo = {}
def addNeighbor(self,nbr,weight=0):
self.connectedTo[nbr] = weight
def __str__(self):
return str(self.id) + ' connectedTo: ' + str([x.id for x in self.connectedTo])
def getConnections(self):
return self.connectedTo.keys()
def getId(self):
return self.id
def getWeight(self,nbr):
return self.connectedTo[nbr]
The Graph class, shown in the next listing, contains a dictionary
that maps vertex names to vertex objects. In Figure 4 this
dictionary object is represented by the shaded gray box. Graph also
provides methods for adding vertices to a graph and connecting one
vertex to another. The getVertices method returns the names of all
of the vertices in the graph. In addition, we have implemented the
__iter__ method to make it easy to iterate over all the vertex
objects in a particular graph. Together, the two methods allow you to
iterate over the vertices in a graph by name, or by the objects
themselves.
Listing 2
class Graph:
def __init__(self):
self.vertList = {}
self.numVertices = 0
def addVertex(self,key):
self.numVertices = self.numVertices + 1
newVertex = Vertex(key)
self.vertList[key] = newVertex
return newVertex
def getVertex(self,n):
if n in self.vertList:
return self.vertList[n]
else:
return None
def __contains__(self,n):
return n in self.vertList
def addEdge(self,f,t,weight=0):
if f not in self.vertList:
nv = self.addVertex(f)
if t not in self.vertList:
nv = self.addVertex(t)
self.vertList[f].addNeighbor(self.vertList[t], weight)
def getVertices(self):
return self.vertList.keys()
def __iter__(self):
return iter(self.vertList.values())
Using the Graph and Vertex classes just defined, the following
Python session creates the graph in Figure 2. First we
create six vertices numbered 0 through 5. Then we display the vertex
dictionary. Notice that for each key 0 through 5 we have created an
instance of a Vertex. Next, we add the edges that connect the
vertices together. Finally, a nested loop verifies that each edge in the
graph is properly stored. You should check the output of the edge list
at the end of this session against Figure 2.
>>> g = Graph()
>>> for i in range(6):
... g.addVertex(i)
>>> g.vertList
{0: <adjGraph.Vertex instance at 0x41e18>,
1: <adjGraph.Vertex instance at 0x7f2b0>,
2: <adjGraph.Vertex instance at 0x7f288>,
3: <adjGraph.Vertex instance at 0x7f350>,
4: <adjGraph.Vertex instance at 0x7f328>,
5: <adjGraph.Vertex instance at 0x7f300>}
>>> g.addEdge(0,1,5)
>>> g.addEdge(0,5,2)
>>> g.addEdge(1,2,4)
>>> g.addEdge(2,3,9)
>>> g.addEdge(3,4,7)
>>> g.addEdge(3,5,3)
>>> g.addEdge(4,0,1)
>>> g.addEdge(5,4,8)
>>> g.addEdge(5,2,1)
>>> for v in g:
... for w in v.getConnections():
... print("( %s , %s )" % (v.getId(), w.getId()))
...
( 0 , 5 )
( 0 , 1 )
( 1 , 2 )
( 2 , 3 )
( 3 , 4 )
( 3 , 5 )
( 4 , 0 )
( 5 , 4 )
( 5 , 2 )