# Python Program to Implement Breadth-First Search on a Graph

This is a Python program to implement Breadth-First Search on a graph.

Problem Description

The program creates a graph object and allows the user to perform BFS traversal on it.

Problem Solution

1. Create classes for Graph, Vertex and Queue.
2. Create a function display_bfs that takes a Vertex object as argument.
3. The function begins by creating an empty set called visited and a Queue object, q.
4. It enqueues the passed Vertex object and also adds it to the set visited.
5. A while loop is created which runs as long as the queue is not empty.
6. In each iteration of the loop, the queue is dequeued, the dequeued element is displayed, and all of its neighbours are enqueued which have not already been visited.
7. In addition to enqueuing, they are also added to the visited set.
8. This algorithm also works for undirected graphs. In an undirected graph, whenever edge (u, v) is added to the graph, the reverse edge (v, u) is also added.

Program/Source Code

Here is the source code of a Python program to implement BFS traversal on a graph. The program output is shown below.

```class Graph:
def __init__(self):
# dictionary containing keys that map to the corresponding vertex object
self.vertices = {}

"""Add a vertex with the given key to the graph."""
vertex = Vertex(key)
self.vertices[key] = vertex

def get_vertex(self, key):
"""Return vertex object with the corresponding key."""
return self.vertices[key]

def __contains__(self, key):
return key in self.vertices

"""Add edge from src_key to dest_key with given weight."""

def does_edge_exist(self, src_key, dest_key):
"""Return True if there is an edge from src_key to dest_key."""
return self.vertices[src_key].does_it_point_to(self.vertices[dest_key])

def __iter__(self):
return iter(self.vertices.values())

class Vertex:
def __init__(self, key):
self.key = key
self.points_to = {}

def get_key(self):
"""Return key corresponding to this vertex object."""
return self.key

"""Make this vertex point to dest with given edge weight."""
self.points_to[dest] = weight

def get_neighbours(self):
"""Return all vertices pointed to by this vertex."""
return self.points_to.keys()

def get_weight(self, dest):
"""Get weight of edge from this vertex to dest."""
return self.points_to[dest]

def does_it_point_to(self, dest):
"""Return True if this vertex points to dest."""
return dest in self.points_to

class Queue:
def __init__(self):
self.items = []

def is_empty(self):
return self.items == []

def enqueue(self, data):
self.items.append(data)

def dequeue(self):
return self.items.pop(0)

def display_bfs(vertex):
"""Display BFS Traversal starting at vertex."""
visited = set()
q = Queue()
q.enqueue(vertex)
while not q.is_empty():
current = q.dequeue()
print(current.get_key(), end=' ')
for dest in current.get_neighbours():
if dest not in visited:
q.enqueue(dest)

g = Graph()
print('bfs <vertex key>')
print('display')
print('quit')

while True:
do = input('What would you like to do? ').split()

operation = do[0]
suboperation = do[1]
if suboperation == 'vertex':
key = int(do[2])
if key not in g:
else:
elif suboperation == 'edge':
src = int(do[2])
dest = int(do[3])
if src not in g:
print('Vertex {} does not exist.'.format(src))
elif dest not in g:
print('Vertex {} does not exist.'.format(dest))
else:
if not g.does_edge_exist(src, dest):
else:

elif operation == 'bfs':
key = int(do[1])
vertex = g.get_vertex(key)
display_bfs(vertex)
print()

elif operation == 'display':
print('Vertices: ', end='')
for v in g:
print(v.get_key(), end=' ')
print()

print('Edges: ')
for v in g:
for dest in v.get_neighbours():
w = v.get_weight(dest)
print('(src={}, dest={}, weight={}) '.format(v.get_key(),
dest.get_key(), w))
print()

elif operation == 'quit':
break```
Program Explanation

1. An instance of Graph is created.
2. A menu is presented to the user to perform various operations on the graph.
3. To perform BFS traversal starting at some vertex, display_bfs is called on that vertex.

Runtime Test Cases
```Case 1:
bfs <vertex key>
display
quit
What would you like to do? add vertex 1
What would you like to do? add vertex 2
What would you like to do? add vertex 3
What would you like to do? add vertex 4
What would you like to do? add vertex 5
What would you like to do? add vertex 6
What would you like to do? add vertex 7
What would you like to do? add vertex 8
What would you like to do? add vertex 9
What would you like to do? add vertex 10
What would you like to do? add edge 1 2
What would you like to do? add edge 1 3
What would you like to do? add edge 1 5
What would you like to do? add edge 2 6
What would you like to do? add edge 3 7
What would you like to do? add edge 3 8
What would you like to do? add edge 4 8
What would you like to do? add edge 8 10
What would you like to do? add edge 5 10
What would you like to do? add edge 6 9
What would you like to do? add edge 9 10
What would you like to do? bfs 1
Breadth-first Traversal: 1 3 2 5 7 8 6 10 9
What would you like to do? quit

Case 2:
bfs <vertex key>
display
quit
What would you like to do? add vertex 1
What would you like to do? bfs 1
What would you like to do? add vertex 2
What would you like to do? add edge 1 2
What would you like to do? bfs 1
What would you like to do? bfs 2
What would you like to do? add edge 2 1
What would you like to do? bfs 2
What would you like to do? add vertex 3
What would you like to do? add edge 2 3
What would you like to do? bfs 1
What would you like to do? quit```

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