# Python Program to Find All Nodes Reachable from a Node using BFS in a Graph

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This is a Python program to find all nodes reachable from a node using BFS in a graph.

Problem Description

The program creates a graph object and allows the user to find all nodes reachable from a node.

Problem Solution

1. Create classes for Graph, Vertex and Queue.
2. Create a function find_all_reachable_nodes 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 no empty.
6. In each iteration of the loop, the queue is dequeued 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. After the loop is finished, the set visited is returned. The set contains all vertices that can be reached from the source vertex.
9. 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 find all nodes reachable from a node using BFS in 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 find_all_reachable_nodes(vertex):
"""Return set containing all vertices reachable from vertex."""
visited = set()
q = Queue()
q.enqueue(vertex)
while not q.is_empty():
current = q.dequeue()
for dest in current.get_neighbours():
if dest not in visited:
q.enqueue(dest)
return visited

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

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

operation = do
suboperation = do
if suboperation == 'vertex':
key = int(do)
if key not in g:
else:
elif suboperation == 'edge':
src = int(do)
dest = int(do)
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 == 'reachable':
key = int(do)
vertex = g.get_vertex(key)
reachable = find_all_reachable_nodes(vertex)
print('All nodes reachable from {}:'.format(key),
[v.get_key() for v in reachable])

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 find all nodes reachable from a vertex, find_all_reachable_nodes is called.

Runtime Test Cases
```Case 1:
reachable <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? reachable 1
All nodes reachable from 1: 
What would you like to do? add edge 1 2
What would you like to do? reachable 1
All nodes reachable from 1: [2, 1]
What would you like to do? reachable 2
All nodes reachable from 2: 
What would you like to do? add edge 2 1
What would you like to do? reachable 2
All nodes reachable from 2: [2, 1]
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? add vertex 4
What would you like to do? add edge 3 4
What would you like to do? reachable 1
All nodes reachable from 1: [2, 3, 1, 4]
What would you like to do? quit

Case 2:
reachable <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 edge 1 2
What would you like to do? add edge 2 3
What would you like to do? add edge 5 4
What would you like to do? reachable 4
All nodes reachable from 4: 
What would you like to do? reachable 5
All nodes reachable from 5: [4, 5]
What would you like to do? reachable 1
All nodes reachable from 1: [2, 3, 1]
What would you like to do? reachable 2
All nodes reachable from 2: [2, 3]
What would you like to do? reachable 3
All nodes reachable from 3: 
What would you like to do? quit```

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