Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. BFS and its application in finding connected components of graphs were invented in 1945 by Konrad Zuse, in his (rejected) Ph.D. thesis on the Plankalkül programming language, but this was not published until 1972.

COMING SOON!

```
"""Breath First Search (BFS) can be used when finding the shortest path
from a given source node to a target node in an unweighted graph.
"""
graph = {
"A": ["B", "C", "E"],
"B": ["A", "D", "E"],
"C": ["A", "F", "G"],
"D": ["B"],
"E": ["A", "B", "D"],
"F": ["C"],
"G": ["C"],
}
from typing import Dict
class Graph:
def __init__(self, graph: Dict[str, str], source_vertex: str) -> None:
"""Graph is implemented as dictionary of adjancency lists. Also,
Source vertex have to be defined upon initialization.
"""
self.graph = graph
# mapping node to its parent in resulting breadth first tree
self.parent = {}
self.source_vertex = source_vertex
def breath_first_search(self) -> None:
"""This function is a helper for running breath first search on this graph.
>>> g = Graph(graph, "G")
>>> g.breath_first_search()
>>> g.parent
{'G': None, 'C': 'G', 'A': 'C', 'F': 'C', 'B': 'A', 'E': 'A', 'D': 'B'}
"""
visited = {self.source_vertex}
self.parent[self.source_vertex] = None
queue = [self.source_vertex] # first in first out queue
while queue:
vertex = queue.pop(0)
for adjancent_vertex in self.graph[vertex]:
if adjancent_vertex not in visited:
visited.add(adjancent_vertex)
self.parent[adjancent_vertex] = vertex
queue.append(adjancent_vertex)
def shortest_path(self, target_vertex: str) -> str:
"""This shortest path function returns a string, describing the result:
1.) No path is found. The string is a human readable message to indicate this.
2.) The shortest path is found. The string is in the form `v1(->v2->v3->...->vn)`,
where v1 is the source vertex and vn is the target vertex, if it exists separately.
>>> g = Graph(graph, "G")
>>> g.breath_first_search()
Case 1 - No path is found.
>>> g.shortest_path("Foo")
'No path from vertex:G to vertex:Foo'
Case 2 - The path is found.
>>> g.shortest_path("D")
'G->C->A->B->D'
>>> g.shortest_path("G")
'G'
"""
if target_vertex == self.source_vertex:
return f"{self.source_vertex}"
elif not self.parent.get(target_vertex):
return f"No path from vertex:{self.source_vertex} to vertex:{target_vertex}"
else:
return self.shortest_path(self.parent[target_vertex]) + f"->{target_vertex}"
if __name__ == "__main__":
import doctest
doctest.testmod()
g = Graph(graph, "G")
g.breath_first_search()
print(g.shortest_path("D"))
print(g.shortest_path("G"))
print(g.shortest_path("Foo"))
```