mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
87 lines
2.8 KiB
Python
87 lines
2.8 KiB
Python
"""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.
|
|
"""
|
|
from __future__ import annotations
|
|
|
|
from typing import Optional
|
|
|
|
graph = {
|
|
"A": ["B", "C", "E"],
|
|
"B": ["A", "D", "E"],
|
|
"C": ["A", "F", "G"],
|
|
"D": ["B"],
|
|
"E": ["A", "B", "D"],
|
|
"F": ["C"],
|
|
"G": ["C"],
|
|
}
|
|
|
|
|
|
class Graph:
|
|
def __init__(self, graph: dict[str, list[str]], source_vertex: str) -> None:
|
|
"""
|
|
Graph is implemented as dictionary of adjacency 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: dict[str, Optional[str]] = {}
|
|
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 adjacent_vertex in self.graph[vertex]:
|
|
if adjacent_vertex not in visited:
|
|
visited.add(adjacent_vertex)
|
|
self.parent[adjacent_vertex] = vertex
|
|
queue.append(adjacent_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 self.source_vertex
|
|
|
|
target_vertex_parent = self.parent.get(target_vertex)
|
|
if target_vertex_parent is None:
|
|
return f"No path from vertex:{self.source_vertex} to vertex:{target_vertex}"
|
|
|
|
return self.shortest_path(target_vertex_parent) + f"->{target_vertex}"
|
|
|
|
|
|
if __name__ == "__main__":
|
|
g = Graph(graph, "G")
|
|
g.breath_first_search()
|
|
print(g.shortest_path("D"))
|
|
print(g.shortest_path("G"))
|
|
print(g.shortest_path("Foo"))
|