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308505f18f
* Create breadth_first_search_shortest_path.py
* updating DIRECTORY.md
* Reduce side effect of `shortest_path`
For the sake of future testing and documentation -
* fixup! Format Python code with psf/black push
* Fix typo `separately`
* Change to get() from dictionary
Co-Authored-By: Christian Clauss <cclauss@me.com>
* Move graph to the top
* fixup! Format Python code with psf/black push
* Add doctest for shortest path
* Add doctest for BFS
* fixup! Format Python code with psf/black push
* Add typings for breadth_first_search_shortest_path
* fixup! Format Python code with psf/black push
* Remove assert from doctests
* Add blank line to doctest
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: John Law <johnlaw.po@gmail.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: John Law <johnlaw@linux.com>
82 lines
2.8 KiB
Python
82 lines
2.8 KiB
Python
"""Breath First Search (BFS) can be used when finding the shortest path
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from a given source node to a target node in an unweighted graph.
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"""
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graph = {
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"A": ["B", "C", "E"],
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"B": ["A", "D", "E"],
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"C": ["A", "F", "G"],
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"D": ["B"],
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"E": ["A", "B", "D"],
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"F": ["C"],
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"G": ["C"],
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}
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from typing import Dict
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class Graph:
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def __init__(self, graph: Dict[str, str], source_vertex: str) -> None:
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"""Graph is implemented as dictionary of adjancency lists. Also,
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Source vertex have to be defined upon initialization.
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"""
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self.graph = graph
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# mapping node to its parent in resulting breadth first tree
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self.parent = {}
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self.source_vertex = source_vertex
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def breath_first_search(self) -> None:
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"""This function is a helper for running breath first search on this graph.
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>>> g = Graph(graph, "G")
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>>> g.breath_first_search()
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>>> g.parent
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{'G': None, 'C': 'G', 'A': 'C', 'F': 'C', 'B': 'A', 'E': 'A', 'D': 'B'}
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"""
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visited = {self.source_vertex}
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self.parent[self.source_vertex] = None
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queue = [self.source_vertex] # first in first out queue
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while queue:
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vertex = queue.pop(0)
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for adjancent_vertex in self.graph[vertex]:
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if adjancent_vertex not in visited:
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visited.add(adjancent_vertex)
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self.parent[adjancent_vertex] = vertex
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queue.append(adjancent_vertex)
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def shortest_path(self, target_vertex: str) -> str:
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"""This shortest path function returns a string, describing the result:
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1.) No path is found. The string is a human readable message to indicate this.
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2.) The shortest path is found. The string is in the form `v1(->v2->v3->...->vn)`,
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where v1 is the source vertex and vn is the target vertex, if it exists separately.
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>>> g = Graph(graph, "G")
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>>> g.breath_first_search()
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Case 1 - No path is found.
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>>> g.shortest_path("Foo")
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'No path from vertex:G to vertex:Foo'
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Case 2 - The path is found.
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>>> g.shortest_path("D")
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'G->C->A->B->D'
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>>> g.shortest_path("G")
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'G'
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"""
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if target_vertex == self.source_vertex:
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return f"{self.source_vertex}"
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elif not self.parent.get(target_vertex):
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return f"No path from vertex:{self.source_vertex} to vertex:{target_vertex}"
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else:
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return self.shortest_path(self.parent[target_vertex]) + f"->{target_vertex}"
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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g = Graph(graph, "G")
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g.breath_first_search()
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print(g.shortest_path("D"))
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print(g.shortest_path("G"))
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print(g.shortest_path("Foo"))
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