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Breadth First Search Shortest Path

"""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

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, str | None] = {}
        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:
                    self.parent[adjacent_vertex] = 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")
        Traceback (most recent call last):
        ValueError: No path from vertex: G to vertex: Foo

        Case 2 - The path is found.
        >>> g.shortest_path("D")
        >>> g.shortest_path("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:
            msg = (
                f"No path from vertex: {self.source_vertex} to vertex: {target_vertex}"
            raise ValueError(msg)

        return self.shortest_path(target_vertex_parent) + f"->{target_vertex}"

if __name__ == "__main__":
    g = Graph(graph, "G")