
"""simple docstring"""







from __future__ import annotations
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     int:







							"""simple docstring"""


							for i in range(1							,    len(matrix[0] ) ):
														matrix[0][i] += matrix[0][i - 1]

							# preprocessing the first column
							for i in range(1							,    len(SCREAMING_SNAKE_CASE ) ):
														matrix[i][0] += matrix[i - 1][0]

							# updating the path cost for current position
							for i in range(1							,    len(SCREAMING_SNAKE_CASE ) ):
														for j in range(1							,    len(matrix[0] ) ):
																					matrix[i][j] += min(matrix[i - 1][j]							,    matrix[i][j - 1] )

							return matrix[-1][-1]


if __name__ == "__main__":
		import doctest

		doctest.testmod()


"""simple docstring"""







from __future__ import annotations

_SCREAMING_SNAKE_CASE	       =      {
    """A""": ["""B""", """C""", """E"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F""", """G"""],
    """D""": ["""B"""],
    """E""": ["""A""", """B""", """D"""],
    """F""": ["""C"""],
    """G""": ["""C"""],
}







class 							__magic_name__     :





					def __init__(				self   :							Any							,						snake_case_   :							dict[str, list[str]]							,						snake_case_   :							str    ):
												__snake_case     			=       graph
												# mapping node to its parent in resulting breadth first tree
												__snake_case     			=       {}
												__snake_case     			=       source_vertex





					def 							lowerCAmelCase      (				self   :							Union[str, Any]    ):
												__snake_case     			=       {self.source_vertex}
												__snake_case     			=       None
												__snake_case     			=       [self.source_vertex]  # first in first out queue

												while queue:
																			__snake_case     			=       queue.pop(0    )
																			for adjacent_vertex in self.graph[vertex]:
																										if adjacent_vertex not in visited:
																																	visited.add(snake_case_    )
																																	__snake_case     			=       vertex
																																	queue.append(snake_case_    )





					def 							lowerCAmelCase      (				self   :							Dict							,						snake_case_   :							str    ):
												if target_vertex == self.source_vertex:
																			return self.source_vertex

												__snake_case     			=       self.parent.get(snake_case_    )
												if target_vertex_parent is None:
																			__snake_case     			=       (
																			    F'''No path from vertex: {self.source_vertex} to vertex: {target_vertex}'''
																			)
																			raise ValueError(snake_case_    )

												return self.shortest_path(snake_case_    ) + F'''->{target_vertex}'''


if __name__ == "__main__":
		_SCREAMING_SNAKE_CASE	       =      Graph(graph, """G""")
		g.breath_first_search()
		print(g.shortest_path("""D"""))
		print(g.shortest_path("""G"""))
		print(g.shortest_path("""Foo"""))
