


from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray

def       lowercase_		(		_A			:    float    ,					_A			:    float    ,					_A			:    bool = False						):

      """simple docstring"""




      if radian_mode:
            return [magnitude * cos(_A						), magnitude * sin(_A						)]
      return [magnitude * cos(radians(_A						)						), magnitude * sin(radians(_A						)						)]

def       lowercase_		(		_A			:    NDArray[floataa]    ,					_A			:    NDArray[floataa]    ,					_A			:    float = 10**-1						):

      """simple docstring"""




      lowerCamelCase__		:				NDArray[floataa]    =  cross(_A    ,					_A						)
      lowerCamelCase__		:				float    =  sum(_A						)
      return abs(_A						) < eps


if __name__ == "__main__":
    # Test to check if it works
    A      :    Union[str, Any]		=					array(
        [
            polar_force(7_1_8.4, 180 - 30),
            polar_force(8_7_9.5_4, 45),
            polar_force(100, -90),
        ]
    )

    A      :    NDArray[floataa]		=					array([[0, 0], [0, 0], [0, 0]])

    assert in_static_equilibrium(forces, location)

    # Problem 1 in image_data/2D_problems.jpg
    A      :    Dict		=					array(
        [
            polar_force(30 * 9.8_1, 15),
            polar_force(215, 180 - 45),
            polar_force(264, 90 - 30),
        ]
    )

    A      :    Dict		=					array([[0, 0], [0, 0], [0, 0]])

    assert in_static_equilibrium(forces, location)

    # Problem in image_data/2D_problems_1.jpg
    A      :    List[str]		=					array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])

    A      :    Any		=					array([[0, 0], [6, 0], [10, 0], [12, 0]])

    assert in_static_equilibrium(forces, location)

    import doctest

    doctest.testmod()






from __future__ import annotations

A      :    Union[str, Any]		=					{
    "A": ["B", "C", "E"],
    "B": ["A", "D", "E"],
    "C": ["A", "F", "G"],
    "D": ["B"],
    "E": ["A", "B", "D"],
    "F": ["C"],
    "G": ["C"],
}







class 			_lowercase :


       """simple docstring"""




       def __init__(   self							:			Tuple					,      __lowerCamelCase							:			dict[str, list[str]]					,      __lowerCamelCase							:			str       ):


             '''simple docstring'''



             lowerCamelCase__		:				Union[str, Any]    =  graph
             # mapping node to its parent in resulting breadth first tree
             lowerCamelCase__		:				dict[str, str | None]    =  {}
             lowerCamelCase__		:				Dict    =  source_vertex





       def 						lowerCAmelCase     (   self							:			Any       ):


             '''simple docstring'''



             lowerCamelCase__		:				int    =  {self.source_vertex}
             lowerCamelCase__		:				Optional[int]    =  None
             lowerCamelCase__		:				Dict    =  [self.source_vertex]  # first in first out queue

             while queue:
                   lowerCamelCase__		:				Optional[int]    =  queue.pop(0       )
                   for adjacent_vertex in self.graph[vertex]:
                         if adjacent_vertex not in visited:
                               visited.add(__lowerCamelCase       )
                               lowerCamelCase__		:				List[str]    =  vertex
                               queue.append(__lowerCamelCase       )





       def 						lowerCAmelCase     (   self							:			Optional[Any]					,      __lowerCamelCase							:			str       ):


             '''simple docstring'''



             if target_vertex == self.source_vertex:
                   return self.source_vertex

             lowerCamelCase__		:				Tuple    =  self.parent.get(__lowerCamelCase       )
             if target_vertex_parent is None:
                   lowerCamelCase__		:				Tuple    =  (
                       f"No path from vertex: {self.source_vertex} to vertex: {target_vertex}"
                   )
                   raise ValueError(__lowerCamelCase       )

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


if __name__ == "__main__":
    A      :    List[str]		=					Graph(graph, "G")
    g.breath_first_search()
    print(g.shortest_path("D"))
    print(g.shortest_path("G"))
    print(g.shortest_path("Foo"))


