


"""simple docstring"""







# using dfs for finding eulerian path traversal


def      lowercase			(				A_  ,   A_  ,   A_  ,   A_=None       )->      Dict:
  '''simple docstring'''







  a						:		Tuple      							=			(path or []) + [u]
  for v in graph[u]:
    if visited_edge[u][v] is False:
      a							,		a						:		Optional[Any]      							=			True, True
      a						:		List[str]      							=			dfs(A_  ,   A_  ,   A_  ,   A_       )
  return path


def      lowercase			(				A_  ,   A_       )->      Optional[int]:
  '''simple docstring'''







  a						:		Any      							=			0
  a						:		Dict      							=			-1
  for i in range(A_       ):
    if i not in graph.keys():
      continue
    if len(graph[i]       ) % 2 == 1:
      odd_degree_nodes += 1
      a						:		str      							=			i
  if odd_degree_nodes == 0:
    return 1, odd_node
  if odd_degree_nodes == 2:
    return 2, odd_node
  return 3, odd_node


def      lowercase			(				A_  ,   A_       )->      int:
  '''simple docstring'''







  a						:		Tuple      							=			[[False for _ in range(max_node + 1       )] for _ in range(max_node + 1       )]
  a							,		a						:		Optional[Any]      							=			check_circuit_or_path(A_  ,   A_       )
  if check == 3:
    print("graph is not Eulerian"       )
    print("no path"       )
    return
  a						:		Any      							=			1
  if check == 2:
    a						:		List[Any]      							=			odd_node
    print("graph has a Euler path"       )
  if check == 1:
    print("graph has a Euler cycle"       )
  a						:		Optional[Any]      							=			dfs(A_  ,   A_  ,   A_       )
  print(A_       )


def      lowercase			(				)->      Tuple:
  '''simple docstring'''







  a						:		Optional[Any]      							=			{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
  a						:		Union[str, Any]      							=			{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
  a						:		str      							=			{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
  a						:		Dict      							=			{1: [2, 3], 2: [1, 3], 3: [1, 2]}
  a						:		Dict      							=			{
      1: [],
      2: []
      # all degree is zero
  }
  a						:		int      							=			10
  check_euler(A_  ,   A_       )
  check_euler(A_  ,   A_       )
  check_euler(A_  ,   A_       )
  check_euler(A_  ,   A_       )
  check_euler(A_  ,   A_       )


if __name__ == "__main__":
 main()










"""simple docstring"""







from __future__ import annotations

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


def      lowercase			(				A_  ,   A_  ,   A_ = False       )->      list[float]:
  '''simple docstring'''







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


def      lowercase			(				A_  ,   A_  ,   A_ = 10**-1       )->      bool:
  '''simple docstring'''







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


if __name__ == "__main__":
 # Test to check if it works
 __lowercase    					=      array(
     [
         polar_force(7_18.4, 180 - 30),
         polar_force(8_79.54, 45),
         polar_force(100, -90),
     ]
 )

 __lowercase    					=      array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

 # Problem 1 in image_data/2D_problems.jpg
 __lowercase    					=      array(
     [
         polar_force(30 * 9.81, 15),
         polar_force(215, 180 - 45),
         polar_force(264, 90 - 30),
     ]
 )

 __lowercase    					=      array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

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

 __lowercase    					=      array([[0, 0], [6, 0], [10, 0], [12, 0]])

 assert in_static_equilibrium(forces, location)

 import doctest

 doctest.testmod()






