





from __future__ import annotations

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







def  _SCREAMING_SNAKE_CASE				(   a					,						a					,						a = False  )      ->      list[float]:
					if radian_mode:
										return [magnitude * cos(a  ), magnitude * sin(a  )]
					return [magnitude * cos(radians(a  )  ), magnitude * sin(radians(a  )  )]







def  _SCREAMING_SNAKE_CASE				(   a					,						a					,						a = 10**-1  )      ->      bool:
					__A	:						NDArray[floataa]       =				cross(a					,						a  )
					__A	:						float       =				sum(a  )
					return abs(a  ) < eps


if __name__ == "__main__":
				# Test to check if it works
				UpperCAmelCase						:   Tuple			  =     array(
				    [
				        polar_force(718.4, 1_80 - 30),
				        polar_force(879.54, 45),
				        polar_force(1_00, -90),
				    ]
				)

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

				assert in_static_equilibrium(forces, location)

				# Problem 1 in image_data/2D_problems.jpg
				UpperCAmelCase						:   Dict			  =     array(
				    [
				        polar_force(30 * 9.81, 15),
				        polar_force(2_15, 1_80 - 45),
				        polar_force(2_64, 90 - 30),
				    ]
				)

				UpperCAmelCase						:   List[Any]			  =     array([[0, 0], [0, 0], [0, 0]])

				assert in_static_equilibrium(forces, location)

				# Problem in image_data/2D_problems_1.jpg
				UpperCAmelCase						:   Dict			  =     array([[0, -20_00], [0, -12_00], [0, 1_56_00], [0, -1_24_00]])

				UpperCAmelCase						:   int			  =     array([[0, 0], [6, 0], [10, 0], [12, 0]])

				assert in_static_equilibrium(forces, location)

				import doctest

				doctest.testmod()











from heapq import heappop, heappush

import numpy as np







def  _SCREAMING_SNAKE_CASE				(   a					,						a					,						a					,						a					,						)      ->      tuple[float | int, list[tuple[int, int]]]:
					__A    ,				__A	:						int       =				grid.shape
					__A	:						Any       =				[-1, 1, 0, 0]
					__A	:						Optional[Any]       =				[0, 0, -1, 1]
					if allow_diagonal:
										dx += [-1, -1, 1, 1]
										dy += [-1, 1, -1, 1]

					__A    ,				__A	:						Optional[int]       =				[(0, source)], set()
					__A	:						Any       =				np.full((rows, cols)					,						np.inf  )
					__A	:						Any       =				0
					__A	:						Any       =				np.empty((rows, cols)					,						dtype=a  )
					__A	:						Optional[Any]       =				None

					while queue:
										((__A)    ,				(__A))	:						List[str]       =				heappop(a  )
										if (x, y) in visited:
															continue
										visited.add((x, y)  )

										if (x, y) == destination:
															__A	:						int       =				[]
															while (x, y) != source:
																				path.append((x, y)  )
																				__A    ,				__A	:						Optional[int]       =				predecessors[x, y]
															path.append(a  )  # add the source manually
															path.reverse()
															return matrix[destination], path

										for i in range(len(a  )  ):
															__A    ,				__A	:						Union[str, Any]       =				x + dx[i], y + dy[i]
															if 0 <= nx < rows and 0 <= ny < cols:
																				__A	:						Optional[int]       =				grid[nx][ny]
																				if next_node == 1 and matrix[nx, ny] > dist + 1:
																									heappush(a					,						(dist + 1, (nx, ny))  )
																									__A	:						List[Any]       =				dist + 1
																									__A	:						Union[str, Any]       =				(x, y)

					return np.inf, []


if __name__ == "__main__":
				import doctest

				doctest.testmod()




