





"""simple docstring"""
from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
_snake_case					:		Dict							=			20

# Time between time steps in seconds
_snake_case					:		Union[str, Any]							=			INTERVAL / 1000






class  _UpperCAmelCase       :


					def __init__( self      :Dict					,	__UpperCamelCase      :float					,	__UpperCamelCase      :float					,	__UpperCamelCase      :float					,	__UpperCamelCase      :float					,	__UpperCamelCase      :float = 1.0					,	__UpperCamelCase      :float = 1.0					,	__UpperCamelCase      :str = "blue"					,	):
												A		=  position_x
												A		=  position_y
												A		=  velocity_x
												A		=  velocity_y
												A		=  mass
												A		=  size
												A		=  color


					@property
					def      lowerCamelCase	( self      :Union[str, Any]		):
												return self.position_x, self.position_y


					@property
					def      lowerCamelCase	( self      :int		):
												return self.velocity_x, self.velocity_y


					def      lowerCamelCase	( self      :Optional[int]					,	__UpperCamelCase      :float					,	__UpperCamelCase      :float					,	__UpperCamelCase      :float		):
												self.velocity_x += force_x * delta_time
												self.velocity_y += force_y * delta_time


					def      lowerCamelCase	( self      :List[str]					,	__UpperCamelCase      :float		):
												self.position_x += self.velocity_x * delta_time
												self.position_y += self.velocity_y * delta_time







class  _UpperCAmelCase       :


					def __init__( self      :List[str]					,	__UpperCamelCase      :list[Body]					,	__UpperCamelCase      :float = 1.0					,	__UpperCamelCase      :float = 1.0					,	__UpperCamelCase      :float = 0.0					,	):
												A		=  bodies
												A		=  gravitation_constant
												A		=  time_factor
												A		=  softening_factor


					def __len__( self      :Any		):
												return len(self.bodies		)


					def      lowerCamelCase	( self      :Tuple					,	__UpperCamelCase      :float		):
												for bodya in self.bodies:
																			A		=  0.0
																			A		=  0.0
																			for bodya in self.bodies:
																										if bodya != bodya:
																																	A		=  bodya.position_x - bodya.position_x
																																	A		=  bodya.position_y - bodya.position_y

																																	# Calculation of the distance using Pythagoras's theorem
																																	# Extra factor due to the softening technique
																																	A		=  (dif_x**2 + dif_y**2 + self.softening_factor) ** (
																																	    1 / 2
																																	)

																																	# Newton's law of universal gravitation.
																																	force_x += (
																																	    self.gravitation_constant * bodya.mass * dif_x / distance**3
																																	)
																																	force_y += (
																																	    self.gravitation_constant * bodya.mass * dif_y / distance**3
																																	)

            # Update the body's velocity once all the force components have been added
																			bodya.update_velocity(__UpperCamelCase					,	__UpperCamelCase					,	delta_time * self.time_factor		)

												# Update the positions only after all the velocities have been updated
												for body in self.bodies:
																			body.update_position(delta_time * self.time_factor		)







def  A__    (      UpperCamelCase ,  UpperCamelCase ,  UpperCamelCase	):
							body_system.update_system(UpperCamelCase	)

							# Update the positions of the patches
							for patch, body in zip(UpperCamelCase ,  body_system.bodies	):
														A		=  (body.position_x, body.position_y)






def  A__    (      UpperCamelCase ,  UpperCamelCase ,  UpperCamelCase = -1 ,  UpperCamelCase = 1 ,  UpperCamelCase = -1 ,  UpperCamelCase = 1 ,  ):
							A		=  plt.figure()
							fig.canvas.set_window_title(UpperCamelCase	)
							A		=  plt.axes(
							    xlim=(x_start, x_end) ,  ylim=(y_start, y_end)	)  # Set section to be plotted
							plt.gca().set_aspect("equal"	)  # Fix aspect ratio

							# Each body is drawn as a patch by the plt-function
							A		=  [
							    plt.Circle((body.position_x, body.position_y) ,  body.size ,  fc=body.color	)
							    for body in body_system.bodies
							]

							for patch in patches:
														ax.add_patch(UpperCamelCase	)

							# Function called at each step of the animation
							def update(UpperCamelCase	) -> list[plt.Circle]:
														update_step(UpperCamelCase ,  UpperCamelCase ,  UpperCamelCase	)
														return patches

							A		=  animation.FuncAnimation(  # noqa: F841
							    UpperCamelCase ,  UpperCamelCase ,  interval=UpperCamelCase ,  blit=UpperCamelCase	)

							plt.show()






def  A__    (      ):
							A		=  0.9_70_04_36
							A		=  -0.24_30_87_53
							A		=  0.4_66_20_36_85
							A		=  0.43_23_65_73

							A		=  [
							    Body(UpperCamelCase ,  UpperCamelCase ,  UpperCamelCase ,  UpperCamelCase ,  size=0.2 ,  color="red"	),
							    Body(-position_x ,  -position_y ,  UpperCamelCase ,  UpperCamelCase ,  size=0.2 ,  color="green"	),
							    Body(0 ,  0 ,  -2 * velocity_x ,  -2 * velocity_y ,  size=0.2 ,  color="blue"	),
							]
							return BodySystem(UpperCamelCase ,  time_factor=3	)






def  A__    (      ):
							A		=  7.3476E22
							A		=  5.972E24
							A		=  1_022
							A		=  384_399_000
							A		=  6.674E-11

							# Calculation of the respective velocities so that total impulse is zero,
							# i.e. the two bodies together don't move
							A		=  earth_mass * velocity_dif / (earth_mass + moon_mass)
							A		=  moon_velocity - velocity_dif

							A		=  Body(-earth_moon_distance ,  0 ,  0 ,  UpperCamelCase ,  UpperCamelCase ,  10_000_000 ,  "grey"	)
							A		=  Body(0 ,  0 ,  0 ,  UpperCamelCase ,  UpperCamelCase ,  50_000_000 ,  "blue"	)
							return BodySystem([earth, moon] ,  UpperCamelCase ,  time_factor=1_000_000	)






def  A__    (      ):
							A		=  []
							for _ in range(10	):
														A		=  random.uniform(-0.5 ,  0.5	)
														A		=  random.uniform(-0.5 ,  0.5	)

														# Bodies are created pairwise with opposite velocities so that the
														# total impulse remains zero
														bodies.append(
														    Body(
														        random.uniform(-0.5 ,  0.5	) ,  random.uniform(-0.5 ,  0.5	) ,  UpperCamelCase ,  UpperCamelCase ,  size=0.05 ,  )	)
														bodies.append(
														    Body(
														        random.uniform(-0.5 ,  0.5	) ,  random.uniform(-0.5 ,  0.5	) ,  -velocity_x ,  -velocity_y ,  size=0.05 ,  )	)
							return BodySystem(UpperCamelCase ,  0.01 ,  10 ,  0.1	)


if __name__ == "__main__":
		plot('Figure-8 solution to the 3-body-problem', example_a(), -2, 2, -2, 2)
		plot(
		    'Moon\'s orbit around the earth',
		    example_a(),
		    -4_3000_0000,
		    4_3000_0000,
		    -4_3000_0000,
		    4_3000_0000,
		)
		plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)









"""simple docstring"""
from __future__ import annotations






class  _UpperCAmelCase       :


					def __init__( self      :Optional[Any]					,	__UpperCamelCase      :int		):
												A		=  vertices
												A		=  [[0] * vertices for _ in range(__UpperCamelCase		)]


					def      lowerCamelCase	( self      :Optional[Any]					,	__UpperCamelCase      :list[int]		):
												print("Vertex \t Distance from Source"		)
												for vertex in range(self.vertices		):
																			print(__UpperCamelCase					,	"\t\t"					,	distances_from_source[vertex]		)


					def      lowerCamelCase	( self      :Union[str, Any]					,	__UpperCamelCase      :list[int]					,	__UpperCamelCase      :list[bool]		):
												A		=  1e7
												A		=  0

												# Search not nearest vertex not in the shortest path tree
												for vertex in range(self.vertices		):
																			if distances_from_source[vertex] < minimum and visited[vertex] is False:
																										A		=  distances_from_source[vertex]
																										A		=  vertex
												return min_index


					def      lowerCamelCase	( self      :List[Any]					,	__UpperCamelCase      :int		):
												A		=  [int(1e7		)] * self.vertices  # distances from the source
												A		=  0
												A		=  [False] * self.vertices

												for _ in range(self.vertices		):
																			A		=  self.minimum_distance(__UpperCamelCase					,	__UpperCamelCase		)
																			A		=  True

																			# Update dist value of the adjacent vertices
																			# of the picked vertex only if the current
																			# distance is greater than new distance and
																			# the vertex in not in the shortest path tree
																			for v in range(self.vertices		):
																										if (
																										    self.graph[u][v] > 0
																										    and visited[v] is False
																										    and distances[v] > distances[u] + self.graph[u][v]
																										):
																																	A		=  distances[u] + self.graph[u][v]

												self.print_solution(__UpperCamelCase		)


if __name__ == "__main__":
		_snake_case					:		List[Any]							=			Graph(9)
		_snake_case					:		List[str]							=			[
		    [0, 4, 0, 0, 0, 0, 0, 8, 0],
		    [4, 0, 8, 0, 0, 0, 0, 11, 0],
		    [0, 8, 0, 7, 0, 4, 0, 0, 2],
		    [0, 0, 7, 0, 9, 14, 0, 0, 0],
		    [0, 0, 0, 9, 0, 10, 0, 0, 0],
		    [0, 0, 4, 14, 10, 0, 2, 0, 0],
		    [0, 0, 0, 0, 0, 2, 0, 1, 6],
		    [8, 11, 0, 0, 0, 0, 1, 0, 7],
		    [0, 0, 2, 0, 0, 0, 6, 7, 0],
		]
		graph.dijkstra(0)


