




'''simple docstring'''






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
_lowerCAmelCase       =   20

# Time between time steps in seconds
_lowerCAmelCase       =   INTERVAL / 1000



class    A						:




				'''simple docstring'''





				def __init__(self					,    _UpperCAmelCase					,    _UpperCAmelCase					,    _UpperCAmelCase					,    _UpperCAmelCase					,    _UpperCAmelCase = 1.0					,    _UpperCAmelCase = 1.0					,    _UpperCAmelCase = "blue"					,    )      ->			None:
							__UpperCamelCase :     int										=  position_x
							__UpperCamelCase :     Optional[Any]										=  position_y
							__UpperCamelCase :     Optional[Any]										=  velocity_x
							__UpperCamelCase :     List[str]										=  velocity_y
							__UpperCamelCase :     Optional[Any]										=  mass
							__UpperCamelCase :     int										=  size
							__UpperCamelCase :     int										=  color
				@property
				def 			a_			(self     )      ->			tuple[float, float]:
							return self.position_x, self.position_y
				@property
				def 			a_			(self     )      ->			tuple[float, float]:
							return self.velocity_x, self.velocity_y
				def 			a_			(self					,    _UpperCAmelCase					,    _UpperCAmelCase					,    _UpperCAmelCase     )      ->			None:
							self.velocity_x += force_x * delta_time
							self.velocity_y += force_y * delta_time





				def 			a_			(self					,    _UpperCAmelCase     )      ->			None:
							self.position_x += self.velocity_x * delta_time
							self.position_y += self.velocity_y * delta_time







class    A						:




				'''simple docstring'''





				def __init__(self					,    _UpperCAmelCase					,    _UpperCAmelCase = 1.0					,    _UpperCAmelCase = 1.0					,    _UpperCAmelCase = 0.0					,    )      ->			None:
							__UpperCamelCase :     List[Any]										=  bodies
							__UpperCamelCase :     Optional[int]										=  gravitation_constant
							__UpperCamelCase :     List[Any]										=  time_factor
							__UpperCamelCase :     Dict										=  softening_factor
				def __len__(self     )      ->			int:
							return len(self.bodies     )





				def 			a_			(self					,    _UpperCAmelCase     )      ->			None:
							for bodya in self.bodies:
										__UpperCamelCase :     str										=  0.0
										__UpperCamelCase :     Dict										=  0.0
										for bodya in self.bodies:
													if bodya != bodya:
																__UpperCamelCase :     Dict										=  bodya.position_x - bodya.position_x
																__UpperCamelCase :     int										=  bodya.position_y - bodya.position_y

																# Calculation of the distance using Pythagoras's theorem
																# Extra factor due to the softening technique
																__UpperCamelCase :     str										=  (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      __lowerCAmelCase   (       snake_case__   , snake_case__   , snake_case__		):
			body_system.update_system(snake_case__		)

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

def      __lowerCAmelCase   (       snake_case__   , snake_case__   , snake_case__ = -1   , snake_case__ = 1   , snake_case__ = -1   , snake_case__ = 1   , ):
			__UpperCamelCase :     List[Any]										=  plt.figure()
			fig.canvas.set_window_title(snake_case__		)
			__UpperCamelCase :     int										=  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
			__UpperCamelCase :     Optional[Any]										=  [
			    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(snake_case__		)

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

			__UpperCamelCase :     Any										=  animation.FuncAnimation(  # noqa: F841
			    snake_case__   , snake_case__   , interval=snake_case__   , blit=snake_case__		)

			plt.show()

def      __lowerCAmelCase   (       ):
			__UpperCamelCase :     int										=  0.9700436
			__UpperCamelCase :     Dict										=  -0.24308753
			__UpperCamelCase :     Union[str, Any]										=  0.466203685
			__UpperCamelCase :     Union[str, Any]										=  0.43236573

			__UpperCamelCase :     List[Any]										=  [
			    Body(snake_case__   , snake_case__   , snake_case__   , snake_case__   , size=0.2   , color="red"		),
			    Body(-position_x   , -position_y   , snake_case__   , snake_case__   , size=0.2   , color="green"		),
			    Body(0   , 0   , -2 * velocity_x   , -2 * velocity_y   , size=0.2   , color="blue"		),
			]
			return BodySystem(snake_case__   , time_factor=3		)

def      __lowerCAmelCase   (       ):
			__UpperCamelCase :     List[Any]										=  7.34_76E22
			__UpperCamelCase :     Optional[Any]										=  5.9_72E24
			__UpperCamelCase :     Any										=  1_022
			__UpperCamelCase :     Tuple										=  384_399_000
			__UpperCamelCase :     List[str]										=  6.6_74E-11

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

			__UpperCamelCase :     str										=  Body(-earth_moon_distance   , 0   , 0   , snake_case__   , snake_case__   , 10_000_000   , "grey"		)
			__UpperCamelCase :     Optional[int]										=  Body(0   , 0   , 0   , snake_case__   , snake_case__   , 50_000_000   , "blue"		)
			return BodySystem([earth, moon]   , snake_case__   , time_factor=1_000_000		)

def      __lowerCAmelCase   (       ):
			__UpperCamelCase :     Any										=  []
			for _ in range(10		):
						__UpperCamelCase :     int										=  random.uniform(-0.5   , 0.5		)
						__UpperCamelCase :     int										=  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		)   , snake_case__   , snake_case__   , 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(snake_case__   , 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(),
				    -430000000,
				    430000000,
				    -430000000,
				    430000000,
				)
				plot('''Random system with many bodies''', example_a(), -1.5, 1.5, -1.5, 1.5)









'''simple docstring'''






def      __lowerCAmelCase   (       snake_case__		):
			__UpperCamelCase :     int										=  word.upper()
			__UpperCamelCase :     List[str]										=  0
			__UpperCamelCase :     int										=  {}
			__UpperCamelCase :     Tuple										=  []

			for letter in word:
						if letter not in letter_nums:
									__UpperCamelCase :     Tuple										=  str(snake_case__		)
									next_num += 1
						word_pattern.append(letter_nums[letter]		)
			return ".".join(snake_case__		)


if __name__ == "__main__":
				import pprint
				import time

				_lowerCAmelCase       =   time.time()
				with open('''dictionary.txt''') as in_file:
								_lowerCAmelCase       =   in_file.read().splitlines()

				_lowerCAmelCase       =   {}
				for word in word_list:
								_lowerCAmelCase       =   get_word_pattern(word)
								if pattern in all_patterns:
												all_patterns[pattern].append(word)
								else:
												_lowerCAmelCase       =   [word]

				with open('''word_patterns.txt''', '''w''') as out_file:
								out_file.write(pprint.pformat(all_patterns))

				_lowerCAmelCase       =   round(time.time() - start_time, 2)
				print(f'Done!  {len(all_patterns):,} word patterns found in {total_time} seconds.')
				# Done!  9,581 word patterns found in 0.58 seconds.



