


"""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       lowerCamelCase_		:





				"""simple docstring"""







				def __init__(    self							,		UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__ = 1.0							,		UpperCAmelCase__ = 1.0							,		UpperCAmelCase__ = "blue"							,		):
								SCREAMING_SNAKE_CASE__  				=					position_x
								SCREAMING_SNAKE_CASE__  				=					position_y
								SCREAMING_SNAKE_CASE__  				=					velocity_x
								SCREAMING_SNAKE_CASE__  				=					velocity_y
								SCREAMING_SNAKE_CASE__  				=					mass
								SCREAMING_SNAKE_CASE__  				=					size
								SCREAMING_SNAKE_CASE__  				=					color



				@property
				def 	lowerCAmelCase__		(    self  ):
								return self.position_x, self.position_y



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



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__  ):
								self.velocity_x += force_x * delta_time
								self.velocity_y += force_y * delta_time






				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								self.position_x += self.velocity_x * delta_time
								self.position_y += self.velocity_y * delta_time


class       lowerCamelCase_		:





				"""simple docstring"""







				def __init__(    self							,		UpperCAmelCase__							,		UpperCAmelCase__ = 1.0							,		UpperCAmelCase__ = 1.0							,		UpperCAmelCase__ = 0.0							,		):
								SCREAMING_SNAKE_CASE__  				=					bodies
								SCREAMING_SNAKE_CASE__  				=					gravitation_constant
								SCREAMING_SNAKE_CASE__  				=					time_factor
								SCREAMING_SNAKE_CASE__  				=					softening_factor



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






				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								for bodya in self.bodies:
												SCREAMING_SNAKE_CASE__  				=					0.0
												SCREAMING_SNAKE_CASE__  				=					0.0
												for bodya in self.bodies:
																if bodya != bodya:
																				SCREAMING_SNAKE_CASE__  				=					bodya.position_x - bodya.position_x
																				SCREAMING_SNAKE_CASE__  				=					bodya.position_y - bodya.position_y

																				# Calculation of the distance using Pythagoras's theorem
																				# Extra factor due to the softening technique
																				SCREAMING_SNAKE_CASE__  				=					(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 __lowercase  (   lowerCamelCase_	:   BodySystem    ,       lowerCamelCase_	:   float    ,       lowerCamelCase_	:   list[plt.Circle]	):
				body_system.update_system(lowerCamelCase_	)

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


def __lowercase  (   lowerCamelCase_	:   str    ,       lowerCamelCase_	:   BodySystem    ,       lowerCamelCase_	:   float = -1    ,       lowerCamelCase_	:   float = 1    ,       lowerCamelCase_	:   float = -1    ,       lowerCamelCase_	:   float = 1    ,       ):
				SCREAMING_SNAKE_CASE__  				=					plt.figure()
				fig.canvas.set_window_title(lowerCamelCase_	)
				SCREAMING_SNAKE_CASE__  				=					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
				SCREAMING_SNAKE_CASE__  				=					[
				    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(lowerCamelCase_	)

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

				SCREAMING_SNAKE_CASE__  				=					animation.FuncAnimation(  # noqa: F841
				    lowerCamelCase_    ,       lowerCamelCase_    ,       interval=lowerCamelCase_    ,       blit=lowerCamelCase_	)

				plt.show()


def __lowercase  (   ):
				SCREAMING_SNAKE_CASE__  				=					0.970_0436
				SCREAMING_SNAKE_CASE__  				=					-0.2430_8753
				SCREAMING_SNAKE_CASE__  				=					0.4_6620_3685
				SCREAMING_SNAKE_CASE__  				=					0.4323_6573

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


def __lowercase  (   ):
				SCREAMING_SNAKE_CASE__  				=					7.3_4_7_6e2_2
				SCREAMING_SNAKE_CASE__  				=					5.9_7_2e2_4
				SCREAMING_SNAKE_CASE__  				=					1022
				SCREAMING_SNAKE_CASE__  				=					384399000
				SCREAMING_SNAKE_CASE__  				=					6.6_7_4e-1_1

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

				SCREAMING_SNAKE_CASE__  				=					Body(-earth_moon_distance    ,       0    ,       0    ,       lowerCamelCase_    ,       lowerCamelCase_    ,       10000000    ,       "grey"	)
				SCREAMING_SNAKE_CASE__  				=					Body(0    ,       0    ,       0    ,       lowerCamelCase_    ,       lowerCamelCase_    ,       50000000    ,       "blue"	)
				return BodySystem([earth, moon]    ,       lowerCamelCase_    ,       time_factor=1000000	)


def __lowercase  (   ):
				SCREAMING_SNAKE_CASE__  				=					[]
				for _ in range(10	):
								SCREAMING_SNAKE_CASE__  				=					random.uniform(-0.5    ,       0.5	)
								SCREAMING_SNAKE_CASE__  				=					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	)    ,       lowerCamelCase_    ,       lowerCamelCase_    ,       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(lowerCamelCase_    ,       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"""






from __future__ import annotations

import sys


class       lowerCamelCase_		:





				"""simple docstring"""







				def __init__(    self							,		UpperCAmelCase__							,		UpperCAmelCase__  ):
								SCREAMING_SNAKE_CASE__  				=					letter
								SCREAMING_SNAKE_CASE__  				=					freq
								SCREAMING_SNAKE_CASE__  				=					{}






				def __repr__(    self  ):
								return f'''{self.letter}:{self.freq}'''


class       lowerCamelCase_		:





				"""simple docstring"""







				def __init__(    self							,		UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__  ):
								SCREAMING_SNAKE_CASE__  				=					freq
								SCREAMING_SNAKE_CASE__  				=					left
								SCREAMING_SNAKE_CASE__  				=					right


def __lowercase  (   lowerCamelCase_	:   str	):
				SCREAMING_SNAKE_CASE__  				=					{}
				with open(lowerCamelCase_	) as f:
								while True:
												SCREAMING_SNAKE_CASE__  				=					f.read(1	)
												if not c:
																break
												SCREAMING_SNAKE_CASE__  				=					chars[c] + 1 if c in chars else 1
				return sorted((Letter(lowerCamelCase_    ,       lowerCamelCase_	) for c, f in chars.items())    ,       key=lambda lowerCamelCase_	: x.freq	)


def __lowercase  (   lowerCamelCase_	:   list[Letter]	):
				SCREAMING_SNAKE_CASE__  				=					letters  # type: ignore
				while len(lowerCamelCase_	) > 1:
								SCREAMING_SNAKE_CASE__  				=					response.pop(0	)
								SCREAMING_SNAKE_CASE__  				=					response.pop(0	)
								SCREAMING_SNAKE_CASE__  				=					left.freq + right.freq
								SCREAMING_SNAKE_CASE__  				=					TreeNode(lowerCamelCase_    ,       lowerCamelCase_    ,       lowerCamelCase_	)
								response.append(lowerCamelCase_	)
								response.sort(key=lambda lowerCamelCase_	: x.freq	)
				return response[0]


def __lowercase  (   lowerCamelCase_	:   Letter | TreeNode    ,       lowerCamelCase_	:   str	):
				if isinstance(lowerCamelCase_    ,       lowerCamelCase_	):
								SCREAMING_SNAKE_CASE__  				=					bitstring
								return [root]
				SCREAMING_SNAKE_CASE__  				=					root  # type: ignore
				SCREAMING_SNAKE_CASE__  				=					[]
				letters += traverse_tree(treenode.left    ,       bitstring + "0"	)
				letters += traverse_tree(treenode.right    ,       bitstring + "1"	)
				return letters


def __lowercase  (   lowerCamelCase_	:   str	):
				SCREAMING_SNAKE_CASE__  				=					parse_file(lowerCamelCase_	)
				SCREAMING_SNAKE_CASE__  				=					build_tree(lowerCamelCase_	)
				SCREAMING_SNAKE_CASE__  				=					{
				    k: v for letter in traverse_tree(lowerCamelCase_    ,       ""	) for k, v in letter.bitstring.items()
				}
				print(F'''Huffman Coding  of {file_path}: '''	)
				with open(lowerCamelCase_	) as f:
								while True:
												SCREAMING_SNAKE_CASE__  				=					f.read(1	)
												if not c:
																break
												print(letters[c]    ,       end=" "	)
				print()


if __name__ == "__main__":
	# pass the file path to the huffman function
	huffman(sys.argv[1])
