from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
a     :			Any					    =						2_0

# Time between time steps in seconds
a     :			Optional[Any]					    =						INTERVAL / 1_0_0_0

class 				_lowercase						:






    '''simple docstring'''




    def __init__(						self					,	lowerCamelCase__					,	lowerCamelCase__					,	lowerCamelCase__					,	lowerCamelCase__					,	lowerCamelCase__ = 1.0					,	lowerCamelCase__ = 1.0					,	lowerCamelCase__ = "blue"					,	):
       lowerCAmelCase_:       List[str]         =  position_x
       lowerCAmelCase_:       Tuple         =  position_y
       lowerCAmelCase_:       List[str]         =  velocity_x
       lowerCAmelCase_:       Tuple         =  velocity_y
       lowerCAmelCase_:       int         =  mass
       lowerCAmelCase_:       Tuple         =  size
       lowerCAmelCase_:       Dict         =  color




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




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




    def     _a						(						self					,	lowerCamelCase__					,	lowerCamelCase__					,	lowerCamelCase__   ):
       self.velocity_x += force_x * delta_time
       self.velocity_y += force_y * delta_time




    def     _a						(						self					,	lowerCamelCase__   ):
       self.position_x += self.velocity_x * delta_time
       self.position_y += self.velocity_y * delta_time





class 				_lowercase						:






    '''simple docstring'''




    def __init__(						self					,	lowerCamelCase__					,	lowerCamelCase__ = 1.0					,	lowerCamelCase__ = 1.0					,	lowerCamelCase__ = 0.0					,	):
       lowerCAmelCase_:       Optional[Any]         =  bodies
       lowerCAmelCase_:       Union[str, Any]         =  gravitation_constant
       lowerCAmelCase_:       Optional[Any]         =  time_factor
       lowerCAmelCase_:       Any         =  softening_factor




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




    def     _a						(						self					,	lowerCamelCase__   ):
       for bodya in self.bodies:
          lowerCAmelCase_:       List[Any]         =  0.0
          lowerCAmelCase_:       Union[str, Any]         =  0.0
          for bodya in self.bodies:
             if bodya != bodya:
                lowerCAmelCase_:       int         =  bodya.position_x - bodya.position_x
                lowerCAmelCase_:       str         =  bodya.position_y - bodya.position_y

                # Calculation of the distance using Pythagoras's theorem
                # Extra factor due to the softening technique
                lowerCAmelCase_:       Dict         =  (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(lowerCamelCase__					,	lowerCamelCase__					,	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 		snake_case__  (		lowercase       ,							lowercase       ,							lowercase				):
   body_system.update_system(lowercase				)

   # Update the positions of the patches
   for patch, body in zip(lowercase       ,							body_system.bodies				):
      lowerCAmelCase_:       Dict         =  (body.position_x, body.position_y)
def 		snake_case__  (		lowercase       ,							lowercase       ,							lowercase = -1       ,							lowercase = 1       ,							lowercase = -1       ,							lowercase = 1       ,							):
   lowerCAmelCase_:       List[Any]         =  plt.figure()
   fig.canvas.set_window_title(lowercase				)
   lowerCAmelCase_:       Dict         =  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
   lowerCAmelCase_:       int         =  [
       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(lowercase				)

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

   lowerCAmelCase_:       Union[str, Any]         =  animation.FuncAnimation(  # noqa: F841
       lowercase       ,							lowercase       ,							interval=lowercase       ,							blit=lowercase				)

   plt.show()
def 		snake_case__  (		):
   lowerCAmelCase_:       Tuple         =  0.9700436
   lowerCAmelCase_:       List[str]         =  -0.24308753
   lowerCAmelCase_:       List[Any]         =  0.466203685
   lowerCAmelCase_:       Any         =  0.43236573

   lowerCAmelCase_:       Tuple         =  [
       Body(lowercase       ,							lowercase       ,							lowercase       ,							lowercase       ,							size=0.2       ,							color="red"				),
       Body(-position_x       ,							-position_y       ,							lowercase       ,							lowercase       ,							size=0.2       ,							color="green"				),
       Body(0       ,							0       ,							-2 * velocity_x       ,							-2 * velocity_y       ,							size=0.2       ,							color="blue"				),
   ]
   return BodySystem(lowercase       ,							time_factor=3				)
def 		snake_case__  (		):
   lowerCAmelCase_:       Tuple         =  7.3476E22
   lowerCAmelCase_:       List[Any]         =  5.972E24
   lowerCAmelCase_:       str         =  1022
   lowerCAmelCase_:       Optional[Any]         =  384399000
   lowerCAmelCase_:       str         =  6.674E-11

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

   lowerCAmelCase_:       Tuple         =  Body(-earth_moon_distance       ,							0       ,							0       ,							lowercase       ,							lowercase       ,							10000000       ,							"grey"				)
   lowerCAmelCase_:       str         =  Body(0       ,							0       ,							0       ,							lowercase       ,							lowercase       ,							50000000       ,							"blue"				)
   return BodySystem([earth, moon]       ,							lowercase       ,							time_factor=1000000				)
def 		snake_case__  (		):
   lowerCAmelCase_:       Optional[Any]         =  []
   for _ in range(10				):
      lowerCAmelCase_:       Optional[int]         =  random.uniform(-0.5       ,							0.5				)
      lowerCAmelCase_:       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				)       ,							lowercase       ,							lowercase       ,							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(lowercase       ,							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_3_0_0_0_0_0_0_0,
     4_3_0_0_0_0_0_0_0,
     -4_3_0_0_0_0_0_0_0,
     4_3_0_0_0_0_0_0_0,
 )
 plot("""Random system with many bodies""", example_a(), -1.5, 1.5, -1.5, 1.5)
from .balanced_parentheses import balanced_parentheses
from .stack import Stack
def 		snake_case__  (		lowercase				):
   return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(lowercase       ,							-1				)
def 		snake_case__  (		lowercase				):
   if not balanced_parentheses(lowercase				):
      raise ValueError("Mismatched parentheses"				)
   lowerCAmelCase_:       Stack[str]         =  Stack()
   lowerCAmelCase_:       Union[str, Any]         =  []
   for char in expression_str:
      if char.isalpha() or char.isdigit():
         postfix.append(lowercase				)
      elif char == "(":
         stack.push(lowercase				)
      elif char == ")":
         while not stack.is_empty() and stack.peek() != "(":
            postfix.append(stack.pop()				)
         stack.pop()
      else:
         while not stack.is_empty() and precedence(lowercase				) <= precedence(stack.peek()				):
            postfix.append(stack.pop()				)
         stack.push(lowercase				)
   while not stack.is_empty():
      postfix.append(stack.pop()				)
   return " ".join(lowercase				)


if __name__ == "__main__":
 from doctest import testmod

 testmod()
 a     :			int					    =						"""a+b*(c^d-e)^(f+g*h)-i"""

 print("""Infix to Postfix Notation demonstration:\n""")
 print("""Infix notation: """ + expression)
 print("""Postfix notation: """ + infix_to_postfix(expression))