






'''simple docstring'''

from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np







class 	SCREAMING_SNAKE_CASE	(      lowerCAmelCase_  ):




       def 					a_					(					self      : int	,    A__      : float					):


            """simple docstring"""







            return 0.0

def     __lowercase  (_lowercase,						_lowercase     )   ->     tuple[int | float, int | float]:


     """simple docstring"""
     __lowerCamelCase						:       Tuple				   =				min([-20, np.min(fft_results[1 : samplerate // 2 - 1]     )]     )
     __lowerCamelCase						:       List[str]				   =				max([20, np.max(fft_results[1 : samplerate // 2 - 1]     )]     )
     return lowest, highest
def     __lowercase  (_lowercase,						_lowercase     )   ->     None:


     """simple docstring"""
     __lowerCamelCase						:       Dict				   =				512
     __lowerCamelCase						:       List[Any]				   =				[1] + [0] * (size - 1)
     __lowerCamelCase						:       Union[str, Any]				   =				[filter_type.process(_lowercase     ) for item in inputs]

     __lowerCamelCase						:       int				   =				[0] * (samplerate - size)  # zero-padding
     outputs += filler
     __lowerCamelCase						:       Any				   =				np.abs(np.fft.fft(_lowercase     )     )
     __lowerCamelCase						:       str				   =				20 * np.logaa(_lowercase     )

     # Frequencies on log scale from 24 to nyquist frequency
     plt.xlim(24,						samplerate / 2 - 1     )
     plt.xlabel("""Frequency (Hz)"""     )
     plt.xscale("""log"""     )

     # Display within reasonable bounds
     __lowerCamelCase						:       Optional[int]				   =				get_bounds(_lowercase,						_lowercase     )
     plt.ylim(max([-80, bounds[0]]     ),						min([80, bounds[1]]     )     )
     plt.ylabel("""Gain (dB)"""     )

     plt.plot(_lowercase     )
     plt.show()
def     __lowercase  (_lowercase,						_lowercase     )   ->     None:


     """simple docstring"""
     __lowerCamelCase						:       List[str]				   =				512
     __lowerCamelCase						:       Optional[Any]				   =				[1] + [0] * (size - 1)
     __lowerCamelCase						:       List[Any]				   =				[filter_type.process(_lowercase     ) for item in inputs]

     __lowerCamelCase						:       Optional[int]				   =				[0] * (samplerate - size)  # zero-padding
     outputs += filler
     __lowerCamelCase						:       List[Any]				   =				np.angle(np.fft.fft(_lowercase     )     )

     # Frequencies on log scale from 24 to nyquist frequency
     plt.xlim(24,						samplerate / 2 - 1     )
     plt.xlabel("""Frequency (Hz)"""     )
     plt.xscale("""log"""     )

     plt.ylim(-2 * pi,						2 * pi     )
     plt.ylabel("""Phase shift (Radians)"""     )
     plt.plot(np.unwrap(_lowercase,						-2 * pi     )     )
     plt.show()











'''simple docstring'''

from __future__ import annotations

from random import random







class 	SCREAMING_SNAKE_CASE	:




       def __init__(					self      : Tuple	,    A__      : int | None = None					):


            """simple docstring"""







            __lowerCamelCase						:       int				   =				value
            __lowerCamelCase						:       Dict				   =				random()
            __lowerCamelCase						:       Node | None				   =				None
            __lowerCamelCase						:       Node | None				   =				None




       def __repr__(					self      : Any					):


            """simple docstring"""







            from pprint import pformat

            if self.left is None and self.right is None:
                 return f"'{self.value}: {self.prior:.5}'"
            else:
                 return pformat(
                     {f"{self.value}: {self.prior:.5}": (self.left, self.right)}	,    indent=1					)




       def __str__(					self      : List[Any]					):


            """simple docstring"""







            __lowerCamelCase						:       List[str]				   =				str(self.value					) + """ """
            __lowerCamelCase						:       Any				   =				str(self.left or """"""					)
            __lowerCamelCase						:       List[str]				   =				str(self.right or """"""					)
            return value + left + right

def     __lowercase  (_lowercase,						_lowercase     )   ->     tuple[Node | None, Node | None]:


     """simple docstring"""
     if root is None:  # None tree is split into 2 Nones
          return None, None
     elif root.value is None:
          return None, None
     else:
          if value < root.value:
               __lowerCamelCase   ,      __lowerCamelCase						:       int				   =				split(root.left,						_lowercase     )
               return left, root
          else:
               __lowerCamelCase   ,      __lowerCamelCase						:       Union[str, Any]				   =				split(root.right,						_lowercase     )
               return root, right
def     __lowercase  (_lowercase,						_lowercase     )   ->     Node | None:


     """simple docstring"""
     if (not left) or (not right):  # If one node is None, return the other
          return left or right
     elif left.prior < right.prior:
          __lowerCamelCase						:       Tuple				   =				merge(left.right,						_lowercase     )
          return left
     else:
          __lowerCamelCase						:       int				   =				merge(_lowercase,						right.left     )
          return right
def     __lowercase  (_lowercase,						_lowercase     )   ->     Node | None:


     """simple docstring"""
     __lowerCamelCase						:       List[str]				   =				Node(_lowercase     )
     __lowerCamelCase   ,      __lowerCamelCase						:       List[Any]				   =				split(_lowercase,						_lowercase     )
     return merge(merge(_lowercase,						_lowercase     ),						_lowercase     )
def     __lowercase  (_lowercase,						_lowercase     )   ->     Node | None:


     """simple docstring"""
     __lowerCamelCase   ,      __lowerCamelCase						:       int				   =				split(_lowercase,						value - 1     )
     __lowerCamelCase   ,      __lowerCamelCase						:       List[str]				   =				split(_lowercase,						_lowercase     )
     return merge(_lowercase,						_lowercase     )
def     __lowercase  (_lowercase     )   ->     None:


     """simple docstring"""
     if not root:  # None
          return
     else:
          inorder(root.left     )
          print(root.value,						end=""","""     )
          inorder(root.right     )
def     __lowercase  (_lowercase,						_lowercase     )   ->     Node | None:


     """simple docstring"""
     for arg in args.split():
          if arg[0] == "+":
               __lowerCamelCase						:       Dict				   =				insert(_lowercase,						int(arg[1:]     )     )

          elif arg[0] == "-":
               __lowerCamelCase						:       List[str]				   =				erase(_lowercase,						int(arg[1:]     )     )

          else:
               print("""Unknown command"""     )

     return root
def     __lowercase  ()   ->     None:


     """simple docstring"""
     __lowerCamelCase						:       str				   =				None
     print(
         """enter numbers to create a tree, + value to add value into treap, """
         """- value to erase all nodes with value. 'q' to quit. """     )

     __lowerCamelCase						:       int				   =				input()
     while args != "q":
          __lowerCamelCase						:       List[Any]				   =				interact_treap(_lowercase,						_lowercase     )
          print(_lowercase     )
          __lowerCamelCase						:       List[Any]				   =				input()

     print("""good by!"""     )


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   main()



