




"""simple docstring"""




def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	Any:



       """simple docstring"""

       A__							=   0
       A__							=   len(__lowerCAmelCase						)

       for i in range(n - 1						):
              for j in range(i + 1			,    __lowerCAmelCase						):
                     if arr[i] > arr[j]:
                            num_inversions += 1

       return num_inversions







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	str:



       """simple docstring"""

       if len(__lowerCAmelCase						) <= 1:
              return arr, 0
       A__							=   len(__lowerCAmelCase						) // 2
       A__							=   arr[0:mid]
       A__							=   arr[mid:]

       A__			,							A__							=   count_inversions_recursive(__lowerCAmelCase						)
       A__			,							A__							=   count_inversions_recursive(__lowerCAmelCase						)
       A__			,							A__							=   _count_cross_inversions(__lowerCAmelCase			,    __lowerCAmelCase						)

       A__							=   inversion_p + inversions_q + cross_inversions
       return c, num_inversions







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_						)       ->	Tuple:



       """simple docstring"""

       A__							=   []
       A__							=   A__							=   A__							=   0
       while i < len(__lowerCAmelCase						) and j < len(__lowerCAmelCase						):
              if p[i] > q[j]:
                     # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
                     # These are all inversions. The claim emerges from the
                     # property that P is sorted.
                     num_inversion += len(__lowerCAmelCase						) - i
                     r.append(q[j]						)
                     j += 1
              else:
                     r.append(p[i]						)
                     i += 1

       if i < len(__lowerCAmelCase						):
              r.extend(p[i:]						)
       else:
              r.extend(q[j:]						)

       return r, num_inversion







def SCREAMING_SNAKE_CASE    (	)       ->	Optional[int]:



       """simple docstring"""

       A__							=   [10, 2, 1, 5, 5, 2, 11]

       # this arr has 8 inversions:
       # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

       A__							=   count_inversions_bf(__lowerCAmelCase						)
       A__			,							A__							=   count_inversions_recursive(__lowerCAmelCase						)

       assert num_inversions_bf == num_inversions_recursive == 8

       print('''number of inversions = '''			,    __lowerCAmelCase						)

       # testing an array with zero inversion (a sorted arr_1)

       arr_a.sort()
       A__							=   count_inversions_bf(__lowerCAmelCase						)
       A__			,							A__							=   count_inversions_recursive(__lowerCAmelCase						)

       assert num_inversions_bf == num_inversions_recursive == 0
       print('''number of inversions = '''			,    __lowerCAmelCase						)

       # an empty list should also have zero inversions
       A__							=   []
       A__							=   count_inversions_bf(__lowerCAmelCase						)
       A__			,							A__							=   count_inversions_recursive(__lowerCAmelCase						)

       assert num_inversions_bf == num_inversions_recursive == 0
       print('''number of inversions = '''			,    __lowerCAmelCase						)


if __name__ == "__main__":
  main()








from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np


class     UpperCamelCase_   (			UpperCAmelCase__					):

    '''simple docstring'''






    def 	SCREAMING_SNAKE_CASE							(      self				:     Optional[int] ,			UpperCAmelCase__				:     float)						->float:





           '''simple docstring'''

           return 0.0







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_						)       ->	tuple[int | float, int | float]:



       """simple docstring"""

       A__							=   min([-20, np.min(fft_results[1 : samplerate // 2 - 1]						)]						)
       A__							=   max([20, np.max(fft_results[1 : samplerate // 2 - 1]						)]						)
       return lowest, highest







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_						)       ->	None:



       """simple docstring"""

       A__							=   512
       A__							=   [1] + [0] * (size - 1)
       A__							=   [filter_type.process(lowercase_						) for item in inputs]

       A__							=   [0] * (samplerate - size)  # zero-padding
       outputs += filler
       A__							=   np.abs(np.fft.fft(lowercase_						)						)
       A__							=   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
       A__							=   get_bounds(lowercase_			,    lowercase_						)
       plt.ylim(max([-80, bounds[0]]						)			,    min([80, bounds[1]]						)						)
       plt.ylabel('''Gain (dB)'''						)

       plt.plot(lowercase_						)
       plt.show()







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_						)       ->	None:



       """simple docstring"""

       A__							=   512
       A__							=   [1] + [0] * (size - 1)
       A__							=   [filter_type.process(lowercase_						) for item in inputs]

       A__							=   [0] * (samplerate - size)  # zero-padding
       outputs += filler
       A__							=   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()


