from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np




class 	__snake_case	( __lowerCAmelCase		):





      '''simple docstring'''






      def 	_SCREAMING_SNAKE_CASE    (					self     :				Optional[Any]    ,  _UpperCamelCase     :				float)				->float:


          """simple docstring"""


          return 0.0







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		int 						=						min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
    _lowerCamelCase     :		Tuple 						=						max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
    return lowest, highest







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		Tuple 						=						512
    _lowerCamelCase     :		Tuple 						=						[1] + [0] * (size - 1)
    _lowerCamelCase     :		Optional[Any] 						=						[filter_type.process(__A	) for item in inputs]

    _lowerCamelCase     :		Optional[Any] 						=						[0] * (samplerate - size)  # zero-padding
    outputs += filler
    _lowerCamelCase     :		Tuple 						=						np.abs(np.fft.fft(__A	)	)
    _lowerCamelCase     :		List[Any] 						=						20 * np.logaa(__A	)

    # 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     :		Any 						=						get_bounds(__A   , __A	)
    plt.ylim(max([-80, bounds[0]]	)   , min([80, bounds[1]]	)	)
    plt.ylabel("""Gain (dB)"""	)

    plt.plot(__A	)
    plt.show()







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		Tuple 						=						512
    _lowerCamelCase     :		Union[str, Any] 						=						[1] + [0] * (size - 1)
    _lowerCamelCase     :		int 						=						[filter_type.process(__A	) for item in inputs]

    _lowerCamelCase     :		Optional[Any] 						=						[0] * (samplerate - size)  # zero-padding
    outputs += filler
    _lowerCamelCase     :		Any 						=						np.angle(np.fft.fft(__A	)	)

    # 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(__A   , -2 * pi	)	)
    plt.show()





def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _enforce_args(__A   , __A	)
    if n == 0:
        return 0
    _lowerCamelCase     :		Tuple 						=						float("""-inf"""	)
    for i in range(1   , n + 1	):
        _lowerCamelCase     :		Any 						=						max(
            __A   , prices[i - 1] + naive_cut_rod_recursive(n - i   , __A	)	)

    return max_revue







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _enforce_args(__A   , __A	)
    _lowerCamelCase     :		Optional[Any] 						=						[float("""-inf"""	) for _ in range(n + 1	)]
    return _top_down_cut_rod_recursive(__A   , __A   , __A	)







def 						A__  (					__A   , __A   , __A	):







    '''simple docstring'''
    if max_rev[n] >= 0:
        return max_rev[n]
    elif n == 0:
        return 0
    else:
        _lowerCamelCase     :		int 						=						float("""-inf"""	)
        for i in range(1   , n + 1	):
            _lowerCamelCase     :		Optional[Any] 						=						max(
                __A   , prices[i - 1] + _top_down_cut_rod_recursive(n - i   , __A   , __A	)   , )

        _lowerCamelCase     :		Optional[Any] 						=						max_revenue

    return max_rev[n]







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _enforce_args(__A   , __A	)

    # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
    # length 0.
    _lowerCamelCase     :		List[Any] 						=						[float("""-inf"""	) for _ in range(n + 1	)]
    _lowerCamelCase     :		Any 						=						0

    for i in range(1   , n + 1	):
        _lowerCamelCase     :		Any 						=						max_rev[i]
        for j in range(1   , i + 1	):
            _lowerCamelCase     :		List[Any] 						=						max(__A   , prices[j - 1] + max_rev[i - j]	)

        _lowerCamelCase     :		int 						=						max_revenue_i

    return max_rev[n]







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    if n < 0:
        _lowerCamelCase     :		Any 						=						F"""n must be greater than or equal to 0. Got n = {n}"""
        raise ValueError(__A	)

    if n > len(__A	):
        _lowerCamelCase     :		List[Any] 						=						(
            """Each integral piece of rod must have a corresponding price. """
            F"""Got n = {n} but length of prices = {len(__A	)}"""
        )
        raise ValueError(__A	)







def 						A__  (					):







    '''simple docstring'''
    _lowerCamelCase     :		str 						=						[6, 10, 12, 15, 20, 23]
    _lowerCamelCase     :		List[str] 						=						len(__A	)

    # the best revenue comes from cutting the rod into 6 pieces, each
    # of length 1 resulting in a revenue of 6 * 6 = 36.
    _lowerCamelCase     :		Tuple 						=						36

    _lowerCamelCase     :		Any 						=						top_down_cut_rod(__A   , __A	)
    _lowerCamelCase     :		Dict 						=						bottom_up_cut_rod(__A   , __A	)
    _lowerCamelCase     :		List[str] 						=						naive_cut_rod_recursive(__A   , __A	)

    assert expected_max_revenue == max_rev_top_down
    assert max_rev_top_down == max_rev_bottom_up
    assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
    main()




