
"""simple docstring"""




from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np







class     lowercase(_lowercase       ):



     def 			lowercase__  (							self     ,				__SCREAMING_SNAKE_CASE   )		->     float:







         """simple docstring"""



         return 0.0




def     __magic_name__		(					UpperCamelCase     :		np.ndarray							,		UpperCamelCase     :		int     )     ->						tuple[int | float, int | float]:
    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     __magic_name__		(					UpperCamelCase     :		FilterType							,		UpperCamelCase     :		int     )     ->						None:
    a__		=			512
    a__		=			[1] + [0] * (size - 1)
    a__		=			[filter_type.process(UpperCamelCase     ) for item in inputs]

    a__		=			[0] * (samplerate - size)  # zero-padding
    outputs += filler
    a__		=			np.abs(np.fft.fft(UpperCamelCase     )     )
    a__		=			20 * np.logaa(UpperCamelCase     )

    # 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(UpperCamelCase							,		UpperCamelCase     )
    plt.ylim(max([-80, bounds[0]]     )							,		min([80, bounds[1]]     )     )
    plt.ylabel('Gain (dB)'     )

    plt.plot(UpperCamelCase     )
    plt.show()



def     __magic_name__		(					UpperCamelCase     :		FilterType							,		UpperCamelCase     :		int     )     ->						None:
    a__		=			512
    a__		=			[1] + [0] * (size - 1)
    a__		=			[filter_type.process(UpperCamelCase     ) for item in inputs]

    a__		=			[0] * (samplerate - size)  # zero-padding
    outputs += filler
    a__		=			np.angle(np.fft.fft(UpperCamelCase     )     )

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




"""simple docstring"""




def     __magic_name__		(					UpperCamelCase     :		int							,		UpperCamelCase     :		list[int]							,		UpperCamelCase     :		int     )     ->						int:

    def count_of_possible_combinations(UpperCamelCase     :		int     ) -> int:
        if target < 0:
            return 0
        if target == 0:
            return 1
        return sum(count_of_possible_combinations(target - item     ) for item in array     )

    return count_of_possible_combinations(UpperCamelCase     )



def     __magic_name__		(					UpperCamelCase     :		int							,		UpperCamelCase     :		list[int]							,		UpperCamelCase     :		int     )     ->						int:

    def count_of_possible_combinations_with_dp_array(
        UpperCamelCase     :		int							,		UpperCamelCase     :		list[int]     ) -> int:
        if target < 0:
            return 0
        if target == 0:
            return 1
        if dp_array[target] != -1:
            return dp_array[target]
        a__		=			sum(
            count_of_possible_combinations_with_dp_array(target - item							,		UpperCamelCase     )
            for item in array     )
        a__		=			answer
        return answer

    a__		=			[-1] * (target + 1)
    return count_of_possible_combinations_with_dp_array(UpperCamelCase							,		UpperCamelCase     )



def     __magic_name__		(					UpperCamelCase     :		int							,		UpperCamelCase     :		list[int]							,		UpperCamelCase     :		int     )     ->						int:
    a__		=			[0] * (target + 1)
    a__		=			1

    for i in range(1							,		target + 1     ):
        for j in range(UpperCamelCase     ):
            if i - array[j] >= 0:
                dp_array[i] += dp_array[i - array[j]]

    return dp_array[target]


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    a		:       Optional[Any]     						=       3
    a		:       List[str]     						=       5
    a		:       Dict     						=       [1, 2, 5]
    print(combination_sum_iv(n, array, target))


