
from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt


def     __lowerCAmelCase			(			a__						,    a__						,    a__  )       ->  tuple[int | None, int | None, float]:
				if not arr:
								return None, None, 0
				if low == high:
								return low, high, arr[low]

				__a										=    (low + high) // 2
				__a							,     __a							,     __a										=    max_subarray(a__						,    a__						,    a__  )
				__a							,     __a							,     __a										=    max_subarray(a__						,    mid + 1						,    a__  )
				__a							,     __a							,     __a										=    max_cross_sum(a__						,    a__						,    a__						,    a__  )
				if left_sum >= right_sum and left_sum >= cross_sum:
								return left_low, left_high, left_sum
				elif right_sum >= left_sum and right_sum >= cross_sum:
								return right_low, right_high, right_sum
				return cross_left, cross_right, cross_sum


def     __lowerCAmelCase			(			a__						,    a__						,    a__						,    a__  )       ->  tuple[int, int, float]:
				__a							,     __a										=    float('''-inf'''  ), -1
				__a							,     __a										=    float('''-inf'''  ), -1

				__a										=    0
				for i in range(a__						,    low - 1						,    -1  ):
								summ += arr[i]
								if summ > left_sum:
												__a										=    summ
												__a										=    i

				__a										=    0
				for i in range(mid + 1						,    high + 1  ):
								summ += arr[i]
								if summ > right_sum:
												__a										=    summ
												__a										=    i

				return max_left, max_right, (left_sum + right_sum)


def     __lowerCAmelCase			(			a__  )       ->  float:
				__a										=    [randint(1						,    a__  ) for _ in range(a__  )]
				__a										=    time.time()
				max_subarray(a__						,    0						,    input_size - 1  )
				__a										=    time.time()
				return end - start


def     __lowerCAmelCase			(			)       ->  None:
				__a										=    [10, 100, 1000, 1_0000, 5_0000, 10_0000, 20_0000, 30_0000, 40_0000, 50_0000]
				__a										=    [time_max_subarray(a__  ) for input_size in input_sizes]
				print('''No of Inputs\t\tTime Taken'''  )
				for input_size, runtime in zip(a__						,    a__  ):
								print(a__						,    '''\t\t'''						,    a__  )
				plt.plot(a__						,    a__  )
				plt.xlabel('''Number of Inputs'''  )
				plt.ylabel('''Time taken in seconds'''  )
				plt.show()


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

					testmod()

from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def     __lowerCAmelCase			(			a__						,    a__						,    a__ = 1 / sqrt(2  )  )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)

				__a										=    (1 - _cos) / 2
				__a										=    1 - _cos

				__a										=    1 + alpha
				__a										=    -2 * _cos
				__a										=    1 - alpha

				__a										=    IIRFilter(2  )
				filt.set_coefficients([aa, aa, aa]						,    [ba, ba, ba]  )
				return filt


def     __lowerCAmelCase			(			a__						,    a__						,    a__ = 1 / sqrt(2  )  )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)

				__a										=    (1 + _cos) / 2
				__a										=    -1 - _cos

				__a										=    1 + alpha
				__a										=    -2 * _cos
				__a										=    1 - alpha

				__a										=    IIRFilter(2  )
				filt.set_coefficients([aa, aa, aa]						,    [ba, ba, ba]  )
				return filt


def     __lowerCAmelCase			(			a__						,    a__						,    a__ = 1 / sqrt(2  )  )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)

				__a										=    _sin / 2
				__a										=    0
				__a										=    -ba

				__a										=    1 + alpha
				__a										=    -2 * _cos
				__a										=    1 - alpha

				__a										=    IIRFilter(2  )
				filt.set_coefficients([aa, aa, aa]						,    [ba, ba, ba]  )
				return filt


def     __lowerCAmelCase			(			a__						,    a__						,    a__ = 1 / sqrt(2  )  )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)

				__a										=    1 - alpha
				__a										=    -2 * _cos
				__a										=    1 + alpha

				__a										=    IIRFilter(2  )
				filt.set_coefficients([ba, ba, ba]						,    [ba, ba, ba]  )
				return filt


def     __lowerCAmelCase			(			a__						,    a__						,    a__						,    a__ = 1 / sqrt(2  )						,    )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)
				__a										=    10 ** (gain_db / 40)

				__a										=    1 + alpha * big_a
				__a										=    -2 * _cos
				__a										=    1 - alpha * big_a
				__a										=    1 + alpha / big_a
				__a										=    -2 * _cos
				__a										=    1 - alpha / big_a

				__a										=    IIRFilter(2  )
				filt.set_coefficients([aa, aa, aa]						,    [ba, ba, ba]  )
				return filt


def     __lowerCAmelCase			(			a__						,    a__						,    a__						,    a__ = 1 / sqrt(2  )						,    )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)
				__a										=    10 ** (gain_db / 40)
				__a										=    (big_a + 1) - (big_a - 1) * _cos
				__a										=    (big_a + 1) + (big_a - 1) * _cos
				__a										=    (big_a - 1) - (big_a + 1) * _cos
				__a										=    (big_a - 1) + (big_a + 1) * _cos
				__a										=    2 * sqrt(a__  ) * alpha

				__a										=    big_a * (pmc + aaa)
				__a										=    2 * big_a * mpc
				__a										=    big_a * (pmc - aaa)
				__a										=    ppmc + aaa
				__a										=    -2 * pmpc
				__a										=    ppmc - aaa

				__a										=    IIRFilter(2  )
				filt.set_coefficients([aa, aa, aa]						,    [ba, ba, ba]  )
				return filt






def     __lowerCAmelCase			(			a__						,    a__						,    a__						,    a__ = 1 / sqrt(2  )						,    )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)
				__a										=    10 ** (gain_db / 40)
				__a										=    (big_a + 1) - (big_a - 1) * _cos
				__a										=    (big_a + 1) + (big_a - 1) * _cos
				__a										=    (big_a - 1) - (big_a + 1) * _cos
				__a										=    (big_a - 1) + (big_a + 1) * _cos
				__a										=    2 * sqrt(a__  ) * alpha

				__a										=    big_a * (ppmc + aaa)
				__a										=    -2 * big_a * pmpc
				__a										=    big_a * (ppmc - aaa)
				__a										=    pmc + aaa
				__a										=    2 * mpc
				__a										=    pmc - aaa

				__a										=    IIRFilter(2  )
				filt.set_coefficients([aa, aa, aa]						,    [ba, ba, ba]  )
				return filt