"""simple docstring"""




# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.






def   UpperCAmelCase					(	UpperCamelCase__				):






							"""simple docstring"""





							A__	     =							[False] * len(UpperCamelCase__				)
							A__	     =							[-1] * len(UpperCamelCase__				)

							def dfs(UpperCamelCase__       ,    UpperCamelCase__				):
														A__	     =							True
														A__	     =							c
														for u in graph[v]:
																					if not visited[u]:
																												dfs(UpperCamelCase__       ,    1 - c				)

							for i in range(len(UpperCamelCase__				)				):
														if not visited[i]:
																					dfs(UpperCamelCase__       ,    0				)

							for i in range(len(UpperCamelCase__				)				):
														for j in graph[i]:
																					if color[i] == color[j]:
																												return False

							return True


# Adjacency list of graph
__lowerCamelCase											=  {0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}


print(check_bipartite_dfs(graph))






"""simple docstring"""




from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter






def   UpperCAmelCase					(	UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__ = 1 / sqrt(2				)				):






							"""simple docstring"""





							A__	     =							tau * frequency / samplerate
							A__	     =							sin(UpperCamelCase__				)
							A__	     =							cos(UpperCamelCase__				)
							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   UpperCAmelCase					(	UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__ = 1 / sqrt(2				)				):






							"""simple docstring"""





							A__	     =							tau * frequency / samplerate
							A__	     =							sin(UpperCamelCase__				)
							A__	     =							cos(UpperCamelCase__				)
							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   UpperCAmelCase					(	UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__ = 1 / sqrt(2				)				):






							"""simple docstring"""





							A__	     =							tau * frequency / samplerate
							A__	     =							sin(UpperCamelCase__				)
							A__	     =							cos(UpperCamelCase__				)
							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   UpperCAmelCase					(	UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__ = 1 / sqrt(2				)				):






							"""simple docstring"""





							A__	     =							tau * frequency / samplerate
							A__	     =							sin(UpperCamelCase__				)
							A__	     =							cos(UpperCamelCase__				)
							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   UpperCAmelCase					(	UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__ = 1 / sqrt(2				)       ,    ):






							"""simple docstring"""





							A__	     =							tau * frequency / samplerate
							A__	     =							sin(UpperCamelCase__				)
							A__	     =							cos(UpperCamelCase__				)
							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   UpperCAmelCase					(	UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__ = 1 / sqrt(2				)       ,    ):






							"""simple docstring"""





							A__	     =							tau * frequency / samplerate
							A__	     =							sin(UpperCamelCase__				)
							A__	     =							cos(UpperCamelCase__				)
							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(UpperCamelCase__				) * 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   UpperCAmelCase					(	UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__ = 1 / sqrt(2				)       ,    ):






							"""simple docstring"""





							A__	     =							tau * frequency / samplerate
							A__	     =							sin(UpperCamelCase__				)
							A__	     =							cos(UpperCamelCase__				)
							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(UpperCamelCase__				) * 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





