"""simple docstring"""




from __future__ import annotations

__lowerCamelCase											=  {
    "A": ["B", "C", "E"],
    "B": ["A", "D", "E"],
    "C": ["A", "F", "G"],
    "D": ["B"],
    "E": ["A", "B", "D"],
    "F": ["C"],
    "G": ["C"],
}
class     UpperCamelCase__:





						def __init__(       self		,__UpperCAmelCase		,__UpperCAmelCase     )					->				None:
													A__	     =							graph
													# mapping node to its parent in resulting breadth first tree
													A__	     =							{}
													A__	     =							source_vertex





						def 				snake_case__	(       self     )					->				None:
													A__	     =							{self.source_vertex}
													A__	     =							None
													A__	     =							[self.source_vertex]  # first in first out queue

													while queue:
																				A__	     =							queue.pop(0     )
																				for adjacent_vertex in self.graph[vertex]:
																											if adjacent_vertex not in visited:
																																		visited.add(__UpperCAmelCase     )
																																		A__	     =							vertex
																																		queue.append(__UpperCAmelCase     )





						def 				snake_case__	(       self		,__UpperCAmelCase     )					->				str:
													if target_vertex == self.source_vertex:
																				return self.source_vertex

													A__	     =							self.parent.get(__UpperCAmelCase     )
													if target_vertex_parent is None:
																				A__	     =							(
																				    f'''No path from vertex: {self.source_vertex} to vertex: {target_vertex}'''
																				)
																				raise ValueError(__UpperCAmelCase     )

													return self.shortest_path(__UpperCAmelCase     ) + f'''->{target_vertex}'''


if __name__ == "__main__":
				__lowerCamelCase											=  Graph(graph, "G")
				g.breath_first_search()
				print(g.shortest_path("D"))
				print(g.shortest_path("G"))
				print(g.shortest_path("Foo"))






"""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





