


# 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 		lowercase_	(  _UpperCamelCase	):


			'''simple docstring'''







			__lowercase			       = [False] * len(_UpperCamelCase	)
			__lowercase			       = [-1] * len(_UpperCamelCase	)

			def dfs(_UpperCamelCase							,      _UpperCamelCase	):
						__lowercase			       = True
						__lowercase			       = 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
a			:			int												=					{0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}





print(check_bipartite_dfs(graph))






import doctest
from collections import deque

import numpy as np
class 						lowerCamelCase_							:



					'''simple docstring'''







					def __init__(					self    ) ->      None:







								'''simple docstring'''

								__lowercase			       = [2, 1, 2, -1]
								__lowercase			       = [1, 2, 3, 4]






					def A   (					self    ) ->      list[float]:







								'''simple docstring'''

								__lowercase			       = len(self.first_signal    )
								__lowercase			       = len(self.second_signal    )

								__lowercase			       = max(snake_case_			,							snake_case_    )

								# create a zero matrix of max_length x max_length
								__lowercase			       = [[0] * max_length for i in range(snake_case_    )]

								# fills the smaller signal with zeros to make both signals of same length
								if length_first_signal < length_second_signal:
											self.first_signal += [0] * (max_length - length_first_signal)
								elif length_first_signal > length_second_signal:
											self.second_signal += [0] * (max_length - length_second_signal)
								for i in range(snake_case_    ):
											__lowercase			       = deque(self.second_signal    )
											rotated_signal.rotate(snake_case_    )
											for j, item in enumerate(snake_case_    ):
														matrix[i][j] += item

        # multiply the matrix with the first signal
								__lowercase			       = np.matmul(np.transpose(snake_case_    )			,							np.transpose(self.first_signal    )    )

								# rounding-off to two decimal places
								return [round(snake_case_			,							2    ) for i in final_signal]


if __name__ == "__main__":
	doctest.testmod()


