






import math

import flax.linen as nn
import jax.numpy as jnp

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__ = 1     ,   UpperCAmelCase__ = 1     ,   UpperCAmelCase__ = 1.0E4     ,   UpperCAmelCase__ = False     ,   UpperCAmelCase__ = 1.0     ,   )	->    jnp.ndarray:
  assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
  assert embedding_dim % 2 == 0, F'''Embedding dimension {embedding_dim} should be even'''
  UpperCamelCase_: Tuple   				=    float(embedding_dim // 2  )
  UpperCamelCase_: str   				=    math.log(max_timescale / min_timescale  ) / (num_timescales - freq_shift)
  UpperCamelCase_: str   				=    min_timescale * jnp.exp(jnp.arange(UpperCAmelCase__     ,   dtype=jnp.floataa  ) * -log_timescale_increment  )
  UpperCamelCase_: Optional[Any]   				=    jnp.expand_dims(UpperCAmelCase__     ,   1  ) * jnp.expand_dims(UpperCAmelCase__     ,   0  )

  # scale embeddings
  UpperCamelCase_: Optional[Any]   				=    scale * emb

  if flip_sin_to_cos:
    UpperCamelCase_: Optional[Any]   				=    jnp.concatenate([jnp.cos(UpperCAmelCase__  ), jnp.sin(UpperCAmelCase__  )]     ,   axis=1  )
  else:
    UpperCamelCase_: Any   				=    jnp.concatenate([jnp.sin(UpperCAmelCase__  ), jnp.cos(UpperCAmelCase__  )]     ,   axis=1  )
  UpperCamelCase_: Optional[int]   				=    jnp.reshape(UpperCAmelCase__     ,   [jnp.shape(UpperCAmelCase__  )[0], embedding_dim]  )
  return signal




class     _lowerCAmelCase(	nn.Module ):





       """simple docstring"""







       a    :		int									=32
       a    :		jnp.dtype									=jnp.floataa





       @nn.compact
       def __call__( self  ,      _lowerCamelCase							):
         UpperCamelCase_: Dict   				=    nn.Dense(self.time_embed_dim  ,      dtype=self.dtype  ,      name='linear_1'							)(_lowerCamelCase							)
         UpperCamelCase_: Optional[Any]   				=    nn.silu(_lowerCamelCase							)
         UpperCamelCase_: Optional[int]   				=    nn.Dense(self.time_embed_dim  ,      dtype=self.dtype  ,      name='linear_2'							)(_lowerCamelCase							)
         return temb







class     _lowerCAmelCase(	nn.Module ):





       """simple docstring"""







       a    :		int									=32
       a    :		bool									=False
       a    :		float									=1





       @nn.compact
       def __call__( self  ,      _lowerCamelCase							):
         return get_sinusoidal_embeddings(
             _lowerCamelCase  ,      embedding_dim=self.dim  ,      flip_sin_to_cos=self.flip_sin_to_cos  ,      freq_shift=self.freq_shift							)







# 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   snake_case (UpperCAmelCase__  )	->    List[str]:
  UpperCamelCase_: int   				=    [False] * len(UpperCAmelCase__  )
  UpperCamelCase_: Any   				=    [-1] * len(UpperCAmelCase__  )

  def dfs(UpperCAmelCase__     ,   UpperCAmelCase__  ):
    UpperCamelCase_: Tuple   				=    True
    UpperCamelCase_: Optional[int]   				=    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_		:		Dict		     =			{0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}
print(check_bipartite_dfs(graph))