
'''simple docstring'''
import math

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

def 						UpperCamelCase_     (	__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE = 1,		__SCREAMING_SNAKE_CASE = 1,		__SCREAMING_SNAKE_CASE = 1.0E4,		__SCREAMING_SNAKE_CASE = False,		__SCREAMING_SNAKE_CASE = 1.0,		):
    """simple docstring"""






    assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
    assert embedding_dim % 2 == 0, f'Embedding dimension {embedding_dim} should be even'
    snake_case_ :    List[Any]     			=						float(embedding_dim // 2       )
    snake_case_ :    Any     			=						math.log(max_timescale / min_timescale       ) / (num_timescales - freq_shift)
    snake_case_ :    List[Any]     			=						min_timescale * jnp.exp(jnp.arange(__SCREAMING_SNAKE_CASE,		dtype=jnp.floataa       ) * -log_timescale_increment       )
    snake_case_ :    str     			=						jnp.expand_dims(__SCREAMING_SNAKE_CASE,		1       ) * jnp.expand_dims(__SCREAMING_SNAKE_CASE,		0       )

    # scale embeddings
    snake_case_ :    List[str]     			=						scale * emb

    if flip_sin_to_cos:
        snake_case_ :    Union[str, Any]     			=						jnp.concatenate([jnp.cos(__SCREAMING_SNAKE_CASE       ), jnp.sin(__SCREAMING_SNAKE_CASE       )],		axis=1       )
    else:
        snake_case_ :    Tuple     			=						jnp.concatenate([jnp.sin(__SCREAMING_SNAKE_CASE       ), jnp.cos(__SCREAMING_SNAKE_CASE       )],		axis=1       )
    snake_case_ :    Tuple     			=						jnp.reshape(__SCREAMING_SNAKE_CASE,		[jnp.shape(__SCREAMING_SNAKE_CASE       )[0], embedding_dim]       )
    return signal






class    UpperCAmelCase_				(	nn.Module					):
 UpperCAmelCase_		    =						3_2
 UpperCAmelCase_		    =						jnp.floataa





 @nn.compact
 def __call__(    self ,       lowercase_):
     snake_case_ :    Optional[int]     			=						nn.Dense(self.time_embed_dim ,       dtype=self.dtype ,       name="linear_1")(lowercase_)
     snake_case_ :    Union[str, Any]     			=						nn.silu(lowercase_)
     snake_case_ :    Union[str, Any]     			=						nn.Dense(self.time_embed_dim ,       dtype=self.dtype ,       name="linear_2")(lowercase_)
     return temb






class    UpperCAmelCase_				(	nn.Module					):
 UpperCAmelCase_		    =						3_2
 UpperCAmelCase_		    =						False
 UpperCAmelCase_		    =						1





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






'''simple docstring'''
from __future__ import annotations

import math

def 						UpperCamelCase_     (	__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       ):
    """simple docstring"""






    if depth < 0:
        raise ValueError("Depth cannot be less than 0"       )

    if len(__SCREAMING_SNAKE_CASE       ) == 0:
        raise ValueError("Scores cannot be empty"       )

    if depth == height:
        return scores[node_index]

    if is_max:
        return max(
            minimax(depth + 1,		node_index * 2,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       ),		minimax(depth + 1,		node_index * 2 + 1,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       ),		)

    return min(
        minimax(depth + 1,		node_index * 2,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       ),		minimax(depth + 1,		node_index * 2 + 1,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       ),		)

def 						UpperCamelCase_     (	):
    """simple docstring"""






    snake_case_ :    int     			=						[9_0, 2_3, 6, 3_3, 2_1, 6_5, 1_2_3, 3_4_4_2_3]
    snake_case_ :    Union[str, Any]     			=						math.log(len(__SCREAMING_SNAKE_CASE       ),		2       )
    print("Optimal value : ",		end=""       )
    print(minimax(0,		0,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       )       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()




