'''simple docstring'''


from __future__ import annotations


def  _lowerCamelCase   (				lowerCamelCase_ :							str     ,					lowerCamelCase_ :							list[str] | None = None       ):



     """simple docstring"""





     UpperCAmelCase_							:       Any       =				word_bank or []
     # create a table
     UpperCAmelCase_							:       int       =				len(lowerCamelCase_       ) + 1

     UpperCAmelCase_							:       list[list[list[str]]]       =				[]
     for _ in range(lowerCamelCase_       ):
          table.append([]       )
     # seed value
     UpperCAmelCase_							:       Optional[int]       =				[[]]  # because empty string has empty combination

     # iterate through the indices
     for i in range(lowerCamelCase_       ):
          # condition
          if table[i] != []:
               for word in word_bank:
                    # slice condition
                    if target[i : i + len(lowerCamelCase_       )] == word:
                         UpperCAmelCase_							:       list[list[str]]       =				[
                             [word, *way] for way in table[i]
                         ]
                         # adds the word to every combination the current position holds
                         # now,push that combination to the table[i+len(word)]
                         table[i + len(lowerCamelCase_       )] += new_combinations

                    # combinations are in reverse order so reverse for better output
     for combination in table[len(lowerCamelCase_       )]:
          combination.reverse()

     return table[len(lowerCamelCase_       )]


if __name__ == "__main__":
 print(all_construct("""jwajalapa""", ["""jwa""", """j""", """w""", """a""", """la""", """lapa"""]))
 print(all_construct("""rajamati""", ["""s""", """raj""", """amat""", """raja""", """ma""", """i""", """t"""]))
 print(
     all_construct(
         """hexagonosaurus""",
         ["""h""", """ex""", """hex""", """ag""", """ago""", """ru""", """auru""", """rus""", """go""", """no""", """o""", """s"""],
     )
 )







'''simple docstring'''


import math
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput






class 					__SCREAMING_SNAKE_CASE						(	lowerCamelCase_						,     lowerCamelCase_	):







  '''simple docstring'''






  lowerCamelCase_		:Union[str, Any]						   =		1


  @register_to_config
  def __init__(			self				,		snake_case_ = 1_0_0_0				,		snake_case_ = None						):




       '''simple docstring'''

       self.set_timesteps(snake_case_						)

       # standard deviation of the initial noise distribution
       UpperCAmelCase_							:       Union[str, Any]       =				1.0

       # For now we only support F-PNDM, i.e. the runge-kutta method
       # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
       # mainly at formula (9), (12), (13) and the Algorithm 2.
       UpperCAmelCase_							:       int       =				4

       # running values
       UpperCAmelCase_							:       str       =				[]


  def _UpperCamelCase					(			self				,		snake_case_				,		snake_case_ = None						):




       '''simple docstring'''

       UpperCAmelCase_							:       Union[str, Any]       =				num_inference_steps
       UpperCAmelCase_							:       int       =				torch.linspace(1				,		0				,		num_inference_steps + 1						)[:-1]
       UpperCAmelCase_							:       Tuple       =				torch.cat([steps, torch.tensor([0.0]						)]						)

       if self.config.trained_betas is not None:
            UpperCAmelCase_							:       Optional[int]       =				torch.tensor(self.config.trained_betas				,		dtype=torch.floataa						)
       else:
            UpperCAmelCase_							:       Tuple       =				torch.sin(steps * math.pi / 2						) ** 2

       UpperCAmelCase_							:       Dict       =				(1.0 - self.betas**2) ** 0.5

       UpperCAmelCase_							:       str       =				(torch.atana(self.betas				,		self.alphas						) / math.pi * 2)[:-1]
       UpperCAmelCase_							:       str       =				timesteps.to(snake_case_						)

       UpperCAmelCase_							:       Any       =				[]


  def _UpperCamelCase					(			self				,		snake_case_				,		snake_case_				,		snake_case_				,		snake_case_ = True				,		):




       '''simple docstring'''

       if self.num_inference_steps is None:
            raise ValueError(
                'Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'						)

       UpperCAmelCase_							:       Any       =				(self.timesteps == timestep).nonzero().item()
       UpperCAmelCase_							:       Optional[Any]       =				timestep_index + 1

       UpperCAmelCase_							:       Dict       =				sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
       self.ets.append(snake_case_						)

       if len(self.ets						) == 1:
            UpperCAmelCase_							:       Tuple       =				self.ets[-1]
       elif len(self.ets						) == 2:
            UpperCAmelCase_							:       Any       =				(3 * self.ets[-1] - self.ets[-2]) / 2
       elif len(self.ets						) == 3:
            UpperCAmelCase_							:       List[str]       =				(2_3 * self.ets[-1] - 1_6 * self.ets[-2] + 5 * self.ets[-3]) / 1_2
       else:
            UpperCAmelCase_							:       Union[str, Any]       =				(1 / 2_4) * (5_5 * self.ets[-1] - 5_9 * self.ets[-2] + 3_7 * self.ets[-3] - 9 * self.ets[-4])

       UpperCAmelCase_							:       Union[str, Any]       =				self._get_prev_sample(snake_case_				,		snake_case_				,		snake_case_				,		snake_case_						)

       if not return_dict:
            return (prev_sample,)

       return SchedulerOutput(prev_sample=snake_case_						)


  def _UpperCamelCase					(			self				,		snake_case_				,		*snake_case_				,		**snake_case_						):




       '''simple docstring'''

       return sample


  def _UpperCamelCase					(			self				,		snake_case_				,		snake_case_				,		snake_case_				,		snake_case_						):




       '''simple docstring'''

       UpperCAmelCase_							:       int       =				self.alphas[timestep_index]
       UpperCAmelCase_							:       Union[str, Any]       =				self.betas[timestep_index]

       UpperCAmelCase_							:       Any       =				self.alphas[prev_timestep_index]
       UpperCAmelCase_							:       Dict       =				self.betas[prev_timestep_index]

       UpperCAmelCase_							:       List[Any]       =				(sample - sigma * ets) / max(snake_case_				,		1E-8						)
       UpperCAmelCase_							:       Tuple       =				next_alpha * pred + ets * next_sigma

       return prev_sample






  def __len__(			self						):




       '''simple docstring'''

       return self.config.num_train_timesteps






