


from typing import Any

import numpy as np







class      _lowercase					:


       """simple docstring"""




       def __init__(  self				:     List[Any]   , __lowerCamelCase				:     np.ndarray   , __lowerCamelCase				:     int			):


             '''simple docstring'''



             if np.any(tableau[:, -1]   , where=tableau[:, -1] < 0			):
                   raise ValueError("RHS must be > 0"			)

             lowerCamelCase__						:							int       =    tableau
             lowerCamelCase__       ,  lowerCamelCase__						:							Dict       =    tableau.shape

             # Number of decision variables x1, x2, x3...
             lowerCamelCase__						:							Dict       =    n_vars

             # Number of artificial variables to be minimised
             lowerCamelCase__						:							Optional[Any]       =    len(np.where(tableau[self.n_vars : -1] == -1			)[0]			)

             # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
             lowerCamelCase__						:							Tuple       =    (self.n_art_vars > 0) + 1

             # Number of slack variables added to make inequalities into equalities
             lowerCamelCase__						:							Dict       =    self.n_rows - self.n_stages

             # Objectives for each stage
             lowerCamelCase__						:							str       =    ["max"]

             # In two stage simplex, first minimise then maximise
             if self.n_art_vars:
                   self.objectives.append("min"			)

             lowerCamelCase__						:							Dict       =    [""]

             # Index of current pivot row and column
             lowerCamelCase__						:							Optional[int]       =    None
             lowerCamelCase__						:							Optional[Any]       =    None

             # Does objective row only contain (non)-negative values?
             lowerCamelCase__						:							int       =    False





       @staticmethod
       def 		lowerCAmelCase	(  *__lowerCamelCase				:     int			):


             '''simple docstring'''



             if len(__lowerCamelCase			) != 3:
                   raise ValueError("Must provide n_vars, n_slack, and n_art_vars"			)

             if not all(x >= 0 and isinstance(__lowerCamelCase   , __lowerCamelCase			) for x in args			):
                   raise ValueError("All arguments must be non-negative integers"			)

             # decision | slack | artificial
             lowerCamelCase__						:							Dict       =    ["x", "s", "a"]
             lowerCamelCase__						:							Any       =    []
             for i in range(3			):
                   for j in range(args[i]			):
                         titles.append(string_starts[i] + str(j + 1			)			)
             titles.append("RHS"			)
             return titles





       def 		lowerCAmelCase	(  self				:     List[Any]   , __lowerCamelCase				:     np.ndarray			):


             '''simple docstring'''



             lowerCamelCase__						:							Dict       =    self.objectives[-1]

             # Find entries of highest magnitude in objective rows
             lowerCamelCase__						:							str       =    (objective == "min") - (objective == "max")
             lowerCamelCase__						:							Optional[Any]       =    np.argmax(sign * tableau[0, : self.n_vars]			)

             # Choice is only valid if below 0 for maximise, and above for minimise
             if sign * self.tableau[0, col_idx] <= 0:
                   lowerCamelCase__						:							Optional[Any]       =    True
                   return 0, 0

             # Pivot row is chosen as having the lowest quotient when elements of
             # the pivot column divide the right-hand side

             # Slice excluding the objective rows
             lowerCamelCase__						:							str       =    slice(self.n_stages   , self.n_rows			)

             # RHS
             lowerCamelCase__						:							Tuple       =    tableau[s, -1]

             # Elements of pivot column within slice
             lowerCamelCase__						:							str       =    tableau[s, col_idx]

             # Array filled with nans
             lowerCamelCase__						:							Optional[Any]       =    np.full(self.n_rows - self.n_stages   , np.nan			)

             # If element in pivot column is greater than zeron_stages, return
             # quotient or nan otherwise
             lowerCamelCase__						:							Tuple       =    np.divide(__lowerCamelCase   , __lowerCamelCase   , out=__lowerCamelCase   , where=divisor > 0			)

             # Arg of minimum quotient excluding the nan values. n_stages is added
             # to compensate for earlier exclusion of objective columns
             lowerCamelCase__						:							Dict       =    np.nanargmin(__lowerCamelCase			) + self.n_stages
             return row_idx, col_idx





       def 		lowerCAmelCase	(  self				:     Any   , __lowerCamelCase				:     np.ndarray   , __lowerCamelCase				:     int   , __lowerCamelCase				:     int			):


             '''simple docstring'''



             lowerCamelCase__						:							Optional[int]       =    tableau[row_idx].copy()

             lowerCamelCase__						:							Optional[Any]       =    piv_row[col_idx]

             # Entry becomes 1
             piv_row *= 1 / piv_val

             # Variable in pivot column becomes basic, ie the only non-zero entry
             for idx, coeff in enumerate(tableau[:, col_idx]			):
                   tableau[idx] += -coeff * piv_row
             lowerCamelCase__						:							List[str]       =    piv_row
             return tableau





       def 		lowerCAmelCase	(  self				:     Optional[Any]   , __lowerCamelCase				:     np.ndarray			):


             '''simple docstring'''



             self.objectives.pop()

             if not self.objectives:
                   return tableau

             # Slice containing ids for artificial columns
             lowerCamelCase__						:							str       =    slice(-self.n_art_vars - 1   , -1			)

             # Delete the artificial variable columns
             lowerCamelCase__						:							Any       =    np.delete(__lowerCamelCase   , __lowerCamelCase   , axis=1			)

             # Delete the objective row of the first stage
             lowerCamelCase__						:							Optional[int]       =    np.delete(__lowerCamelCase   , 0   , axis=0			)

             lowerCamelCase__						:							Dict       =    1
             self.n_rows -= 1
             lowerCamelCase__						:							List[Any]       =    0
             lowerCamelCase__						:							Any       =    False
             return tableau





       def 		lowerCAmelCase	(  self				:     List[str]			):


             '''simple docstring'''



             for _ in range(100			):
                   # Completion of each stage removes an objective. If both stages
                   # are complete, then no objectives are left
                   if not self.objectives:
                         lowerCamelCase__						:							Any       =    self.generate_col_titles(
                             self.n_vars   , self.n_slack   , self.n_art_vars			)

                         # Find the values of each variable at optimal solution
                         return self.interpret_tableau(self.tableau   , self.col_titles			)

                   lowerCamelCase__       ,  lowerCamelCase__						:							Tuple       =    self.find_pivot(self.tableau			)

                   # If there are no more negative values in objective row
                   if self.stop_iter:
                         # Delete artificial variable columns and rows. Update attributes
                         lowerCamelCase__						:							Dict       =    self.change_stage(self.tableau			)
                   else:
                         lowerCamelCase__						:							int       =    self.pivot(self.tableau   , __lowerCamelCase   , __lowerCamelCase			)
             return {}





       def 		lowerCAmelCase	(  self				:     List[str]   , __lowerCamelCase				:     np.ndarray   , __lowerCamelCase				:     list[str]			):


             '''simple docstring'''



             lowerCamelCase__						:							int       =    {"P": abs(tableau[0, -1]			)}

             for i in range(self.n_vars			):
                   # Gives ids of nonzero entries in the ith column
                   lowerCamelCase__						:							Any       =    np.nonzero(tableau[:, i]			)
                   lowerCamelCase__						:							Dict       =    len(nonzero[0]			)

                   # First entry in the nonzero ids
                   lowerCamelCase__						:							Tuple       =    nonzero[0][0]
                   lowerCamelCase__						:							Optional[int]       =    tableau[nonzero_rowidx, i]

                   # If there is only one nonzero value in column, which is one
                   if n_nonzero == nonzero_val == 1:
                         lowerCamelCase__						:							str       =    tableau[nonzero_rowidx, -1]
                         lowerCamelCase__						:							str       =    rhs_val

        # Check for basic variables
             for title in col_titles:
                   # Don't add RHS or slack variables to output dict
                   if title[0] not in "R-s-a":
                         output_dict.setdefault(__lowerCamelCase   , 0			)
             return output_dict


if __name__ == "__main__":
    import doctest

    doctest.testmod()






import torch

from transformers import AutoTokenizer







class      _lowercase					(				lowercase__):


       """simple docstring"""




       def __init__(  self				:     Optional[Any]   , __lowerCamelCase				:     Dict			):


             '''simple docstring'''



             lowerCamelCase__						:							int       =    AutoTokenizer.from_pretrained(__lowerCamelCase			)





       def 		lowerCAmelCase	(  self				:     Union[str, Any]   , __lowerCamelCase				:     str			):


             '''simple docstring'''



             if isinstance(__lowerCamelCase   , __lowerCamelCase			) and all(isinstance(_x   , __lowerCamelCase			) for _x in x			):
                   lowerCamelCase__						:							List[Any]       =    None
                   for l in x:
                         lowerCamelCase__						:							str       =    self.tokenizer(
                             __lowerCamelCase   , padding="max_length"   , max_length=384   , truncation=__lowerCamelCase   , return_tensors="pt"   , )
                         lowerCamelCase__						:							Dict       =    torch.tensor([len(__lowerCamelCase			)]			)
                         if d is not None:
                               for k in d.keys():
                                     lowerCamelCase__						:							Tuple       =    torch.cat((d[k], t[k])   , 0			)
                         else:
                               lowerCamelCase__						:							Union[str, Any]       =    t

                   lowerCamelCase__						:							List[Any]       =    torch.tensor(self.tokenizer.convert_tokens_to_ids("[E]"			)			)
                   lowerCamelCase__						:							Dict       =    torch.tensor(self.tokenizer.convert_tokens_to_ids("[/E]"			)			)

             elif isinstance(__lowerCamelCase   , __lowerCamelCase			) and all(isinstance(_x   , __lowerCamelCase			) for _x in x			):
                   lowerCamelCase__						:							Tuple       =    self.tokenizer(
                       __lowerCamelCase   , padding="max_length"   , max_length=384   , truncation=__lowerCamelCase   , return_tensors="pt"   , )

             else:
                   raise Exception(
                       "Type of parameter x was not recognized! Only `list of strings` for query or `list of lists of"
                       " strings` for supports are supported."			)

             return d





       def 		lowerCAmelCase	(  self				:     List[Any]   , __lowerCamelCase				:     List[str]   , __lowerCamelCase				:     List[str]   , __lowerCamelCase				:     Dict   , __lowerCamelCase				:     Any   , __lowerCamelCase				:     Optional[Any]=0.7_0			):


             '''simple docstring'''



             lowerCamelCase__						:							Union[str, Any]       =    []
             for idx in range(len(W_query["input_ids"]			)			):
                   lowerCamelCase__						:							str       =    range(p_start.shape[1]			)

                   lowerCamelCase__						:							int       =    []
                   for start_id in start_indexes:
                         for end_id in end_indexes:
                               if start_id < end_id:
                                     output.append(
                                         (
                                             start_id,
                                             end_id,
                                             p_start[idx][start_id].item(),
                                             p_end[idx][end_id].item(),
                                         )			)

                   output.sort(key=lambda __lowerCamelCase			: (tup[2] * tup[3])   , reverse=__lowerCamelCase			)
                   lowerCamelCase__						:							str       =    []
                   for k in range(len(__lowerCamelCase			)			):
                         if output[k][2] * output[k][3] >= thresh:
                               lowerCamelCase__       ,  lowerCamelCase__						:							Optional[int]       =    output[k][0], output[k][1]
                               lowerCamelCase__						:							Tuple       =    self.tokenizer.decode(W_query["input_ids"][idx][c_start_pos:c_end_pos]			)
                               temp.append((decoded, output[k][2] * output[k][3])			)

                   final_outputs.append(__lowerCamelCase			)

             return final_outputs


