






import bisect
import copy
from collections import defaultdict

import numpy as np
from torch.utils.data import BatchSampler, Sampler

from utils import logger
def   _A       (    SCREAMING_SNAKE_CASE__  :     Tuple					,  SCREAMING_SNAKE_CASE__  :     Optional[int]	):
    UpperCamelCase	:Union[str, Any]     							=       copy.deepcopy(SCREAMING_SNAKE_CASE__	)
    UpperCamelCase	:Union[str, Any]     							=       sorted(SCREAMING_SNAKE_CASE__	)
    UpperCamelCase	:List[Any]     							=       [bisect.bisect_right(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	) for y in x]
    return quantized
def   _A       (    SCREAMING_SNAKE_CASE__  :     Any					,  SCREAMING_SNAKE_CASE__  :     Optional[int]=0	):
    UpperCamelCase	:List[Any]     							=       np.arange(start=3					,  stop=SCREAMING_SNAKE_CASE__					,  step=4	).tolist() if k > 0 else [10]
    UpperCamelCase	:List[Any]     							=       _quantize(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	)
    # count number of elements per group
    UpperCamelCase	:Union[str, Any]     							=       np.unique(SCREAMING_SNAKE_CASE__					,  return_counts=SCREAMING_SNAKE_CASE__	)[1]
    UpperCamelCase	:int     							=       [0] + bins + [np.inf]
    logger.info('''Using {} as bins for aspect lengths quantization'''.format(SCREAMING_SNAKE_CASE__	)	)
    logger.info('''Count of instances per bin: {}'''.format(SCREAMING_SNAKE_CASE__	)	)
    return groups







class       UpperCAmelCase_						( UpperCamelCase_			):



      """simple docstring"""
      def __init__(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			)    ->				Any:




          if not isinstance(lowercase_   ,    lowercase_			):
              raise ValueError(
                  '''sampler should be an instance of torch.utils.data.Sampler, but got sampler={}'''.format(lowercase_			)			)
          UpperCamelCase	:Any     							=       sampler
          UpperCamelCase	:Dict     							=       group_ids
          UpperCamelCase	:Dict     							=       batch_size
      def __iter__(    self			)    ->				str:
          UpperCamelCase	:Union[str, Any]     							=       defaultdict(lowercase_			)
          UpperCamelCase	:Union[str, Any]     							=       defaultdict(lowercase_			)

          UpperCamelCase	:Any     							=       0
          for idx in self.sampler:
              UpperCamelCase	:Any     							=       self.group_ids[idx]
              buffer_per_group[group_id].append(lowercase_			)
              samples_per_group[group_id].append(lowercase_			)
              if len(buffer_per_group[group_id]			) == self.batch_size:
                  yield buffer_per_group[group_id]  # TODO
                  num_batches += 1
                  del buffer_per_group[group_id]
              assert len(buffer_per_group[group_id]			) < self.batch_size

          # now we have run out of elements that satisfy
          # the group criteria, let's return the remaining
          # elements so that the size of the sampler is
          # deterministic
          UpperCamelCase	:Union[str, Any]     							=       len(self			)
          UpperCamelCase	:Dict     							=       expected_num_batches - num_batches
          if num_remaining > 0:
              # for the remaining batches, group the batches by similar lengths
              UpperCamelCase	:Union[str, Any]     							=       []
              for group_id, idxs in sorted(buffer_per_group.items()   ,    key=lambda SCREAMING_SNAKE_CASE_			: x[0]			):
                  batch_idx.extend(lowercase_			)
                  if len(lowercase_			) >= self.batch_size:
                      yield batch_idx[: self.batch_size]
                      UpperCamelCase	:str     							=       batch_idx[self.batch_size :]
                      num_remaining -= 1
              if len(lowercase_			) > 0:
                  yield batch_idx
                  num_remaining -= 1
          assert num_remaining == 0




      def __len__(    self			)    ->				Union[str, Any]:
          return (len(self.sampler			) + self.batch_size - 1) // self.batch_size













def   _A       (    SCREAMING_SNAKE_CASE__  :     list[list[int]]	):
    if len(SCREAMING_SNAKE_CASE__	) == 0 or not all(len(SCREAMING_SNAKE_CASE__	) == 2 for pair in coordinates	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    if len({tuple(SCREAMING_SNAKE_CASE__	) for pair in coordinates}	) != len(SCREAMING_SNAKE_CASE__	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    UpperCamelCase	:str     							=       {x for x, _ in coordinates}
    if len(SCREAMING_SNAKE_CASE__	) == 1:
        return F'''x={coordinates[0][0]}'''

    if len(SCREAMING_SNAKE_CASE__	) != len(SCREAMING_SNAKE_CASE__	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    UpperCamelCase	:List[Any]     							=       len(SCREAMING_SNAKE_CASE__	)

    UpperCamelCase	:Optional[int]     							=       0
    UpperCamelCase	:list[list[float]]     							=       []
    # put the x and x to the power values in a matrix
    while count_of_line < x:
        UpperCamelCase	:Tuple     							=       0
        UpperCamelCase	:Optional[int]     							=       coordinates[count_of_line][0]
        UpperCamelCase	:list[float]     							=       []
        while count_in_line < x:
            count_line.append(a ** (x - (count_in_line + 1))	)
            count_in_line += 1
        matrix.append(SCREAMING_SNAKE_CASE__	)
        count_of_line += 1

    UpperCamelCase	:Optional[int]     							=       0
    # put the y values into a vector
    UpperCamelCase	:list[float]     							=       []
    while count_of_line < x:
        vector.append(coordinates[count_of_line][1]	)
        count_of_line += 1

    UpperCamelCase	:str     							=       0

    while count < x:
        UpperCamelCase	:Optional[Any]     							=       0
        while zahlen < x:
            if count == zahlen:
                zahlen += 1
            if zahlen == x:
                break
            UpperCamelCase	:Union[str, Any]     							=       matrix[zahlen][count] / matrix[count][count]
            for counting_columns, item in enumerate(matrix[count]	):
                # manipulating all the values in the matrix
                matrix[zahlen][counting_columns] -= item * bruch
            # manipulating the values in the vector
            vector[zahlen] -= vector[count] * bruch
            zahlen += 1
        count += 1

    UpperCamelCase	:Optional[int]     							=       0
    # make solutions
    UpperCamelCase	:list[str]     							=       []
    while count < x:
        solution.append(str(vector[count] / matrix[count][count]	)	)
        count += 1

    UpperCamelCase	:Union[str, Any]     							=       0
    UpperCamelCase	:Any     							=       '''f(x)='''

    while count < x:
        UpperCamelCase	:list[str]     							=       solution[count].split('''E'''	)
        if len(SCREAMING_SNAKE_CASE__	) > 1:
            UpperCamelCase	:List[Any]     							=       F'''{remove_e[0]}*10^{remove_e[1]}'''
        solved += F'''x^{x - (count + 1)}*{solution[count]}'''
        if count + 1 != x:
            solved += "+"
        count += 1

    return solved


if __name__ == "__main__":
 print(points_to_polynomial([]))
 print(points_to_polynomial([[]]))
 print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
 print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
 print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
 print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
 print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
 print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
 print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
 print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))





