

import math





class 			__lowerCAmelCase					:




  def __init__(    self							,       lowerCAmelCase							,       lowerCAmelCase							,       lowerCAmelCase							,       lowerCAmelCase )  ->			List[str]:
        '''simple docstring'''






        _lowercase     	=x
        _lowercase     	=y
        _lowercase     	=step_size
        _lowercase     	=function_to_optimize




  def   A__					(    self )  ->			int:
        '''simple docstring'''






        return self.function(self.x							,       self.y )




  def   A__					(    self )  ->			Any:
        '''simple docstring'''






        _lowercase     	=self.step_size
        return [
            SearchProblem(lowerCAmelCase							,       lowerCAmelCase							,       lowerCAmelCase							,       self.function )
            for x, y in (
                (self.x - step_size, self.y - step_size),
                (self.x - step_size, self.y),
                (self.x - step_size, self.y + step_size),
                (self.x, self.y - step_size),
                (self.x, self.y + step_size),
                (self.x + step_size, self.y - step_size),
                (self.x + step_size, self.y),
                (self.x + step_size, self.y + step_size),
            )
        ]




  def __hash__(    self )  ->			Dict:
        '''simple docstring'''






        return hash(str(self ) )




  def __eq__(    self							,       lowerCAmelCase )  ->			Optional[int]:
        '''simple docstring'''






        if isinstance(lowerCAmelCase							,       lowerCAmelCase ):
              return hash(str(self ) ) == hash(str(lowerCAmelCase ) )
        return False




  def __str__(    self )  ->			Optional[int]:
        '''simple docstring'''






        return F'''x: {self.x} y: {self.y}'''
def 					a				(      A__     :       int				,       A__     :       bool = True				,       A__     :       float = math.inf				,       A__     :       float = -math.inf				,       A__     :       float = math.inf				,       A__     :       float = -math.inf				,       A__     :       bool = False				,       A__     :       int = 10000				,       )   ->				SearchProblem:





      """simple docstring"""



      _lowercase     	=search_prob
      _lowercase     	=[]  # list to store the current score at each iteration
      _lowercase     	=0
      _lowercase     	=False
      _lowercase     	=set()
      while not solution_found and iterations < max_iter:
            visited.add(A__					)
            iterations += 1
            _lowercase     	=current_state.score()
            scores.append(A__					)
            _lowercase     	=current_state.get_neighbors()
            _lowercase     	=-math.inf
            _lowercase     	=math.inf
            _lowercase     	=None  # to hold the next best neighbor
            for neighbor in neighbors:
                  if neighbor in visited:
                        continue  # do not want to visit the same state again
                  if (
                      neighbor.x > max_x
                      or neighbor.x < min_x
                      or neighbor.y > max_y
                      or neighbor.y < min_y
                  ):
                        continue  # neighbor outside our bounds
                  _lowercase     	=neighbor.score() - current_score
                  if find_max:  # finding max
                        # going to direction with greatest ascent
                        if change > max_change and change > 0:
                              _lowercase     	=change
                              _lowercase     	=neighbor
                  else:  # finding min
                        # to direction with greatest descent
                        if change < min_change and change < 0:
                              _lowercase     	=change
                              _lowercase     	=neighbor
            if next_state is not None:
                  # we found at least one neighbor which improved the current state
                  _lowercase     	=next_state
            else:
                  # since we have no neighbor that improves the solution we stop the search
                  _lowercase     	=True

      if visualization:
            from matplotlib import pyplot as plt

            plt.plot(range(A__					)				,       A__					)
            plt.xlabel('Iterations'					)
            plt.ylabel('Function values'					)
            plt.show()

      return current_state


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  def 					a				(      A__     :       Dict				,       A__     :       Tuple					)   ->				Optional[Any]:





        """simple docstring"""



        return (x**2) + (y**2)

  # starting the problem with initial coordinates (3, 4)
  lowercase_     =       SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  lowercase_     =       hill_climbing(prob, find_max=False)
  print(
      'The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: '
      f"{local_min.score()}"
  )

  # starting the problem with initial coordinates (12, 47)
  lowercase_     =       SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
  lowercase_     =       hill_climbing(
      prob, find_max=False, max_x=1_0_0, min_x=5, max_y=5_0, min_y=-5, visualization=True
  )
  print(
      'The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 '
      f"and 50 > y > - 5 found via hill climbing: {local_min.score()}"
  )
  def 					a				(      A__     :       Union[str, Any]				,       A__     :       Optional[Any]					)   ->				Optional[int]:





        """simple docstring"""



        return (3 * x**2) - (6 * y)

  lowercase_     =       SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  lowercase_     =       hill_climbing(prob, find_max=True)







  print(
      'The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: '
      f"{local_min.score()}"
  )





#
# Sort large text files in a minimum amount of memory
#
import argparse
import os





class 			__lowerCAmelCase					:
  _a						      =  """block_{0}.dat"""




  def __init__(    self							,       lowerCAmelCase )  ->			List[str]:
        '''simple docstring'''






        _lowercase     	=filename
        _lowercase     	=[]




  def   A__					(    self							,       lowerCAmelCase							,       lowerCAmelCase )  ->			str:
        '''simple docstring'''






        _lowercase     	=self.BLOCK_FILENAME_FORMAT.format(lowerCAmelCase )
        with open(lowerCAmelCase							,       'w' ) as file:
              file.write(lowerCAmelCase )
        self.block_filenames.append(lowerCAmelCase )




  def   A__					(    self )  ->			Dict:
        '''simple docstring'''






        return self.block_filenames




  def   A__					(    self							,       lowerCAmelCase							,       lowerCAmelCase=None )  ->			Dict:
        '''simple docstring'''






        _lowercase     	=0
        with open(self.filename ) as file:
              while True:
                    _lowercase     	=file.readlines(lowerCAmelCase )

                    if lines == []:
                          break

                    if sort_key is None:
                          lines.sort()
                    else:
                          lines.sort(key=lowerCAmelCase )

                    self.write_block(''.join(lowerCAmelCase )							,       lowerCAmelCase )
                    i += 1




  def   A__					(    self )  ->			Optional[Any]:
        '''simple docstring'''






        map(os.remove							,       self.block_filenames )





class 			__lowerCAmelCase					:




  def   A__					(    self							,       lowerCAmelCase )  ->			Union[str, Any]:
        '''simple docstring'''






        _lowercase     	=-1
        _lowercase     	=None

        for i in range(len(lowerCAmelCase ) ):
              if min_str is None or choices[i] < min_str:
                    _lowercase     	=i

        return min_index





class 			__lowerCAmelCase					:




  def __init__(    self							,       lowerCAmelCase )  ->			int:
        '''simple docstring'''






        _lowercase     	=files
        _lowercase     	=set()
        _lowercase     	=len(lowerCAmelCase )
        _lowercase     	={i: None for i in range(self.num_buffers )}




  def   A__					(    self )  ->			int:
        '''simple docstring'''






        return {
            i: self.buffers[i] for i in range(self.num_buffers ) if i not in self.empty
        }




  def   A__					(    self )  ->			Union[str, Any]:
        '''simple docstring'''






        for i in range(self.num_buffers ):
              if self.buffers[i] is None and i not in self.empty:
                    _lowercase     	=self.files[i].readline()

                    if self.buffers[i] == "":
                          self.empty.add(lowerCAmelCase )
                          self.files[i].close()

        if len(self.empty ) == self.num_buffers:
              return False

        return True




  def   A__					(    self							,       lowerCAmelCase )  ->			Optional[int]:
        '''simple docstring'''






        _lowercase     	=self.buffers[index]
        _lowercase     	=None

        return value





class 			__lowerCAmelCase					:




  def __init__(    self							,       lowerCAmelCase )  ->			Any:
        '''simple docstring'''






        _lowercase     	=merge_strategy




  def   A__					(    self							,       lowerCAmelCase							,       lowerCAmelCase							,       lowerCAmelCase )  ->			str:
        '''simple docstring'''






        _lowercase     	=FilesArray(self.get_file_handles(lowerCAmelCase							,       lowerCAmelCase ) )
        with open(lowerCAmelCase							,       'w'							,       lowerCAmelCase ) as outfile:
              while buffers.refresh():
                    _lowercase     	=self.merge_strategy.select(buffers.get_dict() )
                    outfile.write(buffers.unshift(lowerCAmelCase ) )




  def   A__					(    self							,       lowerCAmelCase							,       lowerCAmelCase )  ->			Optional[int]:
        '''simple docstring'''






        _lowercase     	={}

        for i in range(len(lowerCAmelCase ) ):
              _lowercase     	=open(filenames[i]							,       'r'							,       lowerCAmelCase )  # noqa: UP015

        return files





class 			__lowerCAmelCase					:




  def __init__(    self							,       lowerCAmelCase )  ->			Union[str, Any]:
        '''simple docstring'''






        _lowercase     	=block_size




  def   A__					(    self							,       lowerCAmelCase							,       lowerCAmelCase=None )  ->			Dict:
        '''simple docstring'''






        _lowercase     	=self.get_number_blocks(lowerCAmelCase							,       self.block_size )
        _lowercase     	=FileSplitter(lowerCAmelCase )
        splitter.split(self.block_size							,       lowerCAmelCase )

        _lowercase     	=FileMerger(NWayMerge() )
        _lowercase     	=self.block_size / (num_blocks + 1)
        merger.merge(splitter.get_block_filenames()							,       filename + '.out'							,       lowerCAmelCase )

        splitter.cleanup()




  def   A__					(    self							,       lowerCAmelCase							,       lowerCAmelCase )  ->			Tuple:
        '''simple docstring'''






        return (os.stat(lowerCAmelCase ).st_size / block_size) + 1
def 					a				(      A__     :       Tuple					)   ->				Optional[Any]:





      """simple docstring"""



      if string[-1].lower() == "k":
            return int(string[:-1]					) * 1024
      elif string[-1].lower() == "m":
            return int(string[:-1]					) * 1024 * 1024
      elif string[-1].lower() == "g":
            return int(string[:-1]					) * 1024 * 1024 * 1024
      else:
            return int(A__					)
def 					a				(      )   ->				str:





      """simple docstring"""



      _lowercase     	=argparse.ArgumentParser()
      parser.add_argument(
          '-m'				,       '--mem'				,       help='amount of memory to use for sorting'				,       default='100M'					)
      parser.add_argument(
          'filename'				,       metavar='<filename>'				,       nargs=1				,       help='name of file to sort'					)
      _lowercase     	=parser.parse_args()

      _lowercase     	=ExternalSort(parse_memory(args.mem					)					)
      sorter.sort(args.filename[0]					)


if __name__ == "__main__":
  main()


