


from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar



class      snake_case__	(   lowerCamelCase__	):
				@abstractmethod
				def __lt__(	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										pass
				@abstractmethod
				def __gt__(	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										pass





				@abstractmethod
				def __eq__(	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										pass






snake_case__  				=			TypeVar('T', bound=Comparable)



class      snake_case__	(   Generic[T]	):
				def __init__(	self   ):




										"""simple docstring"""




										__magic_name__					:				list[T]				=   []
										__magic_name__					:				int				=   0
				def __repr__(	self   ):




										"""simple docstring"""




										return str(self.h   )
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										if child_idx > 0:
																return (child_idx - 1) // 2
										return None
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										__magic_name__					:				List[Any]				=   2 * parent_idx + 1
										if left_child_index < self.heap_size:
																return left_child_index
										return None
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										__magic_name__					:				Dict				=   2 * parent_idx + 2
										if right_child_index < self.heap_size:
																return right_child_index
										return None
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										if index < self.heap_size:
																__magic_name__					:				int				=   index
																__magic_name__					:				int				=   self.left_child_idx(_UpperCAmelCase   )
																__magic_name__					:				Dict				=   self.right_child_idx(_UpperCAmelCase   )
																# check which child is larger than its parent
																if left_child is not None and self.h[left_child] > self.h[violation]:
																						__magic_name__					:				Optional[int]				=   left_child
																if right_child is not None and self.h[right_child] > self.h[violation]:
																						__magic_name__					:				Tuple				=   right_child
																# if violation indeed exists
																if violation != index:
																						# swap to fix the violation
																						__magic_name__					:				Optional[int]				=   self.h[index], self.h[violation]
																						# fix the subsequent violation recursively if any
																						self.max_heapify(_UpperCAmelCase   )
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										__magic_name__					:				Dict				=   list(_UpperCAmelCase   )
										__magic_name__					:				List[str]				=   len(self.h   )
										if self.heap_size > 1:
																# max_heapify from right to left but exclude leaves (last level)
																for i in range(self.heap_size // 2 - 1  ,   -1  ,   -1   ):
																						self.max_heapify(_UpperCAmelCase   )
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										if self.heap_size >= 2:
																__magic_name__					:				Union[str, Any]				=   self.h[0]
																__magic_name__					:				str				=   self.h.pop(-1   )
																self.heap_size -= 1
																self.max_heapify(0   )
																return me
										elif self.heap_size == 1:
																self.heap_size -= 1
																return self.h.pop(-1   )
										else:
																raise Exception('Empty heap'   )
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										self.h.append(_UpperCAmelCase   )
										__magic_name__					:				Any				=   (self.heap_size - 1) // 2
										self.heap_size += 1
										while idx >= 0:
																self.max_heapify(_UpperCAmelCase   )
																__magic_name__					:				Dict				=   (idx - 1) // 2





				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__					:				Any				=   self.heap_size
										for j in range(size - 1  ,   0  ,   -1   ):
																__magic_name__					:				int				=   self.h[j], self.h[0]
																self.heap_size -= 1
																self.max_heapify(0   )
										__magic_name__					:				Any				=   size


if __name__ == "__main__":
			import doctest

			# run doc test
			doctest.testmod()

			# demo
			for unsorted in [
			    [0],
			    [2],
			    [3, 5],
			    [5, 3],
			    [5, 5],
			    [0, 0, 0, 0],
			    [1, 1, 1, 1],
			    [2, 2, 3, 5],
			    [0, 2, 2, 3, 5],
			    [2, 5, 3, 0, 2, 3, 0, 3],
			    [6, 1, 2, 7, 9, 3, 4, 5, 10, 8],
			    [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
			    [-45, -2, -5],
			]:
						print(F"""unsorted array: {unsorted}""")

						snake_case__  				=			Heap()
						heap.build_max_heap(unsorted)
						print(F"""after build heap: {heap}""")

						print(F"""max value: {heap.extract_max()}""")
						print(F"""after max value removed: {heap}""")

						heap.insert(100)
						print(F"""after new value 100 inserted: {heap}""")

						heap.heap_sort()
						print(F"""heap-sorted array: {heap}\n""")





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

class        _UpperCamelCase	:


  """simple docstring"""





  snake_case_        =    'block_{0}.dat'



  def __init__( self					: int       ,       snake_case					: int      )	->			List[str]:


         '''simple docstring'''





         __magic_name__			:		Optional[int]        =     filename
         __magic_name__			:		Any        =     []



  def 							_UpperCAmelCase      ( self					: Optional[Any]       ,       snake_case					: int       ,       snake_case					: Any      )	->			List[Any]:


         '''simple docstring'''





         __magic_name__			:		Optional[Any]        =     self.BLOCK_FILENAME_FORMAT.format(snake_case      )
         with open(snake_case       ,       '''w'''      ) as file:
                file.write(snake_case      )
         self.block_filenames.append(snake_case      )



  def 							_UpperCAmelCase      ( self					: str      )	->			List[str]:


         '''simple docstring'''





         return self.block_filenames



  def 							_UpperCAmelCase      ( self					: Union[str, Any]       ,       snake_case					: Dict       ,       snake_case					: int=None      )	->			Union[str, Any]:


         '''simple docstring'''





         __magic_name__			:		List[str]        =     0
         with open(self.filename      ) as file:
                while True:
                       __magic_name__			:		Tuple        =     file.readlines(snake_case      )

                       if lines == []:
                              break

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

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




  def 							_UpperCAmelCase      ( self					: Tuple      )	->			Optional[int]:


         '''simple docstring'''





         map(os.remove       ,       self.block_filenames      )

class        _UpperCamelCase	:


  """simple docstring"""





  def 							_UpperCAmelCase      ( self					: List[Any]       ,       snake_case					: Dict      )	->			int:


         '''simple docstring'''





         __magic_name__			:		Any        =     -1
         __magic_name__			:		Union[str, Any]        =     None

         for i in range(len(snake_case      )      ):
                if min_str is None or choices[i] < min_str:
                       __magic_name__			:		Dict        =     i

         return min_index

class        _UpperCamelCase	:


  """simple docstring"""





  def __init__( self					: str       ,       snake_case					: Optional[int]      )	->			Any:


         '''simple docstring'''





         __magic_name__			:		Dict        =     files
         __magic_name__			:		List[str]        =     set()
         __magic_name__			:		Any        =     len(snake_case      )
         __magic_name__			:		int        =     {i: None for i in range(self.num_buffers      )}



  def 							_UpperCAmelCase      ( self					: List[str]      )	->			Optional[Any]:


         '''simple docstring'''





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



  def 							_UpperCAmelCase      ( self					: int      )	->			int:


         '''simple docstring'''





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

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

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

         return True




  def 							_UpperCAmelCase      ( self					: Dict       ,       snake_case					: Optional[Any]      )	->			Optional[Any]:


         '''simple docstring'''





         __magic_name__			:		List[str]        =     self.buffers[index]
         __magic_name__			:		Dict        =     None

         return value

class        _UpperCamelCase	:


  """simple docstring"""





  def __init__( self					: Any       ,       snake_case					: str      )	->			Dict:


         '''simple docstring'''





         __magic_name__			:		Optional[Any]        =     merge_strategy



  def 							_UpperCAmelCase      ( self					: Optional[int]       ,       snake_case					: int       ,       snake_case					: Dict       ,       snake_case					: Dict      )	->			Union[str, Any]:


         '''simple docstring'''





         __magic_name__			:		Union[str, Any]        =     FilesArray(self.get_file_handles(snake_case       ,       snake_case      )      )
         with open(snake_case       ,       '''w'''       ,       snake_case      ) as outfile:
                while buffers.refresh():
                       __magic_name__			:		List[str]        =     self.merge_strategy.select(buffers.get_dict()      )
                       outfile.write(buffers.unshift(snake_case      )      )




  def 							_UpperCAmelCase      ( self					: Union[str, Any]       ,       snake_case					: List[str]       ,       snake_case					: Optional[int]      )	->			Union[str, Any]:


         '''simple docstring'''





         __magic_name__			:		str        =     {}

         for i in range(len(snake_case      )      ):
                __magic_name__			:		Any        =     open(filenames[i]       ,       '''r'''       ,       snake_case      )  # noqa: UP015

         return files

class        _UpperCamelCase	:


  """simple docstring"""





  def __init__( self					: Optional[Any]       ,       snake_case					: Union[str, Any]      )	->			Optional[int]:


         '''simple docstring'''





         __magic_name__			:		int        =     block_size



  def 							_UpperCAmelCase      ( self					: str       ,       snake_case					: Optional[int]       ,       snake_case					: Dict=None      )	->			Optional[Any]:


         '''simple docstring'''





         __magic_name__			:		Tuple        =     self.get_number_blocks(snake_case       ,       self.block_size      )
         __magic_name__			:		str        =     FileSplitter(snake_case      )
         splitter.split(self.block_size       ,       snake_case      )

         __magic_name__			:		int        =     FileMerger(NWayMerge()      )
         __magic_name__			:		Any        =     self.block_size / (num_blocks + 1)
         merger.merge(splitter.get_block_filenames()       ,       filename + '''.out'''       ,       snake_case      )

         splitter.cleanup()




  def 							_UpperCAmelCase      ( self					: Tuple       ,       snake_case					: List[str]       ,       snake_case					: Union[str, Any]      )	->			Tuple:


         '''simple docstring'''





         return (os.stat(snake_case      ).st_size / block_size) + 1







def       UpperCamelCase_					(     lowerCamelCase							:					Union[str, Any]   )						->     Union[str, 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(lowerCamelCase   )







def       UpperCamelCase_					(     )						->     Optional[Any]:



       """simple docstring"""







       __magic_name__			:		Tuple        =     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'''   )
       __magic_name__			:		List[str]        =     parser.parse_args()

       __magic_name__			:		Any        =     ExternalSort(parse_memory(args.mem   )   )
       sorter.sort(args.filename[0]   )


if __name__ == "__main__":
 main()
