from __future__ import annotations

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





class 	_lowercase		(      snake_case_ ):

 @abstractmethod
 def __lt__(				self			:							T     ,   snake_case			:							T    )     ->		bool:

  """simple docstring"""





  pass

 @abstractmethod
 def __gt__(				self			:							T     ,   snake_case			:							T    )     ->		bool:

  """simple docstring"""





  pass


 @abstractmethod
 def __eq__(				self			:							T     ,   snake_case			:							object    )     ->		bool:

  """simple docstring"""





  pass
a_					      = TypeVar('T', bound=Comparable)





class 	_lowercase		(      Generic[T] ):

 def __init__(				self			:							Optional[Any]    )     ->		None:

  """simple docstring"""





  UpperCamelCase_      :		list[T]				=      []
  UpperCamelCase_      :		int				=      0

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

  """simple docstring"""





  return str(self.h    )

 def 		SCREAMING_SNAKE_CASE__     (				self			:							Any     ,   snake_case			:							int    )     ->		int | None:

  """simple docstring"""





  if child_idx > 0:
   return (child_idx - 1) // 2
  return None

 def 		SCREAMING_SNAKE_CASE__     (				self			:							Tuple     ,   snake_case			:							int    )     ->		int | None:

  """simple docstring"""





  UpperCamelCase_      :		int				=      2 * parent_idx + 1
  if left_child_index < self.heap_size:
   return left_child_index
  return None

 def 		SCREAMING_SNAKE_CASE__     (				self			:							Union[str, Any]     ,   snake_case			:							int    )     ->		int | None:

  """simple docstring"""





  UpperCamelCase_      :		Optional[Any]				=      2 * parent_idx + 2
  if right_child_index < self.heap_size:
   return right_child_index
  return None

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

  """simple docstring"""





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

 def 		SCREAMING_SNAKE_CASE__     (				self			:							Dict     ,   snake_case			:							Iterable[T]    )     ->		None:

  """simple docstring"""





  UpperCamelCase_      :		Tuple				=      list(snake_case    )
  UpperCamelCase_      :		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(snake_case    )

 def 		SCREAMING_SNAKE_CASE__     (				self			:							List[Any]    )     ->		T:

  """simple docstring"""





  if self.heap_size >= 2:
   UpperCamelCase_      :		List[Any]				=      self.h[0]
   UpperCamelCase_      :		Tuple				=      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 		SCREAMING_SNAKE_CASE__     (				self			:							Dict     ,   snake_case			:							T    )     ->		None:

  """simple docstring"""





  self.h.append(snake_case    )
  UpperCamelCase_      :		int				=      (self.heap_size - 1) // 2
  self.heap_size += 1
  while idx >= 0:
   self.max_heapify(snake_case    )
   UpperCamelCase_      :		str				=      (idx - 1) // 2


 def 		SCREAMING_SNAKE_CASE__     (				self			:							Any    )     ->		None:

  """simple docstring"""





  UpperCamelCase_      :		int				=      self.heap_size
  for j in range(size - 1     ,   0     ,   -1    ):
   UpperCamelCase_,				UpperCamelCase_      :		Dict				=      self.h[j], self.h[0]
   self.heap_size -= 1
   self.max_heapify(0    )
  UpperCamelCase_      :		str				=      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}""")

      a_					      = 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""")




from __future__ import annotations

from collections import deque
from queue import Queue
from timeit import timeit

a_					      = {
    'A': ['B', 'C'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F'],
    'D': ['B'],
    'E': ['B', 'F'],
    'F': ['C', 'E'],
}





def      __lowercase  (		lowerCamelCase      :  dict						,						lowerCamelCase      :  str			):
 UpperCamelCase_      :		Tuple				=      {start}
 UpperCamelCase_      :		Optional[Any]				=      [start]
 UpperCamelCase_      :		Queue				=      Queue()
 queue.put(lowerCamelCase			)
 while not queue.empty():
  UpperCamelCase_      :		Union[str, Any]				=      queue.get()
  for w in graph[v]:
   if w not in explored:
    explored.add(lowerCamelCase			)
    result.append(lowerCamelCase			)
    queue.put(lowerCamelCase			)
 return result





def      __lowercase  (		lowerCamelCase      :  dict						,						lowerCamelCase      :  str			):
 UpperCamelCase_      :		Dict				=      {start}
 UpperCamelCase_      :		Optional[int]				=      [start]
 UpperCamelCase_      :		Union[str, Any]				=      deque([start]			)
 while queue:
  UpperCamelCase_      :		Optional[int]				=      queue.popleft()
  for child in graph[v]:
   if child not in visited:
    visited.add(lowerCamelCase			)
    result.append(lowerCamelCase			)
    queue.append(lowerCamelCase			)
 return result





def      __lowercase  (		lowerCamelCase      :  str			):
 UpperCamelCase_      :		str				=      F"from __main__ import G, {name}"
 UpperCamelCase_      :		int				=      10000
 UpperCamelCase_      :		Optional[Any]				=      timeit(F"{name}(G, 'A')"						,						setup=lowerCamelCase						,						number=lowerCamelCase			)
 print(F"{name:<35} finished {number} runs in {res:.5f} seconds"			)


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   benchmark_function('breadth_first_search')
   benchmark_function('breadth_first_search_with_deque')
   # breadth_first_search                finished 10000 runs in 0.20999 seconds
   # breadth_first_search_with_deque     finished 10000 runs in 0.01421 seconds



