from .balanced_parentheses import balanced_parentheses
from .stack import Stack





def 	lowerCAmelCase_			(					__lowerCAmelCase    )->	str:






      '''simple docstring'''





      return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(__lowercase		,       -1    )





def 	lowerCAmelCase_			(					__lowerCAmelCase    )->	Optional[int]:






      '''simple docstring'''





      if not balanced_parentheses(__lowercase    ):
            raise ValueError('''Mismatched parentheses'''    )
      UpperCAmelCase     :			Stack[str]     	=Stack()
      UpperCAmelCase     :			int     	=[]
      for char in expression_str:
            if char.isalpha() or char.isdigit():
                  postfix.append(__lowercase    )
            elif char == "(":
                  stack.push(__lowercase    )
            elif char == ")":
                  while not stack.is_empty() and stack.peek() != "(":
                        postfix.append(stack.pop()    )
                  stack.pop()
            else:
                  while not stack.is_empty() and precedence(__lowercase    ) <= precedence(stack.peek()    ):
                        postfix.append(stack.pop()    )
                  stack.push(__lowercase    )
      while not stack.is_empty():
            postfix.append(stack.pop()    )
      return " ".join(__lowercase    )


if __name__ == "__main__":
     from doctest import testmod

     testmod()
     __snake_case         =     'a+b*(c^d-e)^(f+g*h)-i'

     print('''Infix to Postfix Notation demonstration:\n''')
     print('''Infix notation: ''' + expression)
     print('''Postfix notation: ''' + infix_to_postfix(expression))




from __future__ import annotations

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





class 			lowerCAmelCase__(     snake_case__    ):






    '''simple docstring'''





    @abstractmethod
    def __lt__(						self					: T							, __snake_case					: T						):





       '''simple docstring'''
       pass





    @abstractmethod
    def __gt__(						self					: T							, __snake_case					: T						):





       '''simple docstring'''
       pass





    @abstractmethod
    def __eq__(						self					: T							, __snake_case					: object						):





       '''simple docstring'''
       pass





__UpperCamelCase					:	Dict          =				TypeVar('T', bound=Comparable)





class 			lowerCAmelCase__(     Generic[T]    ):






    '''simple docstring'''





    def __init__(						self					: Tuple						):





       '''simple docstring'''
       UpperCAmelCase_				:   list[T]							= []
       UpperCAmelCase_				:   int							= 0





    def __repr__(						self					: Any						):





       '''simple docstring'''
       return str(self.h						)





    def        _lowerCamelCase			(						self					: str							, __snake_case					: int						):





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





    def        _lowerCamelCase			(						self					: str							, __snake_case					: int						):





       '''simple docstring'''
       UpperCAmelCase_				:   Dict							= 2 * parent_idx + 1
       if left_child_index < self.heap_size:
          return left_child_index
       return None





    def        _lowerCamelCase			(						self					: int							, __snake_case					: int						):





       '''simple docstring'''
       UpperCAmelCase_				:   Union[str, Any]							= 2 * parent_idx + 2
       if right_child_index < self.heap_size:
          return right_child_index
       return None





    def        _lowerCamelCase			(						self					: Union[str, Any]							, __snake_case					: int						):





       '''simple docstring'''
       if index < self.heap_size:
          UpperCAmelCase_				:   int							= index
          UpperCAmelCase_				:   List[str]							= self.left_child_idx(__snake_case						)
          UpperCAmelCase_				:   List[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_				:   List[str]							= left_child
          if right_child is not None and self.h[right_child] > self.h[violation]:
             UpperCAmelCase_				:   List[str]							= 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        _lowerCamelCase			(						self					: Optional[Any]							, __snake_case					: Iterable[T]						):





       '''simple docstring'''
       UpperCAmelCase_				:   Union[str, Any]							= list(__snake_case						)
       UpperCAmelCase_				:   int							= 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        _lowerCamelCase			(						self					: Tuple						):





       '''simple docstring'''
       if self.heap_size >= 2:
          UpperCAmelCase_				:   List[str]							= self.h[0]
          UpperCAmelCase_				:   Dict							= 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        _lowerCamelCase			(						self					: List[str]							, __snake_case					: T						):





       '''simple docstring'''
       self.h.append(__snake_case						)
       UpperCAmelCase_				:   Tuple							= (self.heap_size - 1) // 2
       self.heap_size += 1
       while idx >= 0:
          self.max_heapify(__snake_case						)
          UpperCAmelCase_				:   int							= (idx - 1) // 2





    def        _lowerCamelCase			(						self					: List[str]						):





       '''simple docstring'''
       UpperCAmelCase_				:   Tuple							= self.heap_size
       for j in range(size - 1							, 0							, -1						):
          UpperCAmelCase_		,   UpperCAmelCase_				:   Any							= self.h[j], self.h[0]
          self.heap_size -= 1
          self.max_heapify(0						)
       UpperCAmelCase_				:   Union[str, 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}')

              __UpperCamelCase					:	Heap[int]          =				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')