

"""simple docstring"""




from __future__ import annotations

lowerCAmelCase__						=	[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]

class    a__  :
			"""simple docstring"""







			def __init__(      self , lowercase    )					->  None:
							'''simple docstring'''






							A__            =     -1
							A__            =     -1
							A__            =     [-1] * length
							A__            =     None
							A__            =     None


			def __repr__(      self    )					->  str:
							'''simple docstring'''






							return F'Node(min_value={self.minn} max_value={self.maxx})'



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							list[int] )     -> Node | None:




				'''simple docstring'''





				A__            =     Node(len(SCREAMING_SNAKE_CASE_ ) )
				A__      ,			A__            =     min(SCREAMING_SNAKE_CASE_ ), max(SCREAMING_SNAKE_CASE_ )
				# Leaf node case where the node contains only one unique value
				if root.minn == root.maxx:
								return root
				A__            =     (root.minn + root.maxx) // 2

				A__            =     []
				A__            =     []

				for index, num in enumerate(SCREAMING_SNAKE_CASE_ ):
								if num <= pivot:
												left_arr.append(SCREAMING_SNAKE_CASE_ )
								else:
												right_arr.append(SCREAMING_SNAKE_CASE_ )
								A__            =     len(SCREAMING_SNAKE_CASE_ )
				A__            =     build_tree(SCREAMING_SNAKE_CASE_ )
				A__            =     build_tree(SCREAMING_SNAKE_CASE_ )
				return root



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							Node | None		,    SCREAMING_SNAKE_CASE_:							int		,    SCREAMING_SNAKE_CASE_:							int )     -> int:




				'''simple docstring'''





				if index < 0 or node is None:
								return 0
				# Leaf node cases
				if node.minn == node.maxx:
								return index + 1 if node.minn == num else 0
				A__            =     (node.minn + node.maxx) // 2
				if num <= pivot:
								# go the left subtree and map index to the left subtree
								return rank_till_index(node.left		,    SCREAMING_SNAKE_CASE_		,    node.map_left[index] - 1 )
				else:
								# go to the right subtree and map index to the right subtree
								return rank_till_index(node.right		,    SCREAMING_SNAKE_CASE_		,    index - node.map_left[index] )



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							Node | None		,    SCREAMING_SNAKE_CASE_:							int		,    SCREAMING_SNAKE_CASE_:							int		,    SCREAMING_SNAKE_CASE_:							int )     -> int:




				'''simple docstring'''





				if start > end:
								return 0
				A__            =     rank_till_index(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ )
				A__            =     rank_till_index(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_		,    start - 1 )
				return rank_till_end - rank_before_start



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							Node | None		,    SCREAMING_SNAKE_CASE_:							int		,    SCREAMING_SNAKE_CASE_:							int		,    SCREAMING_SNAKE_CASE_:							int )     -> int:




				'''simple docstring'''





				if index > (end - start) or start > end or node is None:
								return -1
				# Leaf node case
				if node.minn == node.maxx:
								return node.minn
				# Number of elements in the left subtree in interval [start, end]
				A__            =     node.map_left[end] - (
				    node.map_left[start - 1] if start else 0
				)
				if num_elements_in_left_tree > index:
								return quantile(
								    node.left		,    SCREAMING_SNAKE_CASE_		,    (node.map_left[start - 1] if start else 0)		,    node.map_left[end] - 1		,    )
				else:
								return quantile(
								    node.right		,    index - num_elements_in_left_tree		,    start - (node.map_left[start - 1] if start else 0)		,    end - node.map_left[end]		,    )



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							Node | None		,    SCREAMING_SNAKE_CASE_:							int		,    SCREAMING_SNAKE_CASE_:							int		,    SCREAMING_SNAKE_CASE_:							int		,    SCREAMING_SNAKE_CASE_:							int )     -> int:




				'''simple docstring'''





				if (
				    start > end
				    or node is None
				    or start_num > end_num
				    or node.minn > end_num
				    or node.maxx < start_num
				):
								return 0
				if start_num <= node.minn and node.maxx <= end_num:
								return end - start + 1
				A__            =     range_counting(
				    node.left		,    (node.map_left[start - 1] if start else 0)		,    node.map_left[end] - 1		,    SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_		,    )
				A__            =     range_counting(
				    node.right		,    start - (node.map_left[start - 1] if start else 0)		,    end - node.map_left[end]		,    SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_		,    )
				return left + right


if __name__ == "__main__":
	import doctest

	doctest.testmod()




from .balanced_parentheses import balanced_parentheses
from .stack import Stack



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							str )     -> int:




				'''simple docstring'''





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



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							str )     -> str:




				'''simple docstring'''





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


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

	testmod()
	lowerCAmelCase__						=	"""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))

