




'''simple docstring'''







from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

A				:					Optional[int]    						=			TypeVar('''T''')






def 				lowerCAmelCase__	(    lowerCamelCase					:      int       ):
       return (position - 1) // 2






def 				lowerCAmelCase__	(    lowerCamelCase					:      int       ):
       return (2 * position) + 1






def 				lowerCAmelCase__	(    lowerCamelCase					:      int       ):
       return (2 * position) + 2


class 			__lowerCamelCase			(	Generic[T]	):
    """simple docstring"""


    def __init__(  self      :							str):
           _A					:     list[tuple[T, int]]     = []
           _A					:     dict[T, int]     = {}
           _A					:     int     = 0


    def __len__(  self      :							Optional[int]):
           return self.elements


    def __repr__(  self      :							str):
           return str(self.heap)


    def        A   (  self      :							Union[str, Any]):
           # Check if the priority queue is empty
           return self.elements == 0


    def        A   (  self      :							List[Any]				,							SCREAMING_SNAKE_CASE      :							T				,							SCREAMING_SNAKE_CASE      :							int):
           # Add an element with given priority to the queue
           self.heap.append((elem, weight))
           _A					:     Optional[Any]     = self.elements
           self.elements += 1
           self._bubble_up(SCREAMING_SNAKE_CASE)


    def        A   (  self      :							str):
           # Remove and return the element with lowest weight (highest priority)
           if self.elements > 1:
                  self._swap_nodes(0				,							self.elements - 1)
           _A					:     str     = self.heap.pop()
           del self.position_map[elem]
           self.elements -= 1
           if self.elements > 0:
                  _A					:     Optional[Any]     = self.heap[0]
                  self._bubble_down(SCREAMING_SNAKE_CASE)
           return elem


    def        A   (  self      :							Tuple				,							SCREAMING_SNAKE_CASE      :							T				,							SCREAMING_SNAKE_CASE      :							int):
           # Update the weight of the given key
           _A					:     Tuple     = self.position_map[elem]
           _A					:     int     = (elem, weight)
           if position > 0:
                  _A					:     List[Any]     = get_parent_position(SCREAMING_SNAKE_CASE)
                  _A					:     List[Any]     = self.heap[parent_position]
                  if parent_weight > weight:
                         self._bubble_up(SCREAMING_SNAKE_CASE)
                  else:
                         self._bubble_down(SCREAMING_SNAKE_CASE)
           else:
                  self._bubble_down(SCREAMING_SNAKE_CASE)


    def        A   (  self      :							int				,							SCREAMING_SNAKE_CASE      :							T):
           # Place a node at the proper position (upward movement) [to be used internally
           # only]
           _A					:     Any     = self.position_map[elem]
           if curr_pos == 0:
                  return None
           _A					:     Dict     = get_parent_position(SCREAMING_SNAKE_CASE)
           _A					:     Tuple     = self.heap[curr_pos]
           _A					:     Optional[Any]     = self.heap[parent_position]
           if parent_weight > weight:
                  self._swap_nodes(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE)
                  return self._bubble_up(SCREAMING_SNAKE_CASE)
           return None


    def        A   (  self      :							List[Any]				,							SCREAMING_SNAKE_CASE      :							T):
           # Place a node at the proper position (downward movement) [to be used
           # internally only]
           _A					:     str     = self.position_map[elem]
           _A					:     int     = self.heap[curr_pos]
           _A					:     Optional[int]     = get_child_left_position(SCREAMING_SNAKE_CASE)
           _A					:     int     = get_child_right_position(SCREAMING_SNAKE_CASE)
           if child_left_position < self.elements and child_right_position < self.elements:
                  _A					:     Tuple     = self.heap[child_left_position]
                  _A					:     str     = self.heap[child_right_position]
                  if child_right_weight < child_left_weight and child_right_weight < weight:
                         self._swap_nodes(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE)
                         return self._bubble_down(SCREAMING_SNAKE_CASE)
           if child_left_position < self.elements:
                  _A					:     str     = self.heap[child_left_position]
                  if child_left_weight < weight:
                         self._swap_nodes(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE)
                         return self._bubble_down(SCREAMING_SNAKE_CASE)
           else:
                  return None
           if child_right_position < self.elements:
                  _A					:     Dict     = self.heap[child_right_position]
                  if child_right_weight < weight:
                         self._swap_nodes(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE)
                         return self._bubble_down(SCREAMING_SNAKE_CASE)
           return None


    def        A   (  self      :							Any				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							int):
           # Swap the nodes at the given positions
           _A					:     List[str]     = self.heap[nodea_pos][0]
           _A					:     List[Any]     = self.heap[nodea_pos][0]
           _A					:     Optional[int]     = (
               self.heap[nodea_pos],
               self.heap[nodea_pos],
           )
           _A					:     int     = nodea_pos
           _A					:     List[str]     = nodea_pos




class 			__lowerCamelCase			(	Generic[T]	):
    """simple docstring"""


    def __init__(  self      :							List[str]):
           _A					:     dict[T, dict[T, int]]     = {}
           _A					:     int     = 0


    def __repr__(  self      :							Union[str, Any]):
           return str(self.connections)


    def __len__(  self      :							List[str]):
           return self.nodes


    def        A   (  self      :							Dict				,							SCREAMING_SNAKE_CASE      :							T):
           # Add a node in the graph if it is not in the graph
           if node not in self.connections:
                  _A					:     List[Any]     = {}
                  self.nodes += 1


    def        A   (  self      :							int				,							SCREAMING_SNAKE_CASE      :							T				,							SCREAMING_SNAKE_CASE      :							T				,							SCREAMING_SNAKE_CASE      :							int):
           # Add an edge between 2 nodes in the graph
           self.add_node(SCREAMING_SNAKE_CASE)
           self.add_node(SCREAMING_SNAKE_CASE)
           _A					:     List[Any]     = weight
           _A					:     str     = weight






def 				lowerCAmelCase__	(    lowerCamelCase					:      GraphUndirectedWeighted[T]  ,):
       _A					:     dict[T, int]     = {node: maxsize for node in graph.connections}
       _A					:     dict[T, T | None]     = {node: None for node in graph.connections}

       _A					:     MinPriorityQueue[T]     = MinPriorityQueue()
       for node, weight in dist.items():
              priority_queue.push(lowerCamelCase  ,lowerCamelCase       )

       if priority_queue.is_empty():
              return dist, parent

       # initialization
       _A					:     Any     = priority_queue.extract_min()
       _A					:     Union[str, Any]     = 0
       for neighbour in graph.connections[node]:
              if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
                     _A					:     Union[str, Any]     = dist[node] + graph.connections[node][neighbour]
                     priority_queue.update_key(lowerCamelCase  ,dist[neighbour]       )
                     _A					:     Optional[int]     = node

    # running prim's algorithm
       while not priority_queue.is_empty():
              _A					:     List[str]     = priority_queue.extract_min()
              for neighbour in graph.connections[node]:
                     if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
                            _A					:     Optional[int]     = dist[node] + graph.connections[node][neighbour]
                            priority_queue.update_key(lowerCamelCase  ,dist[neighbour]       )
                            _A					:     List[str]     = node
       return dist, parent










'''simple docstring'''







A				:					Dict    						=			'''Alexander Joslin'''

import operator as op

from .stack import Stack






def 				lowerCAmelCase__	(    lowerCamelCase					:      str       ):
       _A					:     Dict     = {'*': op.mul, '/': op.truediv, '+': op.add, '-': op.sub}

       _A					:     Stack[int]     = Stack()
       _A					:     Stack[str]     = Stack()

       for i in equation:
              if i.isdigit():
                     # RULE 1
                     operand_stack.push(int(lowerCamelCase       )       )
              elif i in operators:
                     # RULE 2
                     operator_stack.push(lowerCamelCase       )
              elif i == ")":
                     # RULE 4
                     _A					:     List[str]     = operator_stack.peek()
                     operator_stack.pop()
                     _A					:     Dict     = operand_stack.peek()
                     operand_stack.pop()
                     _A					:     Optional[int]     = operand_stack.peek()
                     operand_stack.pop()

                     _A					:     Dict     = operators[opr](lowerCamelCase  ,lowerCamelCase       )
                     operand_stack.push(lowerCamelCase       )

    # RULE 5
       return operand_stack.peek()


if __name__ == "__main__":
   A				:					Dict    						=			'''(5 + ((4 * 2) * (2 + 3)))'''
   # answer = 45
   print(f"""{equation} = {dijkstras_two_stack_algorithm(equation)}""")






