




'''simple docstring'''







from __future__ import annotations

from pathlib import Path



def 					lowerCamelCase__							(			__lowercase    ,      __lowercase							):
     return pointa[0] * pointa[1] - pointa[1] * pointa[0]



def 					lowerCamelCase__							(			__lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase							):
     snake_case :			tuple[int, int]					   = (xa, ya)
     snake_case :			tuple[int, int]					   = (xa - xa, ya - ya)
     snake_case :			tuple[int, int]					   = (xa - xa, ya - ya)
     snake_case :			float					   = -vector_product(__lowercase    ,      __lowercase							) / vector_product(
         __lowercase    ,      __lowercase							)
     snake_case :			float					   = +vector_product(__lowercase    ,      __lowercase							) / vector_product(
         __lowercase    ,      __lowercase							)

     return a > 0 and b > 0 and a + b < 1



def 					lowerCamelCase__							(			__lowercase = "p102_triangles.txt"							):
     snake_case :			str					   = Path(__lowercase							).parent.joinpath(__lowercase							).read_text(encoding="""utf-8"""							)

     snake_case :			list[list[int]]					   = []
     for line in data.strip().split("""\n"""							):
          triangles.append([int(__lowercase							) for number in line.split(""","""							)]							)

     snake_case :			int					   = 0
     snake_case :			list[int]

     for triangle in triangles:
          ret += contains_origin(*__lowercase							)

     return ret


if __name__ == "__main__":
      print(F"""{solution() = }""")









'''simple docstring'''







from .balanced_parentheses import balanced_parentheses
from .stack import Stack



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



def 					lowerCamelCase__							(			__lowercase							):
     if not balanced_parentheses(__lowercase							):
          raise ValueError("""Mismatched parentheses"""							)
     snake_case :			Stack[str]					   = Stack()
     snake_case :			List[Any]					   = []
     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()
      lowercase			:      Tuple			=					"""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))



