"""simple docstring"""



from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
SCREAMING_SNAKE_CASE__:List[Any]		       =       299792458

# Symbols
SCREAMING_SNAKE_CASE__:Union[str, Any]		       =       symbols("""ct x y z""")



def      _lowerCamelCase(     a							):

       if velocity > c:
              raise ValueError("Speed must not exceed light speed 299,792,458 [m/s]!"							)
       elif velocity < 1:
              # Usually the speed should be much higher than 1 (c order of magnitude)
              raise ValueError("Speed must be greater than or equal to 1!"							)

       return velocity / c



def      _lowerCamelCase(     a							):
       return 1 / sqrt(1 - beta(snake_case_							) ** 2							)



def      _lowerCamelCase(     a							):
       return np.array(
           [
               [gamma(snake_case_							), -gamma(snake_case_							) * beta(snake_case_							), 0, 0],
               [-gamma(snake_case_							) * beta(snake_case_							), gamma(snake_case_							), 0, 0],
               [0, 0, 1, 0],
               [0, 0, 0, 1],
           ]							)



def      _lowerCamelCase(     a					,  a = None							):

       if event is None:
              __a	      =  np.array([ct, x, y, z]							)  # Symbolic four vector
       else:
              event[0] *= c  # x0 is ct (speed of light * time)

       return transformation_matrix(snake_case_							) @ event


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   # Example of symbolic vector:
   SCREAMING_SNAKE_CASE__:str		       =       transform(29979245)
   print("""Example of four vector: """)
   print(F'''ct\' = {four_vector[0]}''')
   print(F'''x\' = {four_vector[1]}''')
   print(F'''y\' = {four_vector[2]}''')
   print(F'''z\' = {four_vector[3]}''')

   # Substitute symbols with numerical values
   SCREAMING_SNAKE_CASE__:int		       =       {ct: c, x: 1, y: 1, z: 1}
   SCREAMING_SNAKE_CASE__:Any		       =       [four_vector[i].subs(sub_dict) for i in range(4)]

   print(F'''\n{numerical_vector}''')

'''simple docstring'''

from __future__ import annotations

from dataclasses import dataclass







@dataclass
class 				_lowercase     :


 '''simple docstring'''






 _SCREAMING_SNAKE_CASE     :       float
 _SCREAMING_SNAKE_CASE     :       TreeNode | None      	=					None
 _SCREAMING_SNAKE_CASE     :       TreeNode | None      	=					None







def      UpperCamelCase_						(					snake_case_       :       TreeNode | None      )					->     bool:






 '''simple docstring'''

 def is_valid_tree(snake_case_       :       TreeNode | None      ) -> bool:
  if node is None:
   return True

  if not isinstance(snake_case_						,		snake_case_      ):
   return False

  try:
   float(node.data      )
  except (TypeError, ValueError):
   return False

  return is_valid_tree(node.left      ) and is_valid_tree(node.right      )

 if not is_valid_tree(snake_case_      ):
  raise ValueError(
      """Each node should be type of TreeNode and data should be float."""      )

 def is_binary_search_tree_recursive_check(
     snake_case_       :       TreeNode | None						,		snake_case_       :       float						,		snake_case_       :       float      ) -> bool:

  if node is None:
   return True

  return (
      left_bound < node.data < right_bound
      and is_binary_search_tree_recursive_check(node.left						,		snake_case_						,		node.data      )
      and is_binary_search_tree_recursive_check(
          node.right						,		node.data						,		snake_case_      )
  )

 return is_binary_search_tree_recursive_check(snake_case_						,		-float("""inf"""      )						,		float("""inf"""      )      )


if __name__ == "__main__":
 import doctest

 doctest.testmod()






