





from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
lowerCAmelCase_    =    2_9_9_7_9_2_4_5_8

# Symbols
lowerCAmelCase_  , lowerCAmelCase_  , lowerCAmelCase_  , lowerCAmelCase_    =    symbols('''ct x y z''')






def 					lowerCamelCase_						(    _UpperCamelCase			)		->						float:






				"""simple docstring"""


				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_						(    _UpperCamelCase			)		->						float:






				"""simple docstring"""


				return 1 / sqrt(1 - beta(_UpperCamelCase			) ** 2			)






def 					lowerCamelCase_						(    _UpperCamelCase			)		->						np.ndarray:






				"""simple docstring"""


				return np.array(
				    [
				        [gamma(_UpperCamelCase			), -gamma(_UpperCamelCase			) * beta(_UpperCamelCase			), 0, 0],
				        [-gamma(_UpperCamelCase			) * beta(_UpperCamelCase			), gamma(_UpperCamelCase			), 0, 0],
				        [0, 0, 1, 0],
				        [0, 0, 0, 1],
				    ]			)






def 					lowerCamelCase_						(    _UpperCamelCase			,    _UpperCamelCase = None			)		->						np.ndarray:






				"""simple docstring"""


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

				return transformation_matrix(_UpperCamelCase			) @ event


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	# Example of symbolic vector:
	lowerCAmelCase_    =    transform(2_9_9_7_9_2_4_5)
	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
	lowerCAmelCase_    =    {ct: c, x: 1, y: 1, z: 1}
	lowerCAmelCase_    =    [four_vector[i].subs(sub_dict) for i in range(4)]

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







from collections.abc import Iterator, MutableMapping
from dataclasses import dataclass
from typing import Generic, TypeVar

lowerCAmelCase_    =    TypeVar('''KEY''')
lowerCAmelCase_    =    TypeVar('''VAL''')



@dataclass(frozen=_a,					slots=_a					)
class  __lowerCAmelCase	(      Generic[KEY, VAL]					):
			lowerCamelCase_					:					KEY
			lowerCamelCase_					:					VAL




class  __lowerCAmelCase	(      _Item					):






			def __init__(self   )					->       None:


							'''simple docstring'''



							super().__init__(__magic_name__ ,							__magic_name__   )






			def __bool__(self   )					->       bool:


							'''simple docstring'''



							return False




lowerCAmelCase_    =    _DeletedItem()



class  __lowerCAmelCase	(      MutableMapping[KEY, VAL]					):






			def __init__(self ,							__magic_name__ = 8 ,							__magic_name__ = 0.75   )					->       None:


							'''simple docstring'''



							snake_case_						:   List[Any]           =  initial_block_size
							snake_case_						:   list[_Item | None]           =  [None] * initial_block_size
							assert 0.0 < capacity_factor < 1.0
							snake_case_						:   List[str]           =  capacity_factor
							snake_case_						:   int           =  0






			def       lowerCamelCase  (self ,							__magic_name__   )					->       int:


							'''simple docstring'''



							return hash(__magic_name__   ) % len(self._buckets   )






			def       lowerCamelCase  (self ,							__magic_name__   )					->       int:


							'''simple docstring'''



							return (ind + 1) % len(self._buckets   )






			def       lowerCamelCase  (self ,							__magic_name__ ,							__magic_name__ ,							__magic_name__   )					->       bool:


							'''simple docstring'''



							snake_case_						:   Optional[int]           =  self._buckets[ind]
							if not stored:
											snake_case_						:   Optional[Any]           =  _Item(__magic_name__ ,							__magic_name__   )
											self._len += 1
											return True
							elif stored.key == key:
											snake_case_						:   List[Any]           =  _Item(__magic_name__ ,							__magic_name__   )
											return True
							else:
											return False






			def       lowerCamelCase  (self   )					->       bool:


							'''simple docstring'''



							snake_case_						:   Any           =  len(self._buckets   ) * self._capacity_factor
							return len(self   ) >= int(__magic_name__   )






			def       lowerCamelCase  (self   )					->       bool:


							'''simple docstring'''



							if len(self._buckets   ) <= self._initial_block_size:
											return False
							snake_case_						:   int           =  len(self._buckets   ) * self._capacity_factor / 2
							return len(self   ) < limit






			def       lowerCamelCase  (self ,							__magic_name__   )					->       None:


							'''simple docstring'''



							snake_case_						:   List[str]           =  self._buckets
							snake_case_						:   int           =  [None] * new_size
							snake_case_						:   Optional[int]           =  0
							for item in old_buckets:
											if item:
															self._add_item(item.key ,							item.val   )






			def       lowerCamelCase  (self   )					->       None:


							'''simple docstring'''



							self._resize(len(self._buckets   ) * 2   )






			def       lowerCamelCase  (self   )					->       None:


							'''simple docstring'''



							self._resize(len(self._buckets   ) // 2   )






			def       lowerCamelCase  (self ,							__magic_name__   )					->       Iterator[int]:


							'''simple docstring'''



							snake_case_						:   Dict           =  self._get_bucket_index(__magic_name__   )
							for _ in range(len(self._buckets   )   ):
											yield ind
											snake_case_						:   Tuple           =  self._get_next_ind(__magic_name__   )






			def       lowerCamelCase  (self ,							__magic_name__ ,							__magic_name__   )					->       None:


							'''simple docstring'''



							for ind in self._iterate_buckets(__magic_name__   ):
											if self._try_set(__magic_name__ ,							__magic_name__ ,							__magic_name__   ):
															break






			def __setitem__(self ,							__magic_name__ ,							__magic_name__   )					->       None:


							'''simple docstring'''



							if self._is_full():
											self._size_up()

							self._add_item(__magic_name__ ,							__magic_name__   )






			def __delitem__(self ,							__magic_name__   )					->       None:


							'''simple docstring'''



							for ind in self._iterate_buckets(__magic_name__   ):
											snake_case_						:   Optional[Any]           =  self._buckets[ind]
											if item is None:
															raise KeyError(__magic_name__   )
											if item is _deleted:
															continue
											if item.key == key:
															snake_case_						:   Union[str, Any]           =  _deleted
															self._len -= 1
															break
							if self._is_sparse():
											self._size_down()






			def __getitem__(self ,							__magic_name__   )					->       VAL:


							'''simple docstring'''



							for ind in self._iterate_buckets(__magic_name__   ):
											snake_case_						:   List[Any]           =  self._buckets[ind]
											if item is None:
															break
											if item is _deleted:
															continue
											if item.key == key:
															return item.val
							raise KeyError(__magic_name__   )






			def __len__(self   )					->       int:


							'''simple docstring'''



							return self._len






			def __iter__(self   )					->       Iterator[KEY]:


							'''simple docstring'''



							yield from (item.key for item in self._buckets if item)






			def __repr__(self   )					->       str:


							'''simple docstring'''



							snake_case_						:   List[str]           =  ''' ,'''.join(
							    F'''{item.key}: {item.val}''' for item in self._buckets if item   )
							return F'''HashMap({val_string})'''
