
from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			NDArray[floataa]						,  _lowerCamelCase :			NDArray[floataa]						,  _lowerCamelCase :			list[int]						,  _lowerCamelCase :			int						,  )					->    list[float]:






							'''simple docstring'''





							__UpperCamelCase   ,						__UpperCamelCase	:   Dict			   =					coefficient_matrix.shape
							__UpperCamelCase   ,						__UpperCamelCase	:   List[Any]			   =					constant_matrix.shape

							if rowsa != colsa:
														__UpperCamelCase	:   Dict			   =					F'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
														raise ValueError(_lowerCamelCase)

							if colsa != 1:
														__UpperCamelCase	:   int			   =					F'Constant matrix must be nx1 but received {rowsa}x{colsa}'
														raise ValueError(_lowerCamelCase)

							if rowsa != rowsa:
														__UpperCamelCase	:   Optional[int]			   =					(
														    "Coefficient and constant matrices dimensions must be nxn and nx1 but "
														    F'received {rowsa}x{colsa} and {rowsa}x{colsa}'
														)
														raise ValueError(_lowerCamelCase)

							if len(_lowerCamelCase) != rowsa:
														__UpperCamelCase	:   Tuple			   =					(
														    "Number of initial values must be equal to number of rows in coefficient "
														    F'matrix but received {len(_lowerCamelCase)} and {rowsa}'
														)
														raise ValueError(_lowerCamelCase)

							if iterations <= 0:
														raise ValueError("Iterations must be at least 1")

							__UpperCamelCase	:   NDArray[floataa]			   =					np.concatenate(
							    (coefficient_matrix, constant_matrix)						,  axis=1)

							__UpperCamelCase   ,						__UpperCamelCase	:   Tuple			   =					table.shape

							strictly_diagonally_dominant(_lowerCamelCase)

							# Iterates the whole matrix for given number of times
							for _ in range(_lowerCamelCase):
														__UpperCamelCase	:   Dict			   =					[]
														for row in range(_lowerCamelCase):
																					__UpperCamelCase	:   Dict			   =					0
																					for col in range(_lowerCamelCase):
																												if col == row:
																																			__UpperCamelCase	:   Optional[Any]			   =					table[row][col]
																												elif col == cols - 1:
																																			__UpperCamelCase	:   Optional[Any]			   =					table[row][col]
																												else:
																																			temp += (-1) * table[row][col] * init_val[col]
																					__UpperCamelCase	:   Tuple			   =					(temp + val) / denom
																					new_val.append(_lowerCamelCase)
														__UpperCamelCase	:   Optional[int]			   =					new_val

							return [float(_lowerCamelCase) for i in new_val]




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			NDArray[floataa])					->    bool:






							'''simple docstring'''





							__UpperCamelCase   ,						__UpperCamelCase	:   Dict			   =					table.shape

							__UpperCamelCase	:   int			   =					True

							for i in range(0						,  _lowerCamelCase):
														__UpperCamelCase	:   Any			   =					0
														for j in range(0						,  cols - 1):
																					if i == j:
																												continue
																					else:
																												total += table[i][j]

														if table[i][i] <= total:
																					raise ValueError("Coefficient matrix is not strictly diagonally dominant")

							return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
		import doctest

		doctest.testmod()

from __future__ import annotations

import sys
from collections import deque
from typing import Generic, TypeVar

lowercase  :					Optional[Any]													=       TypeVar('T')




class  lowerCamelCase__							(				Generic[T]):




	'''simple docstring'''




	_A								=     42  # Cache store of keys
	_A								=     42  # References of the keys in cache
	_A								=     1_0  # Maximum capacity of cache







	def __init__(					self		:Optional[Any]     ,   a		:int						)		-> None:
								__UpperCamelCase	:   Union[str, Any]			   =					deque()
								__UpperCamelCase	:   str			   =					set()
								if not n:
															__UpperCamelCase	:   Union[str, Any]			   =					sys.maxsize
								elif n < 0:
															raise ValueError("n should be an integer greater than 0."						)
								else:
															__UpperCamelCase	:   Any			   =					n







	def    _lowerCamelCase				(					self		:Tuple     ,   a		:T						)		-> None:
								if x not in self.key_reference:
															if len(self.dq_store						) == LRUCache._MAX_CAPACITY:
																						__UpperCamelCase	:   int			   =					self.dq_store.pop()
																						self.key_reference.remove(a						)
								else:
															self.dq_store.remove(a						)

								self.dq_store.appendleft(a						)
								self.key_reference.add(a						)







	def    _lowerCamelCase				(					self		:Any						)		-> None:
								for k in self.dq_store:
															print(a						)







	def __repr__(					self		:Tuple						)		-> str:
								return f'LRUCache({self._MAX_CAPACITY}) => {list(self.dq_store						)}'


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		lowercase  :					LRUCache[str | int]													=       LRUCache(4)
		lru_cache.refer('A')
		lru_cache.refer(2)
		lru_cache.refer(3)
		lru_cache.refer('A')
		lru_cache.refer(4)
		lru_cache.refer(5)
		lru_cache.display()

		print(lru_cache)
		assert str(lru_cache) == "LRUCache(4) => [5, 4, 'A', 3]"