
'''simple docstring'''







from __future__ import annotations

lowercase					:							List[str]   =      []







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A			) ->			bool:
	for i in range(len(__A			)			):
		if board[row][i] == 1:
			return False
	for i in range(len(__A			)			):
		if board[i][column] == 1:
			return False
	for i, j in zip(range(__A    ,       -1    ,       -1			)    ,       range(__A    ,       -1    ,       -1			)			):
		if board[i][j] == 1:
			return False
	for i, j in zip(range(__A    ,       -1    ,       -1			)    ,       range(__A    ,       len(__A			)			)			):
		if board[i][j] == 1:
			return False
	return True







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			bool:
	if row >= len(__A			):
		solution.append(__A			)
		printboard(__A			)
		print()
		return True
	for i in range(len(__A			)			):
		if is_safe(__A    ,       __A    ,       __A			):
			_snake_case     		=	1
			solve(__A    ,       row + 1			)
			_snake_case     		=	0
	return False







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			None:
	for i in range(len(__A			)			):
		for j in range(len(__A			)			):
			if board[i][j] == 1:
				print('Q'    ,       end=' '			)
			else:
				print('.'    ,       end=' '			)
		print()


# n=int(input("The no. of queens"))
lowercase					:							Union[str, Any]   =      8
lowercase					:							Union[str, Any]   =      [[0 for i in range(n)] for j in range(n)]
solve(board, 0)





print("The total no. of solutions are :", len(solution))



'''simple docstring'''







from typing import Any

import numpy as np







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			bool:
	return np.array_equal(__A    ,       matrix.conjugate().T			)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			Any:
	_snake_case     		=	v.conjugate().T
	_snake_case     		=	v_star.dot(__A			)
	assert isinstance(__A    ,       np.ndarray			)
	return (v_star_dot.dot(__A			)) / (v_star.dot(__A			))







def        SCREAMING_SNAKE_CASE__			(     ) ->			None:
	_snake_case     		=	np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]			)
	_snake_case     		=	np.array([[1], [2], [3]]			)
	assert is_hermitian(__A			), F'{a} is not hermitian.'
	print(rayleigh_quotient(__A    ,       __A			)			)

	_snake_case     		=	np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]			)
	assert is_hermitian(__A			), F'{a} is not hermitian.'
	assert rayleigh_quotient(__A    ,       __A			) == float(3			)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					tests()

