






from __future__ import annotations

UpperCAmelCase__							  =						[-10, -5, 0, 5, 5.1, 11, 13, 21, 3, 4, -21, -10, -5, -1, 0]
UpperCAmelCase__							  =						[-5, 0, 5, 5.1, 11, 13, 21, -1, 4, -1, -10, -5, -1, 0, -1]
def 		_a       ( a					:list[float]					)				->     list[float]:
 a						    = []
 a						    = len(a					)

 for i in range(a					):
  a						    = -1
  for j in range(i + 1      ,				a					):
   if arr[i] < arr[j]:
    a						    = arr[j]
    break
  result.append(a					)
 return result
def 		_a       ( a					:list[float]					)				->     list[float]:
 a						    = []
 for i, outer in enumerate(a					):
  a						    = -1
  for inner in arr[i + 1 :]:
   if outer < inner:
    a						    = inner
    break
  result.append(a					)
 return result
def 		_a       ( a					:list[float]					)				->     list[float]:
 a						    = len(a					)
 a						    = []
 a						    = [-1] * arr_size

 for index in reversed(range(a					)					):
  if stack:
   while stack[-1] <= arr[index]:
    stack.pop()
    if not stack:
     break
  if stack:
   a						    = stack[-1]
  stack.append(arr[index]					)
 return result


if __name__ == "__main__":
     from doctest import testmod
     from timeit import timeit

     testmod()
     print(next_greatest_element_slow(arr))
     print(next_greatest_element_fast(arr))
     print(next_greatest_element(arr))

     UpperCAmelCase__							  =						(
         "from __main__ import arr, next_greatest_element_slow, "
         "next_greatest_element_fast, next_greatest_element"
     )
     print(
         "next_greatest_element_slow():",
         timeit("next_greatest_element_slow(arr)", setup=setup),
     )
     print(
         "next_greatest_element_fast():",
         timeit("next_greatest_element_fast(arr)", setup=setup),
     )
     print(
         "     next_greatest_element():",
         timeit("next_greatest_element(arr)", setup=setup),
     )










from typing import Any

import numpy as np
def 		_a       ( a					:np.ndarray					)				->     bool:
 return np.array_equal(a      ,				matrix.conjugate().T					)
def 		_a       ( a					:np.ndarray      ,				a					:np.ndarray					)				->     Any:
 a						    = v.conjugate().T
 a						    = v_star.dot(a					)
 assert isinstance(a      ,				np.ndarray					)
 return (v_star_dot.dot(a					)) / (v_star.dot(a					))
def 		_a       ( )				->     None:
 a						    = np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]					)
 a						    = np.array([[1], [2], [3]]					)
 assert is_hermitian(a					), F"""{a} is not hermitian."""
 print(rayleigh_quotient(a      ,				a					)					)

 a						    = 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()


