

def     UpperCAmelCase_       (						_A    ):





     '''simple docstring'''




     if not isinstance(_A				,		_A    ):
          raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''    )
     if len(_A    ) == 0:
          raise ValueError('''Input list must be a non empty list'''    )
     if len(_A    ) == 1:
          return True
     SCREAMING_SNAKE_CASE__   =   series[1] - series[0]
     for index in range(len(_A    ) - 1    ):
          if series[index + 1] - series[index] != common_diff:
               return False
     return True
def     UpperCAmelCase_       (						_A    ):





     '''simple docstring'''




     if not isinstance(_A				,		_A    ):
          raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''    )
     if len(_A    ) == 0:
          raise ValueError('''Input list must be a non empty list'''    )
     SCREAMING_SNAKE_CASE__   =   0
     for val in series:
          answer += val
     return answer / len(_A    )


if __name__ == "__main__":
       import doctest

       doctest.testmod()





from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt
def     UpperCAmelCase_       (						_A				,		_A				,		_A    ):





     '''simple docstring'''




     if not arr:
          return None, None, 0
     if low == high:
          return low, high, arr[low]

     SCREAMING_SNAKE_CASE__   =   (low + high) // 2
     SCREAMING_SNAKE_CASE__,SCREAMING_SNAKE_CASE__,SCREAMING_SNAKE_CASE__   =   max_subarray(_A				,		_A				,		_A    )
     SCREAMING_SNAKE_CASE__,SCREAMING_SNAKE_CASE__,SCREAMING_SNAKE_CASE__   =   max_subarray(_A				,		mid + 1				,		_A    )
     SCREAMING_SNAKE_CASE__,SCREAMING_SNAKE_CASE__,SCREAMING_SNAKE_CASE__   =   max_cross_sum(_A				,		_A				,		_A				,		_A    )
     if left_sum >= right_sum and left_sum >= cross_sum:
          return left_low, left_high, left_sum
     elif right_sum >= left_sum and right_sum >= cross_sum:
          return right_low, right_high, right_sum
     return cross_left, cross_right, cross_sum
def     UpperCAmelCase_       (						_A				,		_A				,		_A				,		_A    ):





     '''simple docstring'''




     SCREAMING_SNAKE_CASE__,SCREAMING_SNAKE_CASE__   =   float('''-inf'''    ), -1
     SCREAMING_SNAKE_CASE__,SCREAMING_SNAKE_CASE__   =   float('''-inf'''    ), -1

     SCREAMING_SNAKE_CASE__   =   0
     for i in range(_A				,		low - 1				,		-1    ):
          summ += arr[i]
          if summ > left_sum:
               SCREAMING_SNAKE_CASE__   =   summ
               SCREAMING_SNAKE_CASE__   =   i

     SCREAMING_SNAKE_CASE__   =   0
     for i in range(mid + 1				,		high + 1    ):
          summ += arr[i]
          if summ > right_sum:
               SCREAMING_SNAKE_CASE__   =   summ
               SCREAMING_SNAKE_CASE__   =   i

     return max_left, max_right, (left_sum + right_sum)
def     UpperCAmelCase_       (						_A    ):





     '''simple docstring'''




     SCREAMING_SNAKE_CASE__   =   [randint(1				,		_A    ) for _ in range(_A    )]
     SCREAMING_SNAKE_CASE__   =   time.time()
     max_subarray(_A				,		0				,		input_size - 1    )
     SCREAMING_SNAKE_CASE__   =   time.time()
     return end - start
def     UpperCAmelCase_       (						):





     '''simple docstring'''




     SCREAMING_SNAKE_CASE__   =   [10, 1_00, 10_00, 1_00_00, 5_00_00, 10_00_00, 20_00_00, 30_00_00, 40_00_00, 50_00_00]
     SCREAMING_SNAKE_CASE__   =   [time_max_subarray(_A    ) for input_size in input_sizes]
     print('''No of Inputs\t\tTime Taken'''    )
     for input_size, runtime in zip(_A				,		_A    ):
          print(_A				,		'''\t\t'''				,		_A    )
     plt.plot(_A				,		_A    )
     plt.xlabel('''Number of Inputs'''    )
     plt.ylabel('''Time taken in seconds'''    )
     plt.show()


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

       testmod()


