






from __future__ import annotations

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

from matplotlib import pyplot as plt







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     Dict:






     """simple docstring"""




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

     UpperCamelCase__      :       Any	    =  (low + high) // 2
     UpperCamelCase__      :       Union[str, Any]	    =  max_subarray(A__ ,   A__ ,   A__      )
     UpperCamelCase__      :       Optional[Any]	    =  max_subarray(A__ ,   mid + 1 ,   A__      )
     UpperCamelCase__      :       int	    =  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 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     str:






     """simple docstring"""




     UpperCamelCase__      :       Any	    =  float("-inf"      ), -1
     UpperCamelCase__      :       Any	    =  float("-inf"      ), -1

     UpperCamelCase__      :       int | float	    =  0
     for i in range(A__ ,   low - 1 ,   -1      ):
          summ += arr[i]
          if summ > left_sum:
               UpperCamelCase__      :       Any	    =  summ
               UpperCamelCase__      :       str	    =  i

     UpperCamelCase__      :       List[str]	    =  0
     for i in range(mid + 1 ,   high + 1      ):
          summ += arr[i]
          if summ > right_sum:
               UpperCamelCase__      :       List[Any]	    =  summ
               UpperCamelCase__      :       Tuple	    =  i

     return max_left, max_right, (left_sum + right_sum)







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     int:






     """simple docstring"""




     UpperCamelCase__      :       Optional[int]	    =  [randint(1 ,   A__      ) for _ in range(A__      )]
     UpperCamelCase__      :       List[str]	    =  time.time()
     max_subarray(A__ ,   0 ,   input_size - 1      )
     UpperCamelCase__      :       str	    =  time.time()
     return end - start







def 		SCREAMING_SNAKE_CASE							( )			->     Optional[Any]:






     """simple docstring"""




     UpperCamelCase__      :       str	    =  [10, 100, 1000, 1_0000, 5_0000, 10_0000, 20_0000, 30_0000, 40_0000, 50_0000]
     UpperCamelCase__      :       Tuple	    =  [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()







from __future__ import annotations







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase = None ,   __lowerCAmelCase = None      )			->     None:
     if start is None:
          UpperCamelCase__      :       Union[str, Any]	    =  0

     if end is None:
          UpperCamelCase__      :       List[Any]	    =  len(__lowerCAmelCase      ) - 1

     if start >= end:
          return

     UpperCamelCase__      :       Union[str, Any]	    =  (start + end) // 2

     slowsort(__lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )
     slowsort(__lowerCAmelCase ,   mid + 1 ,   __lowerCAmelCase      )

     if sequence[end] < sequence[mid]:
          UpperCamelCase__    ,					UpperCamelCase__      :       Optional[int]	    =  sequence[mid], sequence[end]

     slowsort(__lowerCAmelCase ,   __lowerCAmelCase ,   end - 1      )


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

 testmod()