



"""simple docstring"""
from __future__ import annotations

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

from matplotlib import pyplot as plt





def    __magic_name__ (							lowercase							,	lowercase							,	lowercase       ):





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

   SCREAMING_SNAKE_CASE_:       Union[str, Any]   	=(low + high) // 2
   SCREAMING_SNAKE_CASE_:       Dict   	=max_subarray(lowercase							,	lowercase							,	lowercase       )
   SCREAMING_SNAKE_CASE_:       int   	=max_subarray(lowercase							,	mid + 1							,	lowercase       )
   SCREAMING_SNAKE_CASE_:       Union[str, Any]   	=max_cross_sum(lowercase							,	lowercase							,	lowercase							,	lowercase       )
   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    __magic_name__ (							lowercase							,	lowercase							,	lowercase							,	lowercase       ):
   SCREAMING_SNAKE_CASE_:       Any   	=float("""-inf"""       ), -1
   SCREAMING_SNAKE_CASE_:       str   	=float("""-inf"""       ), -1

   SCREAMING_SNAKE_CASE_:       int | float   	=0
   for i in range(lowercase							,	low - 1							,	-1       ):
      summ += arr[i]
      if summ > left_sum:
         SCREAMING_SNAKE_CASE_:       Optional[int]   	=summ
         SCREAMING_SNAKE_CASE_:       List[Any]   	=i

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

   return max_left, max_right, (left_sum + right_sum)





def    __magic_name__ (							lowercase       ):
   SCREAMING_SNAKE_CASE_:       Optional[Any]   	=[randint(1							,	lowercase       ) for _ in range(lowercase       )]
   SCREAMING_SNAKE_CASE_:       Union[str, Any]   	=time.time()
   max_subarray(lowercase							,	0							,	input_size - 1       )
   SCREAMING_SNAKE_CASE_:       str   	=time.time()
   return end - start





def    __magic_name__ (							):
   SCREAMING_SNAKE_CASE_:       Any   	=[10, 100, 1000, 1_0000, 5_0000, 10_0000, 20_0000, 30_0000, 40_0000, 50_0000]
   SCREAMING_SNAKE_CASE_:       List[Any]   	=[time_max_subarray(lowercase       ) for input_size in input_sizes]
   print("""No of Inputs\t\tTime Taken"""       )
   for input_size, runtime in zip(lowercase							,	lowercase       ):
      print(lowercase							,	"""\t\t"""							,	lowercase       )
   plt.plot(lowercase							,	lowercase       )
   plt.xlabel("""Number of Inputs"""       )
   plt.ylabel("""Time taken in seconds"""       )
   plt.show()


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

   testmod()








'''simple docstring'''





from maths.prime_factors import prime_factors
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    if not isinstance(UpperCamelCase							,    UpperCamelCase			):
        lowerCAmelCase__ :  int							      =					f"""Input value of [number={number}] must be an integer"""
        raise TypeError(UpperCamelCase			)
    if number < 1:
        raise ValueError("""Input must be a positive integer"""			)
    return -1 if len(prime_factors(UpperCamelCase			)			) % 2 else 1


if __name__ == "__main__":
 import doctest

 doctest.testmod()


