


'''simple docstring'''
from __future__ import annotations

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

from matplotlib import pyplot as plt

def 					lowerCamelCase_ ( __UpperCamelCase					:       Sequence[float]							,    __UpperCamelCase					:       int							,    __UpperCamelCase					:       int		)					->	tuple[int | None, int | None, float]:







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

     _A				=							(low + high) // 2
     _A		,				_A		,				_A				=							max_subarray(__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase		)
     _A		,				_A		,				_A				=							max_subarray(__UpperCamelCase							,    mid + 1							,    __UpperCamelCase		)
     _A		,				_A		,				_A				=							max_cross_sum(__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase		)
     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 					lowerCamelCase_ ( __UpperCamelCase					:       Sequence[float]							,    __UpperCamelCase					:       int							,    __UpperCamelCase					:       int							,    __UpperCamelCase					:       int		)					->	tuple[int, int, float]:







     """simple docstring"""
     _A		,				_A				=							float('-inf'		), -1
     _A		,				_A				=							float('-inf'		), -1

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

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

     return max_left, max_right, (left_sum + right_sum)

def 					lowerCamelCase_ ( __UpperCamelCase					:       int		)					->	float:







     """simple docstring"""
     _A				=							[randint(1							,    __UpperCamelCase		) for _ in range(__UpperCamelCase		)]
     _A				=							time.time()
     max_subarray(__UpperCamelCase							,    0							,    input_size - 1		)
     _A				=							time.time()
     return end - start

def 					lowerCamelCase_ ( )					->	None:







     """simple docstring"""
     _A				=							[1_0, 1_0_0, 1_0_0_0, 1_0_0_0_0, 5_0_0_0_0, 1_0_0_0_0_0, 2_0_0_0_0_0, 3_0_0_0_0_0, 4_0_0_0_0_0, 5_0_0_0_0_0]
     _A				=							[time_max_subarray(__UpperCamelCase		) for input_size in input_sizes]
     print('No of Inputs\t\tTime Taken'		)
     for input_size, runtime in zip(__UpperCamelCase							,    __UpperCamelCase		):
          print(__UpperCamelCase							,    '\t\t'							,    __UpperCamelCase		)
     plt.plot(__UpperCamelCase							,    __UpperCamelCase		)
     plt.xlabel('Number of Inputs'		)
     plt.ylabel('Time taken in seconds'		)
     plt.show()


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

    testmod()









'''simple docstring'''
from statistics import mean, stdev

def 					lowerCamelCase_ ( __UpperCamelCase					:       list							,    __UpperCamelCase					:       int = 3		)					->	list:







     """simple docstring"""
     _A				=							min(__UpperCamelCase		)
     _A				=							max(__UpperCamelCase		)
     # normalize data
     return [round((x - x_min) / (x_max - x_min)							,    __UpperCamelCase		) for x in data]

def 					lowerCamelCase_ ( __UpperCamelCase					:       list							,    __UpperCamelCase					:       int = 3		)					->	list:







     """simple docstring"""
     _A				=							mean(__UpperCamelCase		)
     _A				=							stdev(__UpperCamelCase		)
     # standardize data
     return [round((x - mu) / (sigma)							,    __UpperCamelCase		) for x in data]





