
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				:    Sequence[float]		,						_lowerCamelCase				:    int		,						_lowerCamelCase				:    int)      ->					tuple[int | None, int | None, float]:






							'''simple docstring'''





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

							__UpperCamelCase			:     Tuple         =      (low + high) // 2
							__UpperCamelCase			:     Dict         =      max_subarray(_lowerCamelCase		,						_lowerCamelCase		,						_lowerCamelCase)
							__UpperCamelCase			:     Optional[int]         =      max_subarray(_lowerCamelCase		,						mid + 1		,						_lowerCamelCase)
							__UpperCamelCase			:     Dict         =      max_cross_sum(_lowerCamelCase		,						_lowerCamelCase		,						_lowerCamelCase		,						_lowerCamelCase)
							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				:    Sequence[float]		,						_lowerCamelCase				:    int		,						_lowerCamelCase				:    int		,						_lowerCamelCase				:    int)      ->					tuple[int, int, float]:






							'''simple docstring'''





							__UpperCamelCase			:     Union[str, Any]         =      float("-inf"), -1
							__UpperCamelCase			:     Optional[int]         =      float("-inf"), -1

							__UpperCamelCase			:     int | float         =      0
							for i in range(_lowerCamelCase		,						low - 1		,						-1):
														summ += arr[i]
														if summ > left_sum:
																					__UpperCamelCase			:     Tuple         =      summ
																					__UpperCamelCase			:     Optional[int]         =      i

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

							return max_left, max_right, (left_sum + right_sum)




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    int)      ->					float:






							'''simple docstring'''





							__UpperCamelCase			:     Tuple         =      [randint(1		,						_lowerCamelCase) for _ in range(_lowerCamelCase)]
							__UpperCamelCase			:     Optional[Any]         =      time.time()
							max_subarray(_lowerCamelCase		,						0		,						input_size - 1)
							__UpperCamelCase			:     Any         =      time.time()
							return end - start




def 			_SCREAMING_SNAKE_CASE      (	)      ->					None:






							'''simple docstring'''





							__UpperCamelCase			:     Dict         =      [10, 100, 1_000, 10_000, 50_000, 100_000, 200_000, 300_000, 400_000, 500_000]
							__UpperCamelCase			:     Union[str, Any]         =      [time_max_subarray(_lowerCamelCase) for input_size in input_sizes]
							print("No of Inputs\t\tTime Taken")
							for input_size, runtime in zip(_lowerCamelCase		,						_lowerCamelCase):
														print(_lowerCamelCase		,						"\t\t"		,						_lowerCamelCase)
							plt.plot(_lowerCamelCase		,						_lowerCamelCase)
							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

import math
from collections import Counter
from string import ascii_lowercase




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    str)      ->					None:






							'''simple docstring'''





							__UpperCamelCase     ,		__UpperCamelCase			:     Optional[Any]         =      analyze_text(_lowerCamelCase)
							__UpperCamelCase			:     List[str]         =      list(" " + ascii_lowercase)
							# what is our total sum of probabilities.
							__UpperCamelCase			:     Any         =      sum(single_char_strings.values())

							# one length string
							__UpperCamelCase			:     Optional[Any]         =      0
							# for each alpha we go in our dict and if it is in it we calculate entropy
							for ch in my_alphas:
														if ch in single_char_strings:
																					__UpperCamelCase			:     List[Any]         =      single_char_strings[ch]
																					__UpperCamelCase			:     List[str]         =      my_str / all_sum
																					my_fir_sum += prob * math.loga(_lowerCamelCase)  # entropy formula.

    # print entropy
							print(F'{round(-1 * my_fir_sum):.1f}')

							# two len string
							__UpperCamelCase			:     Optional[Any]         =      sum(two_char_strings.values())
							__UpperCamelCase			:     Tuple         =      0
							# for each alpha (two in size) calculate entropy.
							for cha in my_alphas:
														for cha in my_alphas:
																					__UpperCamelCase			:     List[str]         =      cha + cha
																					if sequence in two_char_strings:
																												__UpperCamelCase			:     Optional[Any]         =      two_char_strings[sequence]
																												__UpperCamelCase			:     Any         =      int(_lowerCamelCase) / all_sum
																												my_sec_sum += prob * math.loga(_lowerCamelCase)

    # print second entropy
							print(F'{round(-1 * my_sec_sum):.1f}')

							# print the difference between them
							print(F'{round((-1 * my_sec_sum) - (-1 * my_fir_sum)):.1f}')




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    str)      ->					tuple[dict, dict]:






							'''simple docstring'''





							__UpperCamelCase			:     Tuple         =      Counter()  # type: ignore
							__UpperCamelCase			:     Any         =      Counter()  # type: ignore
							single_char_strings[text[-1]] += 1

							# first case when we have space at start.
							two_char_strings[" " + text[0]] += 1
							for i in range(0		,						len(_lowerCamelCase) - 1):
														single_char_strings[text[i]] += 1
														two_char_strings[text[i : i + 2]] += 1
							return single_char_strings, two_char_strings




def 			_SCREAMING_SNAKE_CASE      (	)      ->					List[str]:






							'''simple docstring'''





							import doctest

							doctest.testmod()
							# text = (
							#     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
							#     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
							#     "jointure saw horrible. He private he on be imagine suppose. Fertile "
							#     "beloved evident through no service elderly is. Blind there if every no so "
							#     "at. Own neglected you preferred way sincerity delivered his attempted. To "
							#     "of message cottage windows do besides against uncivil.  Delightful "
							#     "unreserved impossible few estimating men favourable see entreaties. She "
							#     "propriety immediate was improving. He or entrance humoured likewise "
							#     "moderate. Much nor game son say feel. Fat make met can must form into "
							#     "gate. Me we offending prevailed discovery. "
							# )

							# calculate_prob(text)


if __name__ == "__main__":
		main()