
"""simple docstring"""





from __future__ import annotations



def       lowerCamelCase__		(			__snake_case,     __snake_case = None,     __snake_case = None,     __snake_case = False,     )							->		tuple[int, float, str]:


					"""simple docstring"""





					_UpperCamelCase							 =  cipher_alphabet or [chr(__lowerCAmelCase	) for i in range(97,     1_23	)]

					# If the argument is None or the user provided an empty dictionary
					if not frequencies_dict:
										# Frequencies of letters in the english language (how much they show up)
										_UpperCamelCase							 =  {
										    '''a''': 0.08497,
										    '''b''': 0.01492,
										    '''c''': 0.02202,
										    '''d''': 0.04253,
										    '''e''': 0.11162,
										    '''f''': 0.02228,
										    '''g''': 0.02015,
										    '''h''': 0.06094,
										    '''i''': 0.07546,
										    '''j''': 0.00153,
										    '''k''': 0.01292,
										    '''l''': 0.04025,
										    '''m''': 0.02406,
										    '''n''': 0.06749,
										    '''o''': 0.07507,
										    '''p''': 0.01929,
										    '''q''': 0.00095,
										    '''r''': 0.07587,
										    '''s''': 0.06327,
										    '''t''': 0.09356,
										    '''u''': 0.02758,
										    '''v''': 0.00978,
										    '''w''': 0.02560,
										    '''x''': 0.00150,
										    '''y''': 0.01994,
										    '''z''': 0.00077,
										}
					else:
										# Custom frequencies dictionary
										_UpperCamelCase							 =  frequencies_dict

					if not case_sensitive:
										_UpperCamelCase							 =  ciphertext.lower()

					# Chi squared statistic values
					_UpperCamelCase							 =  {}

					# cycle through all of the shifts
					for shift in range(len(__lowerCAmelCase	)	):
										_UpperCamelCase							 =  ''''''

										# decrypt the message with the shift
										for letter in ciphertext:
															try:
																				# Try to index the letter in the alphabet
																				_UpperCamelCase							 =  (alphabet_letters.index(letter.lower()	) - shift) % len(
																				    __lowerCAmelCase	)
																				decrypted_with_shift += (
																				    alphabet_letters[new_key].upper()
																				    if case_sensitive and letter.isupper()
																				    else alphabet_letters[new_key]
																				)
															except ValueError:
																				# Append the character if it isn't in the alphabet
																				decrypted_with_shift += letter

										_UpperCamelCase							 =  0.0

										# Loop through each letter in the decoded message with the shift
										for letter in decrypted_with_shift:
															if case_sensitive:
																				_UpperCamelCase							 =  letter.lower()
																				if letter in frequencies:
																									# Get the amount of times the letter occurs in the message
																									_UpperCamelCase							 =  decrypted_with_shift.lower().count(__lowerCAmelCase	)

																									# Get the excepcted amount of times the letter should appear based
																									# on letter frequencies
																									_UpperCamelCase							 =  frequencies[letter] * occurrences

																									# Complete the chi squared statistic formula
																									_UpperCamelCase							 =  ((occurrences - expected) ** 2) / expected

																									# Add the margin of error to the total chi squared statistic
																									chi_squared_statistic += chi_letter_value
															else:
																				if letter.lower() in frequencies:
																									# Get the amount of times the letter occurs in the message
																									_UpperCamelCase							 =  decrypted_with_shift.count(__lowerCAmelCase	)

																									# Get the excepcted amount of times the letter should appear based
																									# on letter frequencies
																									_UpperCamelCase							 =  frequencies[letter] * occurrences

																									# Complete the chi squared statistic formula
																									_UpperCamelCase							 =  ((occurrences - expected) ** 2) / expected

																									# Add the margin of error to the total chi squared statistic
																									chi_squared_statistic += chi_letter_value

        # Add the data to the chi_squared_statistic_values dictionary
										_UpperCamelCase							 =  (
										    chi_squared_statistic,
										    decrypted_with_shift,
										)

					# Get the most likely cipher by finding the cipher with the smallest chi squared
					# statistic
					def chi_squared_statistic_values_sorting_key(__snake_case	) -> tuple[float, str]:
										return chi_squared_statistic_values[key]

					_UpperCamelCase							 =  min(
					    __lowerCAmelCase,     key=__lowerCAmelCase,     )

					# Get all the data from the most likely cipher (key, decoded message)
					(
					    (
					    _UpperCamelCase 
					) ,  (
					    _UpperCamelCase 
					) ,   
					)							 =  chi_squared_statistic_values[most_likely_cipher]

					# Return the data on the most likely shift
					return (
					    most_likely_cipher,
					    most_likely_cipher_chi_squared_value,
					    decoded_most_likely_cipher,
					)














from __future__ import annotations

from itertools import permutations
from random import randint
from timeit import repeat


def __A    (      )->  tuple[list[int], int]:





						"""simple docstring"""



						_UpperCAmelCase									=			[randint(-1_000 ,		1_000	) for i in range(10	)]
						_UpperCAmelCase									=			randint(-5_000 ,		5_000	)
						return (arr, r)


_a      	=  make_dataset()


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  tuple[int, ...]:





						"""simple docstring"""



						for triplet in permutations(__lowerCAmelCase ,		3	):
												if sum(__lowerCAmelCase	) == target:
																		return tuple(sorted(__lowerCAmelCase	)	)
						return (0, 0, 0)


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  tuple[int, int, int]:





						"""simple docstring"""



						arr.sort()
						_UpperCAmelCase									=			len(__lowerCAmelCase	)
						for i in range(n - 1	):
												_UpperCAmelCase					, _UpperCAmelCase									=			i + 1, n - 1
												while left < right:
																		if arr[i] + arr[left] + arr[right] == target:
																								return (arr[i], arr[left], arr[right])
																		elif arr[i] + arr[left] + arr[right] < target:
																								left += 1
																		elif arr[i] + arr[left] + arr[right] > target:
																								right -= 1
						return (0, 0, 0)


def __A    (      )->  tuple[float, float]:





						"""simple docstring"""



						_UpperCAmelCase									=			'\nfrom __main__ import dataset, triplet_sum1, triplet_sum2\n'
						_UpperCAmelCase									=			'\ntriplet_sum1(*dataset)\n'
						_UpperCAmelCase									=			'\ntriplet_sum2(*dataset)\n'
						_UpperCAmelCase									=			repeat(setup=__lowerCAmelCase ,		stmt=__lowerCAmelCase ,		repeat=5 ,		number=10_000	)
						_UpperCAmelCase									=			repeat(setup=__lowerCAmelCase ,		stmt=__lowerCAmelCase ,		repeat=5 ,		number=10_000	)
						return (min(__lowerCAmelCase	), min(__lowerCAmelCase	))


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

		testmod()
		_a      	=  solution_times()
		print(F'''The time for naive implementation is {times[0]}.''')
		print(F'''The time for optimized implementation is {times[1]}.''')
