





"""simple docstring"""





from __future__ import annotations

UpperCamelCase_					:						List[str]				= list[list[int]]

# assigning initial values to the grid
UpperCamelCase_					:						Matrix				= [
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
UpperCamelCase_					:						Matrix				= [
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]
def 							A_     (__a				,   __a				,   __a				,   __a				):

					'''simple docstring'''





					for i in range(9				):
										if grid[row][i] == n or grid[i][column] == n:
															return False

					for i in range(3				):
										for j in range(3				):
															if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
																				return False

					return True
def 							A_     (__a				):

					'''simple docstring'''





					for i in range(9				):
										for j in range(9				):
															if grid[i][j] == 0:
																				return i, j
					return None
def 							A_     (__a				):

					'''simple docstring'''





					if location := find_empty_location(__a				):
										A_ ,    A_				 =						location
					else:
										# If the location is ``None``, then the grid is solved.
										return grid

					for digit in range(1				,   10				):
										if is_safe(__a				,   __a				,   __a				,   __a				):
															A_				 =						digit

															if sudoku(__a				) is not None:
																				return grid

															A_				 =						0

					return None
def 							A_     (__a				):

					'''simple docstring'''





					for row in grid:
										for cell in row:
															print(__a				,   end=" "				)
										print()


if __name__ == "__main__":
		# make a copy of grid so that you can compare with the unmodified grid
		for example_grid in (initial_grid, no_solution):
				print('''\nExample grid:\n''' + '''=''' * 20)
				print_solution(example_grid)
				print('''\nExample grid solution:''')
				UpperCamelCase_					:						int				= sudoku(example_grid)
				if solution is not None:
						print_solution(solution)
				else:
						print('''Cannot find a solution.''')






"""simple docstring"""





from __future__ import annotations
def 							A_     (__a				,   __a = None				,   __a = None				,   __a = False				,   ):

					'''simple docstring'''





					A_				 =						cipher_alphabet or [chr(__a				) for i in range(97				,   123				)]

					# 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)
										A_				 =						{
										    "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
										A_				 =						frequencies_dict

					if not case_sensitive:
										A_				 =						ciphertext.lower()

					# Chi squared statistic values
					A_				 =						{}

					# cycle through all of the shifts
					for shift in range(len(__a				)				):
										A_				 =						""

										# decrypt the message with the shift
										for letter in ciphertext:
															try:
																				# Try to index the letter in the alphabet
																				A_				 =						(alphabet_letters.index(letter.lower()				) - shift) % len(
																				    __a				)
																				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

										A_				 =						0.0

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

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

																									# Complete the chi squared statistic formula
																									A_				 =						((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
																									A_				 =						decrypted_with_shift.count(__a				)

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

																									# Complete the chi squared statistic formula
																									A_				 =						((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
										A_				 =						(
										    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(__a				) -> tuple[float, str]:
										return chi_squared_statistic_values[key]

					A_				 =						min(
					    __a				,   key=__a				,   )

					# Get all the data from the most likely cipher (key, decoded message)
					(
					    (
					    A_
					) ,    (
					    A_
					) ,    
					)				 =						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,
					)




