


"""simple docstring"""






def 							A_					(   snake_case__		)				->     str:
			if len(snake_case__		) == 0 or not all(len(snake_case__		) == 2 for pair in coordinates		):
						raise ValueError('''The program cannot work out a fitting polynomial.'''		)

			if len({tuple(snake_case__		) for pair in coordinates}		) != len(snake_case__		):
						raise ValueError('''The program cannot work out a fitting polynomial.'''		)

			_UpperCamelCase				:Tuple				    =  {x for x, _ in coordinates}
			if len(snake_case__		) == 1:
						return f"x={coordinates[0][0]}"

			if len(snake_case__		) != len(snake_case__		):
						raise ValueError('''The program cannot work out a fitting polynomial.'''		)

			_UpperCamelCase				:str				    =  len(snake_case__		)

			_UpperCamelCase				:Optional[Any]				    =  0
			_UpperCamelCase				:list[list[float]]				    =  []
			# put the x and x to the power values in a matrix
			while count_of_line < x:
						_UpperCamelCase				:Tuple				    =  0
						_UpperCamelCase				:Optional[int]				    =  coordinates[count_of_line][0]
						_UpperCamelCase				:list[float]				    =  []
						while count_in_line < x:
									count_line.append(a ** (x - (count_in_line + 1))		)
									count_in_line += 1
						matrix.append(snake_case__		)
						count_of_line += 1

			_UpperCamelCase				:Optional[Any]				    =  0
			# put the y values into a vector
			_UpperCamelCase				:list[float]				    =  []
			while count_of_line < x:
						vector.append(coordinates[count_of_line][1]		)
						count_of_line += 1

			_UpperCamelCase				:Union[str, Any]				    =  0

			while count < x:
						_UpperCamelCase				:Optional[Any]				    =  0
						while zahlen < x:
									if count == zahlen:
												zahlen += 1
									if zahlen == x:
												break
									_UpperCamelCase				:str				    =  matrix[zahlen][count] / matrix[count][count]
									for counting_columns, item in enumerate(matrix[count]		):
												# manipulating all the values in the matrix
												matrix[zahlen][counting_columns] -= item * bruch
									# manipulating the values in the vector
									vector[zahlen] -= vector[count] * bruch
									zahlen += 1
						count += 1

			_UpperCamelCase				:Union[str, Any]				    =  0
			# make solutions
			_UpperCamelCase				:list[str]				    =  []
			while count < x:
						solution.append(str(vector[count] / matrix[count][count]		)		)
						count += 1

			_UpperCamelCase				:Dict				    =  0
			_UpperCamelCase				:str				    =  '''f(x)='''

			while count < x:
						_UpperCamelCase				:list[str]				    =  solution[count].split('''E'''		)
						if len(snake_case__		) > 1:
									_UpperCamelCase				:List[Any]				    =  f"{remove_e[0]}*10^{remove_e[1]}"
						solved += f"x^{x - (count + 1)}*{solution[count]}"
						if count + 1 != x:
									solved += "+"
						count += 1

			return solved


if __name__ == "__main__":
					print(points_to_polynomial([]))
					print(points_to_polynomial([[]]))
					print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
					print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
					print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
					print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
					print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
					print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
					print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
					print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))





"""simple docstring"""






def 							A_					(   snake_case__		)				->     str:
			_UpperCamelCase				:Tuple				    =  word.upper()
			_UpperCamelCase				:Dict				    =  0
			_UpperCamelCase				:Union[str, Any]				    =  {}
			_UpperCamelCase				:Optional[int]				    =  []

			for letter in word:
						if letter not in letter_nums:
									_UpperCamelCase				:Dict				    =  str(snake_case__		)
									next_num += 1
						word_pattern.append(letter_nums[letter]		)
			return ".".join(snake_case__		)


if __name__ == "__main__":
					import pprint
					import time

					UpperCamelCase__							:Dict       =  time.time()
					with open("""dictionary.txt""") as in_file:
										UpperCamelCase__							:str       =  in_file.read().splitlines()

					UpperCamelCase__							:dict       =  {}
					for word in word_list:
										UpperCamelCase__							:List[Any]       =  get_word_pattern(word)
										if pattern in all_patterns:
															all_patterns[pattern].append(word)
										else:
															UpperCamelCase__							:Tuple       =  [word]

					with open("""word_patterns.txt""", """w""") as out_file:
										out_file.write(pprint.pformat(all_patterns))

					UpperCamelCase__							:Dict       =  round(time.time() - start_time, 2)
					print(F"""Done!  {len(all_patterns):,} word patterns found in {total_time} seconds.""")
					# Done!  9,581 word patterns found in 0.58 seconds.

