



'''simple docstring'''

def     __UpperCamelCase					(				_lowercase,					_lowercase,					_lowercase,					_lowercase,					_lowercase,					_lowercase,					)			->      tuple[list[list[int]], list[list[str]]]:
	_lowercase       :							str  	=		list(_lowercase       )
	_lowercase       :							Any  	=		list(_lowercase       )
	_lowercase       :							Tuple  	=		len(_lowercase       )
	_lowercase       :							Dict  	=		len(_lowercase       )

	_lowercase       :							Optional[Any]  	=		[
	    [0 for _ in range(len_destination_seq + 1       )] for _ in range(len_source_seq + 1       )
	]
	_lowercase       :							Union[str, Any]  	=		[
	    ['0' for _ in range(len_destination_seq + 1       )] for _ in range(len_source_seq + 1       )
	]

	for i in range(1,					len_source_seq + 1       ):
		_lowercase       :							int  	=		i * delete_cost
		_lowercase       :							List[Any]  	=		f'''D{source_seq[i - 1]:c}'''

	for i in range(1,					len_destination_seq + 1       ):
		_lowercase       :							str  	=		i * insert_cost
		_lowercase       :							Union[str, Any]  	=		f'''I{destination_seq[i - 1]:c}'''

	for i in range(1,					len_source_seq + 1       ):
		for j in range(1,					len_destination_seq + 1       ):
			if source_seq[i - 1] == destination_seq[j - 1]:
				_lowercase       :							List[str]  	=		costs[i - 1][j - 1] + copy_cost
				_lowercase       :							Any  	=		f'''C{source_seq[i - 1]:c}'''
			else:
				_lowercase       :							List[Any]  	=		costs[i - 1][j - 1] + replace_cost
				_lowercase       :							Optional[int]  	=		f'''R{source_seq[i - 1]:c}''' + str(destination_seq[j - 1]       )

			if costs[i - 1][j] + delete_cost < costs[i][j]:
				_lowercase       :							Optional[int]  	=		costs[i - 1][j] + delete_cost
				_lowercase       :							Tuple  	=		f'''D{source_seq[i - 1]:c}'''

			if costs[i][j - 1] + insert_cost < costs[i][j]:
				_lowercase       :							str  	=		costs[i][j - 1] + insert_cost
				_lowercase       :							Dict  	=		f'''I{destination_seq[j - 1]:c}'''

	return costs, ops







def     __UpperCamelCase					(				_lowercase,					_lowercase,					_lowercase       )			->      list[str]:
	if i == 0 and j == 0:
		return []
	else:
		if ops[i][j][0] == "C" or ops[i][j][0] == "R":
			_lowercase       :							Any  	=		assemble_transformation(_lowercase,					i - 1,					j - 1       )
			seq.append(ops[i][j]       )
			return seq
		elif ops[i][j][0] == "D":
			_lowercase       :							str  	=		assemble_transformation(_lowercase,					i - 1,					_lowercase       )
			seq.append(ops[i][j]       )
			return seq
		else:
			_lowercase       :							List[str]  	=		assemble_transformation(_lowercase,					_lowercase,					j - 1       )
			seq.append(ops[i][j]       )
			return seq


if __name__ == "__main__":
		_A    ,      _A					:     str      =compute_transform_tables('''Python''', '''Algorithms''', -1, 1, 2, 2)

		_A					:     Optional[Any]      =len(operations)
		_A					:     List[str]      =len(operations[0])
		_A					:     Optional[int]      =assemble_transformation(operations, m - 1, n - 1)

		_A					:     str      =list('''Python''')
		_A					:     Dict      =0
		_A					:     List[Any]      =0

		with open('''min_cost.txt''', '''w''') as file:
				for op in sequence:
						print(''''''.join(string))

						if op[0] == "C":
								file.write('''%-16s''' % '''Copy %c''' % op[1])
								file.write('''\t\t\t''' + ''''''.join(string))
								file.write('''\r\n''')

								cost -= 1
						elif op[0] == "R":
								_A					:     Any      =op[2]

								file.write('''%-16s''' % ('''Replace %c''' % op[1] + ''' with ''' + str(op[2])))
								file.write('''\t\t''' + ''''''.join(string))
								file.write('''\r\n''')

								cost += 1
						elif op[0] == "D":
								string.pop(i)

								file.write('''%-16s''' % '''Delete %c''' % op[1])
								file.write('''\t\t\t''' + ''''''.join(string))
								file.write('''\r\n''')

								cost += 2
						else:
								string.insert(i, op[1])

								file.write('''%-16s''' % '''Insert %c''' % op[1])
								file.write('''\t\t\t''' + ''''''.join(string))
								file.write('''\r\n''')

								cost += 2

						i += 1

				print(''''''.join(string))
				print('''Cost: ''', cost)

				file.write('''\r\nMinimum cost: ''' + str(cost))





'''simple docstring'''

from __future__ import annotations

_A					:     Union[str, Any]      ='''Alexander Joslin'''







def     __UpperCamelCase					(				_lowercase       )			->      int:

	if number <= 0:
		_lowercase       :							Optional[Any]  	=		f'''n must be greater than 0. Got n = {number}'''
		raise ValueError(_lowercase       )

	_lowercase       :							List[str]  	=		[number + 1] * (number + 1)

	# starting position
	_lowercase       :							str  	=		0
	for i in range(1,					_lowercase       ):
		_lowercase       :							Union[str, Any]  	=		min(table[i + 1],					table[i] + 1       )
		# check if out of bounds
		if i * 2 <= number:
			_lowercase       :							Optional[Any]  	=		min(table[i * 2],					table[i] + 1       )
		# check if out of bounds
		if i * 3 <= number:
			_lowercase       :							Any  	=		min(table[i * 3],					table[i] + 1       )
	return table[number]


if __name__ == "__main__":
		import doctest

		doctest.testmod()
