






"""simple docstring"""







def 						lowercase__(A ,		A						)    ->Optional[Any]:




						"""simple docstring"""



						assert x is not None
						assert y is not None

						lowercase__    :				int=	len(A						)
						lowercase__    :				Optional[int]=	len(A						)

						# declaring the array for storing the dp values
						lowercase__    :				Dict=	[[0] * (n + 1) for _ in range(m + 1						)]  # noqa: E741

						for i in range(1 ,		m + 1						):
												for j in range(1 ,		n + 1						):
																		lowercase__    :				Any=	1 if x[i - 1] == y[j - 1] else 0

																		lowercase__    :				Dict=	max(l[i - 1][j] ,		l[i][j - 1] ,		l[i - 1][j - 1] + match						)

						lowercase__    :				Optional[int]=	""
						lowercase__,     lowercase__    :				List[str]=	m, n
						while i > 0 and j > 0:
												lowercase__    :				Optional[Any]=	1 if x[i - 1] == y[j - 1] else 0

												if l[i][j] == l[i - 1][j - 1] + match:
																		if match == 1:
																								lowercase__    :				List[Any]=	x[i - 1] + seq
																		i -= 1
																		j -= 1
												elif l[i][j] == l[i - 1][j]:
																		i -= 1
												else:
																		j -= 1

						return l[m][n], seq


if __name__ == "__main__":
			a			:    str				 =		"""AGGTAB"""
			a			:    Optional[int]				 =		"""GXTXAYB"""
			a			:    Optional[int]				 =		4
			a			:    Optional[int]				 =		"""GTAB"""

			a ,		a			:    Tuple				 =		longest_common_subsequence(a, b)
			print("""len =""", ln, """, sub-sequence =""", subseq)
			import doctest

			doctest.testmod()














"""simple docstring"""







from __future__ import annotations





def 						lowercase__(A						)    ->int:




						"""simple docstring"""



						for i in range(1 ,		len(matrix[0]						)						):
												matrix[0][i] += matrix[0][i - 1]

						# preprocessing the first column
						for i in range(1 ,		len(A						)						):
												matrix[i][0] += matrix[i - 1][0]

						# updating the path cost for current position
						for i in range(1 ,		len(A						)						):
												for j in range(1 ,		len(matrix[0]						)						):
																		matrix[i][j] += min(matrix[i - 1][j] ,		matrix[i][j - 1]						)

						return matrix[-1][-1]


if __name__ == "__main__":
			import doctest

			doctest.testmod()






