




'''simple docstring'''



def   lowercase__(			__UpperCamelCase:					str      ,__UpperCamelCase:					str    ):

      """simple docstring"""






      assert x is not None
      assert y is not None

      SCREAMING_SNAKE_CASE   :      Dict    					=						len(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Any    					=						len(__UpperCamelCase    )

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

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

                  SCREAMING_SNAKE_CASE   :      List[Any]    					=						max(l[i - 1][j]      ,l[i][j - 1]      ,l[i - 1][j - 1] + match    )

      SCREAMING_SNAKE_CASE   :      Dict    					=						''
      SCREAMING_SNAKE_CASE					,    SCREAMING_SNAKE_CASE   :      Tuple    					=						m, n
      while i > 0 and j > 0:
            SCREAMING_SNAKE_CASE   :      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:
                        SCREAMING_SNAKE_CASE   :      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__":
      UpperCamelCase_    	=				"AGGTAB"
      UpperCamelCase_    	=				"GXTXAYB"
      UpperCamelCase_    	=				4
      UpperCamelCase_    	=				"GTAB"

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

      doctest.testmod()








'''simple docstring'''



from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst




def   lowercase__(			):

      """simple docstring"""






      SCREAMING_SNAKE_CASE					,    SCREAMING_SNAKE_CASE   :      str    					=						9, 14  # noqa: F841
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						[
          [0, 1, 4],
          [0, 7, 8],
          [1, 2, 8],
          [7, 8, 7],
          [7, 6, 1],
          [2, 8, 2],
          [8, 6, 6],
          [2, 3, 7],
          [2, 5, 4],
          [6, 5, 2],
          [3, 5, 14],
          [3, 4, 9],
          [5, 4, 10],
          [1, 7, 11],
      ]

      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						defaultdict(__UpperCamelCase    )
      for nodea, nodea, cost in edges:
            adjancency[nodea].append([nodea, cost]    )
            adjancency[nodea].append([nodea, cost]    )

      SCREAMING_SNAKE_CASE   :      Dict    					=						mst(__UpperCamelCase    )

      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						[
          [7, 6, 1],
          [2, 8, 2],
          [6, 5, 2],
          [0, 1, 4],
          [2, 5, 4],
          [2, 3, 7],
          [0, 7, 8],
          [3, 4, 9],
      ]

      for answer in expected:
            SCREAMING_SNAKE_CASE   :      Any    					=						tuple(answer[:2]    )
            SCREAMING_SNAKE_CASE   :      List[Any]    					=						tuple(edge[::-1]    )
            assert edge in result or reverse in result


