Longest Common Subsequences Quiz

What is the goal of the longest common subsequence (LCS) problem?

• To count the number of common elements in two sequences

• To find the shortest subsequence of two sequences

• To find a maximum-length common subsequence of two sequences

• To determine if two sequences are identical

Which of the following is a characteristic of the LCS problem?

• It has an optimal substructure property

• It is always solvable in linear time

• It can be solved using a brute-force approach efficiently

• It requires only one sequence to solve

In the context of LCS, what does the variable 'c[i, j]' represent?

• The maximum length of any subsequence

• The length of the longest common subsequence of Xi and Yj

• The total number of subsequences of X

• The index of the longest subsequence found

What is the time complexity of the LCS algorithm when using a dynamic programming approach?

• O(m+n)

• O(m^2)

• Θ(mn)

• O(n log n)

Which of the following statements is true regarding the space complexity of the LCS algorithm?

• It requires Θ(mn) space

• It requires O(m+n) space

• It requires O(m^2) space

• It can be solved in constant space

What is the output of the PRINT-LCS procedure for the sequences X = (A, B, C, B, D, A, B) and Y = (B, D, C, A, B, A)?

• (B, D, A)

• (A, B, C)

• (B, C, B, A)

• (B, C, A)

What is one way to improve the LCS algorithm mentioned in the text?

• By using a single array instead of a table

• By eliminating the b table and reconstructing LCS in O(m+n) time

• By increasing the size of the c table

• By using a different programming language

Which of the following is NOT a learning outcome of the session?

• Apply algorithm techniques and methods

• Explain fundamental concepts of analysis algorithms

• Compare several algorithm design methods

• Develop a new algorithm from scratch

What is the first step in solving the longest common subsequence problem?

• Characterizing a longest common subsequence

• Computing the length of an LCS

• Improving the code

• Constructing an LCS

What is the example subsequence Z of X given in the text?

• (A, B, C)

• (B, C, D, B)

• (B, C, B, A)

• (C, D, A)