Which technique can be used to find the longest common subsequence?

Which technique can be used to find the longest common subsequence?

• A. Recursive backtracking
• B. Dynamic programming
• C. Greedy algorithms
• D. Binary search

Answer: (B)

Dynamic programming is an effective technique for finding the longest common subsequence (LCS) because it systematically breaks down the problem into smaller, manageable subproblems and utilizes previously computed results to build up the solution. In the context of the LCS problem, dynamic programming constructs a table that captures the length of the longest common subsequence for all prefix pairs of the two sequences being compared. By filling out this table methodically, it allows the algorithm to avoid redundant calculations and efficiently compute the length of the longest common subsequence by referencing already solved subproblems. The approach essentially works by comparing characters from both sequences and deciding whether to include a character in the subsequence or skip it based on previous computations in the table. This method significantly reduces the exponential time complexity of a naive recursive approach, transforming it into a more manageable polynomial time complexity. In contrast, while recursive backtracking might find the solution, it does so inefficiently by exploring all possible subsequences without leveraging previously computed results. Greedy algorithms work well for optimization problems where local optima lead to global optima, but they do not apply effectively to LCS since the choice of subsequence elements does not guarantee a globally optimal solution. Binary search is not relevant to finding subsequences,

Dynamic programming is an effective technique for finding the longest common subsequence (LCS) because it systematically breaks down the problem into smaller, manageable subproblems and utilizes previously computed results to build up the solution.

In the context of the LCS problem, dynamic programming constructs a table that captures the length of the longest common subsequence for all prefix pairs of the two sequences being compared. By filling out this table methodically, it allows the algorithm to avoid redundant calculations and efficiently compute the length of the longest common subsequence by referencing already solved subproblems.

The approach essentially works by comparing characters from both sequences and deciding whether to include a character in the subsequence or skip it based on previous computations in the table. This method significantly reduces the exponential time complexity of a naive recursive approach, transforming it into a more manageable polynomial time complexity.

In contrast, while recursive backtracking might find the solution, it does so inefficiently by exploring all possible subsequences without leveraging previously computed results. Greedy algorithms work well for optimization problems where local optima lead to global optima, but they do not apply effectively to LCS since the choice of subsequence elements does not guarantee a globally optimal solution. Binary search is not relevant to finding subsequences,