Which algorithm uses dynamic programming to solve the longest common subsequence

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Question: Which algorithm uses dynamic programming to solve the longest common subsequence problem?

Options:

Correct Answer: LCS Algorithm

Solution:

The Longest Common Subsequence (LCS) problem is solved using a dynamic programming approach.

Which algorithm uses dynamic programming to solve the longest common subsequence problem?

Which algorithm uses dynamic programming to solve the longest common subsequence problem?

Step 1: Understand what the Longest Common Subsequence (LCS) problem is. It involves finding the longest sequence that appears in the same order in two different sequences, but not necessarily consecutively.
Step 2: Recognize that dynamic programming is a method used to solve problems by breaking them down into simpler subproblems and storing the results of these subproblems to avoid redundant calculations.
Step 3: Learn that the LCS problem can be solved using a dynamic programming approach by creating a table (or matrix) to store the lengths of the longest common subsequences for different pairs of prefixes of the two sequences.
Step 4: Fill in the table based on the following rules: If the characters from both sequences match, add 1 to the value from the previous characters' subsequence length. If they do not match, take the maximum value from either the left or the top cell in the table.
Step 5: The value in the bottom-right cell of the table will give you the length of the longest common subsequence.

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