Which dynamic programming approach is used to solve the Longest Common Subsequen

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Question: Which dynamic programming approach is used to solve the Longest Common Subsequence problem?

Options:

Correct Answer: Bottom-up

Solution:

The Longest Common Subsequence problem is typically solved using a bottom-up dynamic programming approach.

Which dynamic programming approach is used to solve the Longest Common Subsequence problem?

Which dynamic programming approach is used to solve the Longest Common Subsequence problem?

Step 1: Understand the Longest Common Subsequence (LCS) problem. It involves finding the longest sequence that appears in the same order in two different sequences, but not necessarily consecutively.
Step 2: Identify 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: Recognize that the bottom-up approach starts with the smallest subproblems and builds up to the solution of the larger problem.
Step 4: Create a 2D table (array) where one dimension represents the characters of the first sequence and the other dimension represents the characters of the second sequence.
Step 5: Fill in the table by comparing characters from both sequences. If they match, take the value from the diagonal cell and add 1. If they don't match, take the maximum value from the cell above or the cell to the left.
Step 6: Continue filling the table until all characters have been compared. The value in the bottom-right cell of the table will be the length of the longest common subsequence.

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