Which dynamic programming approach is used to find the longest common subsequenc

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Question: Which dynamic programming approach is used to find the longest common subsequence?

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 find the longest common subsequence?

Which dynamic programming approach is used to find the longest common subsequence?

Step 1: Understand what a subsequence is. A subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
Step 2: Identify the two sequences for which you want to find the longest common subsequence (LCS).
Step 3: Create a table (2D array) where the rows represent the characters of the first sequence and the columns represent the characters of the second sequence.
Step 4: Initialize the first row and first column of the table with zeros. This represents the case where one of the sequences is empty.
Step 5: Fill in the table using the following rules: If the characters from both sequences match, take the value from the top-left diagonal cell and add 1. If they do not match, take the maximum value from the cell directly above or the cell to the left.
Step 6: Continue filling the table until all characters from both sequences have been compared.
Step 7: The value in the bottom-right cell of the table will give you the length of the longest common subsequence.

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