In a dynamic programming solution for the Longest Common Subsequence (LCS), what does the DP table represent?
Practice Questions
1 question
Q1
In a dynamic programming solution for the Longest Common Subsequence (LCS), what does the DP table represent?
The length of the LCS
The characters of the LCS
The indices of the LCS
The number of subsequences
The DP table in LCS represents the length of the longest common subsequence between two strings.
Questions & Step-by-step Solutions
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Q
Q: In a dynamic programming solution for the Longest Common Subsequence (LCS), what does the DP table represent?
Solution: The DP table in LCS represents the length of the longest common subsequence between two strings.
Steps: 6
Step 1: Understand that the Longest Common Subsequence (LCS) is a problem that finds the longest sequence that appears in the same order in two different strings.
Step 2: The DP table is a grid where each cell represents a comparison between characters from the two strings.
Step 3: The rows of the DP table represent characters from the first string, and the columns represent characters from the second string.
Step 4: Each cell in the DP table contains a number that indicates the length of the longest common subsequence found so far between the two strings up to those characters.
Step 5: If the characters from both strings match, the value in the cell is 1 plus the value from the diagonal cell (top-left).
Step 6: If the characters do not match, the value in the cell is the maximum value from either the cell directly above or the cell directly to the left.
