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In the dynamic programming solution for the longest common subsequence, what doe

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Question: In the dynamic programming solution for the longest common subsequence, what does the dp[i][j] cell represent?

Options:

  1. Length of LCS for first i characters of string A and first j characters of string B
  2. Total number of subsequences
  3. Characters in the LCS
  4. Length of the strings A and B

Correct Answer: Length of LCS for first i characters of string A and first j characters of string B

Solution: 

The dp[i][j] cell in the longest common subsequence problem represents the length of the LCS for the first i characters of string A and the first j characters of string B.

In the dynamic programming solution for the longest common subsequence, what doe

Practice Questions

Q1
In the dynamic programming solution for the longest common subsequence, what does the dp[i][j] cell represent?
  1. Length of LCS for first i characters of string A and first j characters of string B
  2. Total number of subsequences
  3. Characters in the LCS
  4. Length of the strings A and B

Questions & Step-by-Step Solutions

In the dynamic programming solution for the longest common subsequence, what does the dp[i][j] cell represent?
  • Step 1: Understand that we have two strings, A and B.
  • Step 2: The characters in string A are indexed from 1 to i.
  • Step 3: The characters in string B are indexed from 1 to j.
  • Step 4: The dp[i][j] cell is part of a table used to store results.
  • Step 5: dp[i][j] specifically stores the length of the longest common subsequence (LCS) between the first i characters of string A and the first j characters of string B.
  • Step 6: This means that dp[i][j] tells us how long the LCS is when we only consider the first i characters of A and the first j characters of B.
  • Dynamic Programming – A method for solving complex problems by breaking them down into simpler subproblems and storing the results of these subproblems to avoid redundant computations.
  • Longest Common Subsequence (LCS) – A classic problem in computer science that involves finding the longest subsequence present in both given sequences.
  • DP Table Representation – Understanding how the DP table is structured and what each cell represents in terms of the problem being solved.
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