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What is the space complexity of the dynamic programming solution for the Longest

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Question: What is the space complexity of the dynamic programming solution for the Longest Common Subsequence problem?

Options:

  1. O(m + n)
  2. O(m * n)
  3. O(m)
  4. O(n)

Correct Answer: O(m * n)

Solution: 

The space complexity of the dynamic programming solution for the Longest Common Subsequence problem is O(m * n), where m and n are the lengths of the two sequences.

What is the space complexity of the dynamic programming solution for the Longest

Practice Questions

Q1
What is the space complexity of the dynamic programming solution for the Longest Common Subsequence problem?
  1. O(m + n)
  2. O(m * n)
  3. O(m)
  4. O(n)

Questions & Step-by-Step Solutions

What is the space complexity of the dynamic programming solution for 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 both sequences, but not necessarily consecutively.
  • Step 2: Recognize that a dynamic programming approach is used to solve the LCS problem. This involves creating a table (or matrix) to store the lengths of common subsequences.
  • Step 3: Identify the dimensions of the table. If the first sequence has length m and the second sequence has length n, the table will have m+1 rows and n+1 columns.
  • Step 4: Calculate the total number of cells in the table. The total number of cells is (m + 1) * (n + 1).
  • Step 5: Simplify the space complexity. In big O notation, we focus on the highest order terms and ignore constants. Thus, we can express the space complexity as O(m * n).
  • Step 6: Conclude that the space complexity of the dynamic programming solution for the LCS problem is O(m * n).
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