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Intermediate Topic 27 of 51 Algorithms

Longest Common Subsequence

Finding the longest shared ordered subsequence of two sequences.

How it works

The longest common subsequence of two sequences is the longest sequence that appears in both in the same order, not necessarily contiguous. A dynamic programming table L[i][j] stores the answer for the first i and j characters: matching characters extend the diagonal value by one, otherwise take the maximum of the left and upper cells. Time and space are O(mn), and space can be reduced with rolling rows.

Where it is used

The diff tool and version control, DNA and protein comparison, plagiarism detection and file synchronization use LCS to compare sequences.

Common pitfall

Confusing subsequence with substring, which must be contiguous, is common. Recovering the actual sequence requires walking back through the table. For very large inputs, O(mn) memory is a problem, which Hirschberg's algorithm addresses. Handle empty strings in the base row and column.

Where it fits in the course

Longest Common Subsequence is topic 27 of 51 in Algorithms, rated Intermediate. It follows Knapsack Problem. The next topic is Edit Distance.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Algorithms quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Longest Common Subsequence?
Finding the longest shared ordered subsequence of two sequences. It belongs to Algorithms and is an intermediate-level topic.
Where do people use Longest Common Subsequence?
The diff tool and version control, DNA and protein comparison, plagiarism detection and file synchronization use LCS to compare sequences.
What is the most common mistake with Longest Common Subsequence?
Confusing subsequence with substring, which must be contiguous, is common.
What should I learn before this topic?
Start with Knapsack Problem, the topic just before it in Algorithms.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Algorithms quiz. You can also explore DP Table (LCS) in the Visual Lab.
Is Longest Common Subsequence hard to learn?
It is an Intermediate topic. Be comfortable with the Beginner topics in this area first, then read the common pitfall carefully, since it is where most mistakes happen.
How long does it take to learn Longest Common Subsequence?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Longest Common Subsequence?
Knapsack Problem, Edit Distance, Dynamic Programming are closely connected. The full list is in the related topics section of this page.
What should I study after Longest Common Subsequence?
Continue with Edit Distance, the next topic in Algorithms.

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