Design & Analysis of Algorithms - Vol 3 | 4. Longest Common Subsequence by Abraham | Learn Smarter
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4. Longest Common Subsequence

This chapter explores the concept of the longest common subsequence (LCS) and its significance in fields like bioinformatics and text comparison. It details the algorithmic approach to finding LCS, comparing it to the longest common subword problem, and discusses the computational efficiency using dynamic programming. The application of LCS in real-world scenarios, such as genetic sequencing and text file comparison, highlights its relevance.

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Sections

  • 4.

    Longest Common Subsequence

    This section discusses the concept of the longest common subsequence (LCS) problem in computational methods, highlighting its significance and applications.

    Learning Practice

  • 4.1

    General Problem

    This section introduces the longest common subsequence problem and its significance, especially in computational contexts like bioinformatics.

    Learning Practice

  • 4.2

    Interesting Applications

    This section discusses the importance of the longest common subsequence (LCS) algorithm and its applications in various fields, including bioinformatics and text comparison tools.

    Learning Practice

  • 4.3

    Inductive Structure

    This section introduces the inductive structure of the longest common subsequence (LCS) problem, discussing how elements between two sequences can be matched and dropped to find optimal solutions.

    Learning Practice

  • 4.3.1

    Case When Characters Match

    This section discusses the longest common subsequence (LCS) problem, explaining its significance in computational contexts, particularly in bioinformatics and text comparison.

    Learning Practice

  • 4.3.2

    Case When Characters Do Not Match

    This section explores the concept of the Longest Common Subsequence (LCS) problem, where gaps (or dropped letters) are allowed in the matching process.

    Learning Practice

  • 4.4

    Subproblem Dependency

    This section explores the concept of Subproblem Dependency in the context of the Longest Common Subsequence problem, highlighting how dependencies can be structured for efficient dynamic programming solutions.

    Learning Practice

  • 4.5

    Filling The Lcs Table

    This section discusses the method for filling the Longest Common Subsequence (LCS) table using dynamic programming to find matches in sequences while allowing for the dropping of letters.

    Learning Practice

  • 4.6

    Tracing Back The Lcs

    This section introduces the concept of the Longest Common Subsequence (LCS) and its computational significance across various domains.

    Learning Practice

  • 4..7

    Lcs Code Implementation

    This section discusses the Longest Common Subsequence (LCS) problem, its computational significance, and a dynamic programming approach for its solution.

    Learning Practice

References

ch47 part b.pdf

Class Notes

Memorization

What we have learnt

  • The longest common subseque...
  • The LCS problem can be appl...
  • Dynamic programming and mem...

Final Test

Revision Tests