LCS for Multiple Sequences (Multistage)
Find the longest common subsequence across multiple sequences using a multistage approach
Multistage Longest Common Subsequence
An extension of the classic LCS problem to handle multiple sequences by processing them in stages.
Theory & Concepts
Definition:
Multistage LCS finds the longest subsequence that appears in the same relative order across multiple input sequences.
Key Points:
- Stage 1: Find pairwise LCS between consecutive sequences
- Stage 2: Merge results to find common elements across all sequences
- Uses dynamic programming principles recursively
- More complex than standard 2-sequence LCS
Applications:
- Bioinformatics: Multiple sequence alignment
- Text analysis: Finding common patterns across documents
- Version control: Identifying common changes
- Data mining: Pattern discovery in multiple datasets
University Guidelines
Exam Weightage
8-10 marks MarksSyllabus Coverage:
- Multiple sequence LCS problem
- Multistage dynamic programming approach
- Pairwise LCS computation
- Result merging strategies
- Complexity analysis for multiple sequences
Common Questions:
- Extend LCS to multiple sequences
- Show multistage processing steps
- Compare with standard LCS approach
- Analyze time complexity for n sequences
Exam Tips:
Process sequences in stages clearly
Show pairwise LCS computations
Demonstrate merging process
Include final common subsequence
Algorithm Details
O(n × m₁ × m₂) where n is number of sequences, mᵢ is length of sequence i
Time Complexity
O(m₁ × m₂) for each pairwise computation
Space Complexity
Algorithm Steps:
- 1Stage 1: Compute pairwise LCS for consecutive sequence pairs
- 2Create intermediate results for each pair
- 3Stage 2: Find common elements across all pairwise results
- 4Merge results maintaining order constraints
- 5Return final longest common subsequence
Configure Sequences
Input Sequences:
Seq 1:ABCDGH
Seq 2:AEDFHR
Seq 3:ABFGHR
Multistage Results
🔤
Configure your sequences and click "Find Multistage LCS" to see the results