Question

What is the approximate time taken in dynamic programming for the alignment of 3 sequences of length n?

• A. 5n3
• B. 6n3
• C. 7n3
• D. 8n3

Hint:

Dynamic programming for sequence alignment with 3 sequences has a time complexity of \(O(n^3)\), where \(n\) is the sequence length.

Answer 1

The Correct Option is C

Step 1: Understanding Dynamic Programming for Sequence Alignment 
The time complexity of dynamic programming for sequence alignment between multiple sequences is \(O(n^3)\), where \(n\) is the length of each sequence, and there are three sequences being aligned. 
Step 2: Evaluating the Options 
- \(5n^3\): Incorrect time complexity for three sequences. 
- \(6n^3\): Incorrect, does not match the expected time complexity. 
- \(7n^3\) Correct, the time complexity is typically \(O(n^3)\) for three sequences. 
- \(8n^3\): Incorrect, does not match the expected time complexity. 
Step 3: Conclusion 
The time complexity for dynamic programming for aligning three sequences is \(O(n^3)\), which corresponds to the option \(7n^3\).