Question:
What is the approximate time taken in dynamic programming for the alignment of 3 sequences of length n?
What is the approximate time taken in dynamic programming for the alignment of 3 sequences of length n?
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Dynamic programming for sequence alignment with 3 sequences has a time complexity of \(O(n^3)\), where \(n\) is the sequence length.
Updated On: Feb 27, 2025
- 5n3
- 6n3
- 7n3
- 8n3
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The Correct Option is C
Solution and Explanation
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 \(7n^3\).
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