Sequence Alignment Problem in C++

In this article, we will discuss the Sequence Alignment problem in C++ with its approach, an example, time complexity, and space complexity.

Sequence Alignment problem:

One of the most fundamental problems in the biological sciences is the Sequence Alignment problem, which asks how similar two amino acid sequences are to one another. Since it provides essential data about evolution, genetic relationships, and biological development, comparing amino acid sequences is important.

In order to solve this problem, Saul B. Needleman and Christian D. Wunsch presented the Needleman-Wunsch algorithm, a dynamic programming method, in 1970. By efficiently identifying the best correspondence between two sequences, this approach established a foundation for subsequent sequence alignment methods. To increase time and space complexity and make sequence alignment more effective for large data sets, several improvements have been put forth throughout the years. However, these optimizations are beyond the scope of this discussion.

Approach:

Dynamic programming provides an effective approach to this problem. In order to ensure that the sequences are of equal length, the best course of action is to create intervals between them. Adding more gaps after the lengths are equalized will only result in a higher alignment penalty and a less favorable result. Consequently, the objective is to minimize the penalty while finding exactly the best gap placement.

Example:

Let us take an example to illustrate the Sequence Alignment problem in C++

Output:

Enter the first sequence: AGCCCT
Enter the second sequence: AGGCA
Enter mismatch penalty: 3
Enter gap penalty: 2
Minimum Alignment Penalty: 8
Aligned Sequences: 
AGCCCT
AG_GCA   

Complexity Analysis:

• Time Complexity: O(n*m)
• Space Complexity: O(n*m)

Explanation:

The Needleman-Wunsch approach for sequence alignment is implemented using dynamic programming in this C++ program. The least penalty needed to align two input sequences is determined by taking the user’s mismatch and gap penalties into consideration. The optimal solutions for subproblems are stored in a dynamic programming table (dp), and the alignment is restored by going back through the table. Once unnecessary leading gaps have been eliminated, the aligned sequences are saved in two arrays and printed. The program makes sure that gaps are placed as efficiently as possible to minimize penalties. This method has an O(m * n) time complexity, where m and n are the input sequence lengths. This program is helpful for quickly comparing DNA, RNA, or protein sequences in bioinformatics.