Given two sequences X and Y, a sequence G is said to be a common subsequence of X and Y, if G is a subsequence of both X and Y.
Given X as above, and
A common subsequence of X and Y could be
This would not be the longest common subsequence, since G only has length 3, and the sequence < B,E,E,B > has length 4.
It turns out the longest common subsequence of X and Y would be < B,E,G,C,E,B >
Subsequences have applications to computer science, especially in the discipline of Bioinformatics, where computers are used to compare, analyze, and store DNA strands.
Take two strands of DNA, say
ORG_{1} = ACGGTGTCGTGCTATGCTGATGCTGACTTATATGCTA
ORG_{2} = CGTTCGGCTATCGTACGTTCTATTCTATGATTTCTAA
Subsequences are used to determine how similar the two strands of DNA are, using the DNA bases: adenine, guanine, cytosine and thymine.
A common problem in subsequences is the Longestcommon subsequence problem, where we use dynamic programming to find a maximum length subsequence of two or more sequences.
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