subsekvens

A subsekvens is a sequence derived from another sequence by deleting zero or more elements from the original sequence. The remaining elements retain their original relative order. For example, if the original sequence is ABCDEFG, then ACEG is a subsekvens, but AGC is not, because the G appears before the C in the original sequence, and the C appears before the G.

In mathematics, particularly in the study of discrete mathematics and computer science, subsekvenses are a fundamental concept. They are used in various algorithms and data structures, such as string matching, pattern recognition, and bioinformatics. The length of a subsekvens can range from zero (the empty sequence) to the length of the original sequence itself (which is a subsekvens of itself).

The problem of finding the longest common subsekvens (LCS) of two sequences is a classic example of dynamic programming. This problem aims to find the longest sequence that is a subsekvens of both input sequences. The solution to the LCS problem has numerous applications, including DNA sequencing, plagiarism detection, and file comparison.

Another related concept is the subsequence, which is often used interchangeably with subsekvens. However, some definitions distinguish between them, with a subsekvens implying a contiguous block of elements from the original sequence, while a subsequence does not require contiguity. In the context provided, subsekvens refers to the non-contiguous version.