A subsequence is defined as a sequence that can be derived from another string/sequence by deleting some or none of the elements without changing the order of the remaining elements.
For example: Let’s take “GeeksForGeeks”, GeeksF will be a subsequence of “GeeksForGeeks”.
Example of Subsequence
Properties of Subsequence:
- A sequence is a subsequence of itself.
- The empty sequence is a subsequence of every sequence.
- The number of possible subsequences of a sequence of length n is 2n.
- A subsequence of a subsequence is also a subsequence of the original sequence.
- The relative order of characters is unchanged.
How it is different from a Substring?
- A substring is a sequence of consecutive characters of a larger string or sequence whereas, in a subsequence, the characters need not to be consecutive.
- The total possible number of substrings for a string of length n is (n*(n+1)/2) whereas the total number of possible subsequences is (2n).
To learn more about the differences, refer to this article.
Applications of Subsequence:
- DNA Sequence Analysis: Subsequence is basically a pattern recognition concept, which can be used to identify similar patterns within the DNA sequence and to find important motifs or functional regions.
- Natural Language Processing: This is done by identifying and extracting subsequences of words that match a given pattern. NLP is focused on making AI more natural to humans, which needs to extract pattern from a large dataset.
- Speech Recognition: Subsequences are used in speech recognition to identify phonemes (the smallest units of sound in a language).
- Computer Vision: Subsequences are used in computer vision to recognize patterns in images or videos. For example, face lock in your mobile phones uses this feature to identify your face.
- Financial Analysis: Subsequences are used in financial analysis to identify patterns and trends in financial data, such as stock prices or sales figures.
Advantages of Subsequence:
- Subsequences are more general than substrings because they can capture non-contiguous patterns.
- They can identify patterns that are more complex and have greater flexibility in capturing features of a sequence.
Disadvantages of Subsequence:
- Finding all possible subsequences of a given sequence can be computationally expensive, especially if the sequence is long.
- Algorithms that use subsequences may have high time and space complexity.