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Subsequence meaning in DSA

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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

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.

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Last Updated : 23 Mar, 2023
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