What is subsequences ?
In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
For example, the sequence is a subsequence of obtained after removal of elements , , and . The relation of one sequence being the subsequence of another is a preorder.
The subsequence should not be confused with substring which can be derived from the above string by deleting substring . The substring is a refinement of the subsequence.
The list of all subsequences for the word "apple" would be "e, l, le, p, pe, pl, ple, p, pe, pl, ple, pp, ppe, ppl, pple, a, ae, al, ale, ap, ape, apl, aple, ap, ape, apl, aple, app, appe, appl, apple".
Problem 1
Kadane's algorithm:
finds maximum sub-array of any size
Problem 2
Longest common subsequence problem:
Find the longest subsequence common to all sequences in a set of sequences
Problem 3
Longest increasing subsequence problem: Find the longest increasing subsequence of a given sequence
Problem 4
Longest palindrome subsequence :
Find the longest increasing subsequence of a given sequence
Problem 5
Longest palindrome substring : (MANCHESTER'S ALGORITHMS)
Find the longest palindrome substring of a given sequence
Problem 5
Shortest common supersequence problem: Find the shortest supersequence that contains two or more sequences as subsequences
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