Given a sequence, print a longest palindromic subsequence of it.
Input : BBABCBCAB Output : BABCBAB The above output is the longest palindromic subsequence of given sequence. "BBBBB" and "BBCBB" are also palindromic subsequences of the given sequence, but not the longest ones. Input : GEEKSFORGEEKS Output : Output can be either EEKEE or EESEE or EEGEE, ..
We have discussed a solution in below post to find length of longest palindromic subsequence.
Dynamic Programming | Set 12 (Longest Palindromic Subsequence)
In this post a solution to print the longest palindromic subsequence is discussed.
This problem is close to the Longest Common Subsequence (LCS) problem. In fact, we can use LCS as a subroutine to solve this problem. Following is the two step solution that uses LCS.
1) Reverse the given sequence and store the reverse in another array say rev[0..n-1]
2) LCS of the given sequence and rev will be the longest palindromic sequence.
3) Once we have found LCS, we can print the LCS.
Below is the implementation of above approach:
- Longest Palindromic Subsequence | DP-12
- Longest Increasing Subsequence using Longest Common Subsequence Algorithm
- Count All Palindromic Subsequence in a given String
- Find the lexicographically largest palindromic Subsequence of a String
- Longest Palindromic Substring | Set 2
- Longest Non-palindromic substring
- Longest Palindromic Substring | Set 1
- Longest subsequence such that every element in the subsequence is formed by multiplying previous element with a prime
- Manacher's Algorithm - Linear Time Longest Palindromic Substring - Part 4
- Manacher's Algorithm - Linear Time Longest Palindromic Substring - Part 3
- Manacher's Algorithm - Linear Time Longest Palindromic Substring - Part 1
- Manacher's Algorithm - Linear Time Longest Palindromic Substring - Part 2
- Longest Zig-Zag Subsequence
- Longest Decreasing Subsequence
- Longest Uncommon Subsequence
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