# Java Program for Longest Palindromic Subsequence | DP-12

• Last Updated : 13 Aug, 2021

Given a sequence, find the length of the longest palindromic subsequence in it.

As another example, if the given sequence is “BBABCBCAB”, then the output should be 7 as “BABCBAB” is the longest palindromic subsequence in it. “BBBBB” and “BBCBB” are also palindromic subsequences of the given sequence, but not the longest ones.

1) Optimal Substructure:
Let X[0..n-1] be the input sequence of length n and L(0, n-1) be the length of the longest palindromic subsequence of X[0..n-1].
If last and first characters of X are same, then L(0, n-1) = L(1, n-2) + 2.
Else L(0, n-1) = MAX (L(1, n-1), L(0, n-2)).

Following is a general recursive solution with all cases handled.

## Java

 `// Java program of above approach` `class` `GFG {`   `    ``// A utility function to get max of two integers` `    ``static` `int` `max(``int` `x, ``int` `y)` `    ``{` `        ``return` `(x > y) ? x : y;` `    ``}` `    ``// Returns the length of the longest palindromic subsequence in seq`   `    ``static` `int` `lps(``char` `seq[], ``int` `i, ``int` `j)` `    ``{` `        ``// Base Case 1: If there is only 1 character` `        ``if` `(i == j) {` `            ``return` `1``;` `        ``}`   `        ``// Base Case 2: If there are only 2 characters and both are same` `        ``if` `(seq[i] == seq[j] && i + ``1` `== j) {` `            ``return` `2``;` `        ``}`   `        ``// If the first and last characters match` `        ``if` `(seq[i] == seq[j]) {` `            ``return` `lps(seq, i + ``1``, j - ``1``) + ``2``;` `        ``}`   `        ``// If the first and last characters do not match` `        ``return` `max(lps(seq, i, j - ``1``), lps(seq, i + ``1``, j));` `    ``}`   `    ``/* Driver program to test above function */` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``String seq = ``"GEEKSFORGEEKS"``;` `        ``int` `n = seq.length();` `        ``System.out.printf(``"The length of the LPS is %d"``,` `                       ``lps(seq.toCharArray(), ``0``, n - ``1``));` `    ``}` `}`

Output:

`The length of the LPS is 5`

Dynamic Programming Solution

## Java

 `// A Dynamic Programming based Java` `// Program for the Egg Dropping Puzzle` `class` `LPS {`   `    ``// A utility function to get max of two integers` `    ``static` `int` `max(``int` `x, ``int` `y) { ``return` `(x > y) ? x : y; }`   `    ``// Returns the length of the longest` `    ``// palindromic subsequence in seq` `    ``static` `int` `lps(String seq)` `    ``{` `        ``int` `n = seq.length();` `        ``int` `i, j, cl;` `        ``// Create a table to store results of subproblems` `        ``int` `L[][] = ``new` `int``[n][n];`   `        ``// Strings of length 1 are palindrome of length 1` `        ``for` `(i = ``0``; i < n; i++)` `            ``L[i][i] = ``1``;`   `        ``// Build the table. Note that the lower` `        ``// diagonal values of table are` `        ``// useless and not filled in the process.` `        ``// The values are filled in a manner similar` `        ``// to Matrix Chain Multiplication DP solution (See` `        ``// https:// www.geeksforgeeks.org/matrix-chain-multiplication-dp-8/).` `        ``// cl is length of substring` `        ``for` `(cl = ``2``; cl <= n; cl++) {` `            ``for` `(i = ``0``; i < n - cl + ``1``; i++) {` `                ``j = i + cl - ``1``;` `                ``if` `(seq.charAt(i) == seq.charAt(j) && cl == ``2``)` `                    ``L[i][j] = ``2``;` `                ``else` `if` `(seq.charAt(i) == seq.charAt(j))` `                    ``L[i][j] = L[i + ``1``][j - ``1``] + ``2``;` `                ``else` `                    ``L[i][j] = max(L[i][j - ``1``], L[i + ``1``][j]);` `            ``}` `        ``}`   `        ``return` `L[``0``][n - ``1``];` `    ``}`   `    ``/* Driver program to test above functions */` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``String seq = ``"GEEKSFORGEEKS"``;` `        ``int` `n = seq.length();` `        ``System.out.println(``"The length of the lps is "` `+ lps(seq));` `    ``}` `}` `/* This code is contributed by Rajat Mishra */`

Output

`The length of the lps is 5`

Please refer complete article on Longest Palindromic Subsequence | DP-12 for more details!

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