Java Program for Longest Palindromic Subsequence | DP-12

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 approachclass 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));    }}
The length of the LPS is 5
 
Dynamic Programming Solution 
Java
// A Dynamic Programming based Java// Program for the Egg Dropping Puzzleclass 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 */
The length of the lps is 5
Please refer complete article on Longest Palindromic Subsequence | DP-12 for more details! 
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