Longest palindrome Sub-sequence from the given String using Dynamic Programming

Write a program to find the longest sub-sequence palindrome from the given string by using dynamic programming. For example

Input String : ABCDQRDC

Longest sub-sequence palindrome: 5

•  So let's see how we will solve and find the longest subsequence palindrome using dynamic programming. 
• 
  
• Construct the solution matrix of size NxN where N is the length of given string. 
• We will calculate the size of each character sequence palindrome size and will the memorised in the solution matrix which will referred for the next incremental sequence.
• For example in above example all strings of 1 character will be palindrome size of 1. A, B, C, D, Q, R, D, C
• On next cycle it will add another character and makes 2 character string like 
• AB, BC, CD, DQ, QR, RD, DC and goes on like 
• ABC, BCD, CDQ, DQR, QRD, RDC etc.,
• Each sequences palindrome size will be stored in the solution array and finally returns the maximum size as output.

Now lets see simple Java code 

 public class LongestPalindromeSequence {

 public static void main(String[] args) {

  String str = "ABCDQRDC";

  LongestPalindromeSequence obj = new LongestPalindromeSequence();

  System.out.println("\nLength of Longest palindrome subsequence : " + obj.lps(str));

 }

 public int lps(String seq) {
  int n = seq.length();
  int j, k, i;
  int L[][] = new int[n][n];

  // Strings of 1 character will be palindrome size of 1 
  // starting with upper matrix and all single character falls diagonally and size will be 1
  for (j = 0; j < n; j++)
   L[j][j] = 1;

  for (i = 2; i <= n; i++) {
   for (j = 0; j < n - i + 1; j++) {

    k = j + i - 1;

    if (seq.charAt(j) == seq.charAt(k)) {
     L[j][k] = L[j + 1][k - 1] + 2;

    } else {
     L[j][k] = Math.max(L[j][k - 1], L[j + 1][k]);
    }
   }
  }

  /*System.out.println("Final solution Matrix :::: ");
  for (j = 0; j < n; j++) {
   System.out.print(seq.charAt(j) +" - ");
   for (k = 0; k < n; k++) {
    System.out.print(L[j][k] + "\t");
   }
   System.out.println();
  }*/
  return L[0][n - 1];
 }
}

OUTPUT:

Length of Longest palindrome subsequence : 5