class Solution {
    // idea: longest palindromic subsequence will be length of LCS
    
    public int longestPalindromeSubseq(String s) {
        int n = s.length();

        // reverse the string and stroe it in new string
        String s2 = new StringBuilder(s).reverse().toString();
        int m = s2.length();

        // step-1 create a matrix
        // t[i][j] = LCS of first i chars of s and first j chars of reversed string
        int[][] t = new int[n+1][m+1];

        // step-2 initialise the matrix with base condition
        for(int i=0; i<n+1; i++)
        {
            for(int j=0; j<m+1; j++)
            {
                // string length is 0, NO LCS found
                if(i == 0 || j == 0)
                    t[i][j] = 0;
            }
        }

        // step-3 iterative code to find length of LCS
        for(int i=1; i<n+1; i++)
        {
            for(int j=1; j<m+1; j++)
            {
                // characters match
                if(s.charAt(i-1) == s2.charAt(j-1))
                    t[i][j] = 1 + t[i-1][j-1];

                // characters do not match
                else
                    t[i][j] = Math.max(t[i-1][j], t[i][j-1]);
            }
        }
        // The bottom-right cell contains the length of LPS
        int lcsLength = t[n][m];
        return lcsLength;
    }
}