[LeetCode] 516. Longest Palindromic Subsequence

Given a string s, find the longest palindromic subsequence's length in s. You may assume that the maximum length of s is 1000.
Example 1:
Input:
"bbbab"
Output:
4
One possible longest palindromic subsequence is "bbbb".
Example 2:
Input:
"cbbd"
Output:
2
One possible longest palindromic subsequence is "bb".

 Thought process:
  1. Sub-problem: f( i, j ) = the LPS's length in the substring s( i, j )
  2. Function: 
    1. If s[ i ] == s[ j ], f( i, j ) = f( i + 1, j - 1 ) + 2.
    2. Else, f( i, j ) = max( f( i + 1, j ), f( i, j - 1 ) ).
  3. Initialization: if i == j, the string has only one character. Its LPS's length is 1.
  4. Result: f( 0, length of s ).

Solution:
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public class Solution {
    public int longestPalindromeSubseq(String s) {
        if (s.length() == 0) {
            return 0;
        }
        
        int[][] f = new int[s.length()][s.length()];
        
        for (int i = 0; i < s.length(); i++) {
            f[i][i] = 1;
        }
        
        for (int i = 1; i < s.length(); i++) {
            for (int j = 0; j + i < s.length(); j++) {
                int k = j + i;
                
                if (s.charAt(j) == s.charAt(k)) {
                    f[j][k] = f[j + 1][k - 1] + 2;
                } else {
                    f[j][k] = Math.max(f[j + 1][k - 1], Math.max(f[j + 1][k], f[j][k - 1]));
                }
            }
        }
        
        return f[0][s.length() - 1];
    }
}

Time complexity:
O(n^2)
Location: Philadelphia, PA, USA

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