516 Longest Palindromic Subsequence

516. Longest Palindromic Subsequence

1. Question

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".

2. Implementation

(1) DP

思路: 和Longest Common Subsequence一样的思路，求Longest Palindromic Subsequence只需要将原来string reverse(记为revS)，然后对s和revS通过LCS算法即可

class Solution {
    public int longestPalindromeSubseq(String s) {
        if (s == null || s.length() == 0) {
            return 0;
        }

        int n = s.length();
        String revS = new StringBuilder(s).reverse().toString();

        int[][] LCS = new int[n + 1][n + 1];

        for (int i = 0; i <= n; i++) {
            for (int j = 0; j <= n; j++) {
                if (i == 0 || j == 0) {
                    LCS[i][j] = 0;
                }
                else if (s.charAt(i - 1) == revS.charAt(j - 1)) {
                    LCS[i][j] = LCS[i - 1][j - 1] + 1;
                }
                else {
                    LCS[i][j] = Math.max(LCS[i - 1][j], LCS[i][j - 1]);
                }
            }
        }
        return LCS[n][n];
    }
}

3. Time & Space Complexity

DP: 时间复杂度O(n^2), 空间复杂度O(n^2)