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Problem

Given a string s, find the longest palindromic subsequence’s length in s.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Example 1:

Input: s = "bbbab"
Output: 4
Explanation: One possible longest palindromic subsequence is "bbbb".

Example 2:

Input: s = "cbbd"
Output: 2
Explanation: One possible longest palindromic subsequence is "bb".

Constraints:

  • 1 <= s.length <= 1000
  • s consists only of lowercase English letters.

Code

647 486

img

dp[i, j]表示在 i 和 j 区间内最长的回文字符串

  • 如果 i 和 j 的字符相同, 那么 i 和 j 之间的最长回文字符串就是[i+1, j-1] + 2
  • 如果 i 和 j 的字符不同, 那么 i 和 j 之间的最长回文字符串就是 max([i+1, j],[i, j-1])

从长度是 1 开始, 因为当长度是 1 的时候, 一定是回文字符串, 即 dp = 1

class Solution {
    public int longestPalindromeSubseq(String s) {
        int[][] dp = new int[s.length()][s.length()];

        for (int len = 1; len <= s.length(); len++) {
            for (int i = 0; i + len <= s.length(); i++) {
                int j = i + len - 1;

                if (i == j) {
                    dp[i][j] = 1;
                    continue;
                }

                if (s.charAt(i) == s.charAt(j)) {
                    dp[i][j] = dp[i + 1][j - 1] + 2;
                } else {
                    dp[i][j] = Math.max(dp[i + 1][j], dp[i][j - 1]);
                }
            }
        }

        return dp[0][s.length() - 1];
    }
}