516. Longest Palindromic Subsequence

最长回文子序列

原创于 2018-08-13 22:36:19 发布 · 71 阅读

0 ·

CC 4.0 BY-SA版权

LeetCode 专栏收录该内容

548 篇文章

订阅专栏

本文介绍了一种使用动态规划算法解决寻找字符串中最长回文子序列的问题，并通过具体示例展示了算法实现的过程。

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:

One possible longest palindromic subsequence is "bbbb".

Example 2:
Input:

"cbbd"

Output:

One possible longest palindromic subsequence is "bb".

DP求解，程序如下所示：

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