516. Longest Palindromic Subsequence

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本文介绍了一种使用动态规划算法来寻找给定字符串中最长回文子序列长度的方法，并通过示例说明了如何实现这一算法。代码示例中详细展示了如何构建二维DP表来记录不同子串间的最长回文子序列长度。

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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".

class Solution {
public:
    int longestPalindromeSubseq(string s) {
        int len = s.length();
        vector<vector<int> > dp(len, vector<int>(len, 0));
        for(int i = 0; i < len; i++)
            dp[i][i] = 1;
        for(int i = 0; i < len - 1; i++){
            if(s[i] == s[i + 1])
                dp[i][i + 1] = 2;
            else
                dp[i][i + 1] = 1;
        }
        for(int l = 3; l <= len; l++){
            for(int j = 0; j < len - l + 1; j++){
                int k = j + l - 1;
                if(s[j] == s[k])
                    dp[j][k] = 2 + dp[j + 1][k - 1];
                else 
                    dp[j][k] = max(dp[j][k - 1], dp[j + 1][k]);
            }
        }
        return dp[0][len - 1];
    }    
};