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”.

思路：建立一个二维数组dp，其中dp[i][j]表示第 i 个字母到第 j 个字母所能构成的最长回文子串的长度，建立一个二层循环，第一层循环从尾到头遍历，第二层循环从 i+1到尾遍历，若s[i] == s[j]，则dp[i][j] = dp[i+1][j-1]+2，否则，dp[i][j] = max(dp[i+1][j]，dp[i][j-1])。

代码：

int longestPalindromeSubseq(string s) {    if (s.size() <= 1)return s.size();    vector<vector<int>> dp(s.size(), vector<int>(s.size()));    for (int i = s.size() - 1; i >= 0; i--){        dp[i][i] = 1;        for (int j = i + 1; j < s.size(); j++){            if (s[i] == s[j])dp[i][j] = dp[i + 1][j - 1] + 2;            else dp[i][j] = max(dp[i + 1][j], dp[i][j - 1]);        }    }    return dp[0][s.size() - 1];}