Leetcode-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.

题目的意思是找到字符串s中最长的回文子序列：

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".

动态规划解法：设dp[i][j]为s[i]~s[j]之间的最长回文子序列

if i==j dp[i][j] = 1

else if i+1=j  

if s[i] == s[j]: dp[i][j] = 2 

else : dp[i][j] = 1

else 

if s[i] == s[j]: dp[i][j] = max(dp[i+1][j-1]+2, dp[i+1][j], dp[i][j-1])

else: dp[i][j] = max(dp[i+1][j-1], dp[i+1][j], dp[i][j-1])

最后返回s[0][s.size()-1]即为s中最长回文子的序列结果

c++ 代码如下：

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