【516】 Longest Palindromic Subsequence

题目：

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：

对于s的任一子序列（i,j）：

若s[i]==s[j]，则(i,j)的最长回文子序列lps[i][j]=lps[i+1][j-1]+2;

否则，lps[i][j]=max(lps[i+1][j],lps[i][j-1]);

代码：

JAVA:

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

C++:

class Solution {public:    int longestPalindromeSubseq(string s) {        int lps[1000][1000];        for (int i=s.length()-1;i>=0;i--) {            lps[i][i]=1;            for (int j=i+1;j<s.length();j++){                if(s[i]==s[j])                    lps[i][j]=lps[i+1][j-1]+2;                else                     lps[i][j]=max(lps[i+1][j],lps[i][j-1]);            }        }        return lps[0][s.length()-1];    }};