【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]; } };