Longest Palindromic Subsequence
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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:
4One possible longest palindromic subsequence is "bbbb".
Example 2:
Input:
"cbbd"Output:
2One possible longest palindromic subsequence is "bb".
解析:
设dp[i][j]为i到j字符串最长的回文长度,if 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]),从i到j距离最短的开始算起。
代码:
class Solution {public: int longestPalindromeSubseq(string s) { int length=s.size(); vector<vector<int>> dp(length,vector<int>(length,0)); for (int i=0; i<s.size(); i++) { dp[i][i]=1; } for (int i=1; i<s.size(); i++) { for (int j=0; j<s.size()-i; j++) { if (s[j]==s[j+i]) { dp[j][j+i]=dp[j+1][j+i-1]+2; } else { dp[j][j+i]=max(dp[j][j+i-1],dp[j+1][j+i]); } } } return dp[0][length-1]; }};
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