Longest-Palindromic-Subsequence

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题目地址

LeetCode#516 Longest Palindromic Subsequence

题目描述

  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: 

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"bbbab"

Output: 

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4

One possible longest palindromic subsequence is “bbbb”.

Example 2:
Input:

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"cbbd"

Output:

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2

One possible longest palindromic subsequence is “bb”.

解题思路

  最长回文子序列，和最长回文字符串不同的地方在于这个不要求连续，做法和最长回文字符串也不差多少。我们使用 DP ，递推公式如下：

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

解题代码【.CPP】

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class Solution {
public:
    int longestPalindromeSubseq(string s) {
        vector<vector<int>> dp(s.size() , vector<int>(s.size() , 0));
        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];
    }
};
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