Longest Palindromic Substring

Given a string S, find the longest palindromic substring in S. You may assume that the maximum length of S is 1000, and there exists one unique longest palindromic substring.

题目描述很简单，就是寻找一个字符串的最大回文。

1.暴力搜索

　穷举所有的可能，算法复杂度是O(n^3);

2.dp求解

　　http://articles.leetcode.com/2011/11/longest-palindromic-substring-part-i.html

3.对称

这里考虑到每个回文单词都是对称的，所以这里可以使用对称的思想进行解答。分别遍历以每个字母为中心的回文字符的最大长度，算法复杂度为O(n ^ 2);空间复杂度是

O(1);

class Solution {
public:
    string expand(string&s, int l, int h)
    {
        while((l >= 0) && (h < s.size()) && (s[l] == s[h]))
        {
            l--; h++;
        }
        
        return s.substr(l+1, h-1-l);
    }
    
    string longestPalindrome(string s) {
        string res = s.substr(0,1);
        
        for(int i = 0; i < s.size(); i++)
        {
            string p;
            p = expand(s, i, i);
            
            if(p.size() > res.size())
                res = p;
            p = expand(s, i, i+1);
            
            if(p.size() > res.size())
                res = p;
        }
        
        return res;
    }
};

4。Manacher’s Algorithm

http://www.felix021.com/blog/read.php?2040

http://articles.leetcode.com/2011/11/longest-palindromic-substring-part-ii.html