Longest Palindromic Substring

標籤：

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.

題目描述很簡單，就是尋找一個字串的最大迴文。

1.暴力搜尋

　窮舉所有的可能，演算法複雜度是O(n^3);

2.dp求解

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

3.對稱

這裡考慮到每個迴文單詞都是對稱的，所以這裡可以使用對稱的思想進行解答。分別遍曆以每個字母為中心的迴文字元的最大長度，演算法複雜度為O(n ^ 2);空間複雜度是

O(1);

 1 class Solution { 2 public: 3     string expand(string&s, int l, int h) 4     { 5         while((l >= 0) && (h < s.size()) && (s[l] == s[h])) 6         { 7             l--; h++; 8         } 9         10         return s.substr(l+1, h-1-l);11     }12     13     string longestPalindrome(string s) {14         string res = s.substr(0,1);15         16         for(int i = 0; i < s.size(); i++)17         {18             string p;19             p = expand(s, i, i);20             21             if(p.size() > res.size())22                 res = p;23             p = expand(s, i, i+1);24             25             if(p.size() > res.size())26                 res = p;27         }28         29         return res;30     }31 };

 

4。Manacher’s Algorithm

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

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

Longest Palindromic Substring