Leetcode 5 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.

 

Solution:

中心扩散法 Spread From Center

时间 O(n^2) 空间 O(1) 外层循环遍历的是子字符串的中心点，内层循环则是从中心扩散，一旦不是回文就不再计算其他以此为中心的较大的字符串。由于中心对称有两种情况，一是奇数个字母以某个字母对称，而是偶数个字母以两个字母中间为对称，所以我们要分别计算这两种对称情况。

 

public string LongestPalindrome(string s) {
        if(s.Length ==1) return s;
        int res = 0;
        int mx = 0;
        int left = 0;
        for(int i = 0;i< s.Length;i++)
        {
            //even
            int j =0;
            while(i-j>=0 && i+j <s.Length-1)
            {
                if(s[i+j+1] == s[i-j]) j++;
                else break;
            }
            if(2*j> mx)
            {
                mx = 2*j;
                left = i - j+1;
            }
            //odd
            int jj =1;
            while(i-jj>=0 && i+jj <s.Length)
            {
                if(s[i+jj] == s[i-jj]) jj++;
                else break;
            }
            if(2*jj -1 >mx)
            {
             left = i - jj + 1;
             mx = 2*jj -1;
            }
           
        }
        return s.Substring(left, mx);
    }

 

Manacher's Algorithm 马拉车算法

https://segmentfault.com/a/1190000002991199

public string LongestPalindrome(string s) {
        var ss = "@#";
        for(int i = 0;i<s.Length;i++)
        {
            ss += s[i];
            ss += "#";
        }
        ss +="$";
        int[] len = new int[ss.Length];
       
        int mx = 0;
        int po = 0;
        int resMx = 0;
        int resId = 0;
        for (int i = 1; i < ss.Length; i++)
        {
            if(mx >i) len[i] =Math.Min(mx - i,len[2*po - i] ) ;
            else len[i] = 1;
            while((i+len[i])<ss.Length &&  ss[i+len[i]] == ss[i - len[i]]) len[i]++;
            if(i+len[i] >mx)
            {
                mx = i+len[i];
                po = i;
            }
            if (resMx < len[i])
            {
                resMx = len[i];
                resId = i;
            }
        }
        return s.Substring((resId - resMx)/2,resMx -1);
    }