算法练习5. Longest Palindromic Substring 最长回文子字符串（Manacher算法）

5. Longest Palindromic Substring

https://leetcode.com/problems/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.

返回字符串中的最长回文子字符串

class Solution {

public:

    string longestPalindrome(strings) {

        string str;

        str = changstr(s);

        int len= str.length(),i;

        int *p = new int[str.length() + 1];

        memset(p, 0, sizeof(p));

        int mx = 0, id = 1;

        for (i = 1; i < len;i++)

        {

            if (mx > i)

            {

                p[i] = min( p[2 * id - i] , (mx- i));

            }

            else

            {

                p[i] = 1;

            }

            while (i - p[i]>0 &&i + p[i]<len&&str.at(i - p[i]) == str.at(i + p[i]))

                p[i]++;

            if (i + p[i] > mx)

            {

                mx = i + p[i];

                id = i;

            }

        }

        //最大回文字符串长度

        int maxlen = 0, index =0;

        for (int i = 0; i<len;i++)

        {

            if (p[i]>maxlen)

            {

                id = i;

                maxlen = p[i];

            }

        }

 

        string result;

        for (i = id - p[id]+1;i < id+maxlen; i++)

        {

            if (str.at(i) != '#')

            {

                result += str.at(i);

            }

        }

        return result;

 

    }

    string changstr(stringstr)

    {

        string str0;

        str0 += "$#";

        for (int i = 0; i <str.size(); i++)

        {

            str0 += str[i];

            str0 += "#";

        }

        return str0;

    }

};

以下内容来自LeetCode官网：

Approach #4 (Expand Around Center)[Accepted]

In fact, wecould solve it in O(n^2)O(n​2​​) time usingonly constant space.

We observe thata palindrome mirrors around its center. Therefore, a palindrome can be expandedfrom its center, and there are only 2n - 12n−1 suchcenters.

You might be asking why there are 2n - 12n−1 butnot nn centers? The reason is the centerof a palindrome can be in between two letters. Such palindromes have evennumber of letters (such as ''abba''''abba'') and its center are between thetwo 'b''b's.

public StringlongestPalindrome(String s) {

    int start= 0, end= 0;

    for(int i= 0; i< s.length(); i++) {

       int len1= expandAroundCenter(s,i, i);

       int len2= expandAroundCenter(s,i, i+ 1);

       int len= Math.max(len1, len2);

       if (len > end - start) {

           start = i- (len - 1)/ 2;

           end = i + len / 2;

       }

    }

    returns.substring(start, end+ 1);

}

 

privateintexpandAroundCenter(String s,int left,int right) {

    int L= left, R = right;

    while(L >= 0&&R < s.length()&& s.charAt(L) == s.charAt(R)) {

       L--;

       R++;

    }

    returnR - L - 1;

}