LeetCode 5. Longest Palindromic Substring（最长回文子串）

原题网址：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.

方法一：动态规划，从2～s.length()逐层检查是否对称，对于每一个长度，从左到右扫描。由于回文子串可能为奇数长度或者偶数长度，所以需要确认两个长度都无法检测到对称，程序才终止。

public class Solution {
    public String longestPalindrome(String s) {
        if (null == s || "".equals(s)) return s;
        boolean[][] palindromic = new boolean[s.length()+1][s.length()];
        for(int j=0; jmaxLength) {
                        maxLength = i;
                        maxFrom = j;
                    }
                }
            }
            if (found) missing = 0;
            else missing ++;
            
            if (missing >= 2) break;
        }
        return s.substring(maxFrom, maxFrom + maxLength);
    }
}

方法二：从左到右扫描中心点，对于每个中心点，从小到大检查是否对称。

public class Solution {
    public String longestPalindrome(String s) {
        char[] sarray = s.toCharArray();
        if (sarray.length == 1) return s;
        int pos = 0;
        int len = 0;
        for(int i=1; i+len/2=0 && i+j<=sarray.length-1; j++) {
                if (sarray[i-j] != sarray[i+j]) break;
                if (j*2+1 > len) {
                    len = j*2+1;
                    pos = i-j;
                }
            }
        }
        for(int i=0; i+1+len/2=0 && i+j+1 len) {
                    len = (j+1)*2;
                    pos = i-j;
                }
            }
        }
        return s.substring(pos, pos+len);
    }
}

方法三：Manacher算法。

public class Solution {
    /*
    根据Manacher算法自己编写，参考：
http://blog.vars.me/blog/2015/04/12/Manachers-algorithm-Longest-palindromic-substring/    
    */
    public String longestPalindrome(String s) {
        char[] origin = s.toCharArray();
        char[] sarray = new char[origin.length * 2 + 1];
        sarray[0] = '#';
        int pos = 1;
        for(int i=0; i= 0 && i + m <= sarray.length-1; m ++) {
                if (sarray[i-m] != sarray[i+m]) break;
                radius[i] = m;
            }
            if (i+radius[i] > maxRight) {
                maxRight = i + radius[i];
                maxCenter = i;
            }
            if (radius[i] > maxRadius) {
                maxRadius = radius[i];
                maxPos = i;
            }
            // System.out.printf("i=%d, s[i]=%c, radius[i]=%d, maxRadius=%d, maxPos=%d, maxCenter=%d, maxRight=%d\n", i, sarray[i], radius[i], maxRadius, maxPos, maxCenter, maxRight);
        }
        char[] longest = new char[maxRadius];
        pos = 0;
        for(int i=maxPos-maxRadius; i<=maxPos+maxRadius; i++) {
            if (sarray[i] != '#') longest[pos++] = sarray[i];
        }
        return new String(longest);
    }
}