5. Longest Palindromic Substring

(laicode: class26 Longest Palindromic Substring)

Given a strings, find the longest palindromic substring ins. You may assume that the maximum length ofsis 1000.

Example:

Input: "babad"
Output: "bab"

Note:
 "aba" is also a valid answer.

Example:

Input: "cbbd"
Output: "bb"

Analysis

中心开花, 从第一个字母开始一直扩展到整个string. i from 0 to string length - 1; j from i to 0;

Induction rule: m[i][j] = s.charAt(i) == s.charAt(j) && (i-j <= 2 || m[i-1][j+1]);

如果第i个与第j个字符相等, 看看i 与 j之间的substring能不能构成palindrome (i与j之间的字符长度小于等于1 或者 m[i-1][j+1] == true).

Solution

public String longestPalindrome(String s) {
    if (s == null || s.length() <= 1) {
        return s;
    }
    boolean[][] m = new boolean[s.length()][s.length()];
    int size = 0; String result = null;
    for (int i = 0; i < s.length(); ++i) {
        for (int j = i; j >= 0; --j) {
            m[i][j] = s.charAt(i) == s.charAt(j) && (i - j <= 2 || m[i - 1][j + 1]);
            if (m[i][j] && i - j + 1 > size) {
                size = i - j + 1;
                result = s.substring(j, i + 1);
            }
        }
    }
    return result;
}