5. Longest Palindromic Substring

找到最长的回文序列

Given a string s, find the longest palindromic substring in s. You may assume that the maximum length of s is 1000.

Example:

Input: "babad" Output: "bab" Note: "aba" is also a valid answer.

 

Example:

Input: "cbbd" Output: "bb"

Solution2://动态规划，plain[i][j]为true表示从字符串从i到j是回文序列。判断是否回文序列前提是s.charAt(i)与s.charAt(j)相同。同时要满足：

1.如果j - i <=2 ，则必然成立，如aa，或aba

2.如果j-i > 2,此时plain[i+1][j-1]必须为true

i从字符串尾部向前遍历，索引j由i向后遍历，发现回文字符串时设置二维数组相应的值，并比较其长度是否大于当前maxLen。 

public String longestPalindrome(String s) {
  if(s.length() <= 1) {
    return s;
  }
  int start = 0;
  int end = 0;
  int maxLen = 0;
  boolean[][] plain = new boolean[s.length()][s.length()];
  for(int i = s.length() - 1; i >= 0; i--){
    for(int j = i + 1; j < s.length(); j++){
      if (s.charAt(i) != s.charAt(j)) {
        continue;
      }
      if (j - i <= 2 || plain[i + 1][j - 1]) {
        plain[i][j] = true;
        if(maxLen < j - i + 1) {
          maxLen = j - i + 1;
          start = i;
          end = j;
        }
      }
    }
  }
  return s.substring(start, end + 1);
}