leetcode-5-Longest Palindromic Substring

题目：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.

Example 1:

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

Example 2:

Input: "cbbd"
Output: "bb"



思路：寻找字符串的最长回文串的题，属于老生常谈的题了，一般要么求出长度为多少，要么求出子串，方法都是一样的：动态规划；中心扩散法；马拉车算法；一般就这三种 
算法思想可看我的另一篇博客：最长回文子串
法1：动态规划（时间复杂度O(n^2）,空间复杂度O(n^2))

class Solution {
   public static String  longestPalindrome(String s){
　　　　　　if(s==null) return null;
       int n=s.length();
        int[][]dp=new int[n+1][n+1];
        int max=1;
        int x=0,y=0;
        for(int i=0;i<=n;i++){
            dp[i][i]=1;
        }
        for(int len=2;len<=n;len++){
            //len表示子串长度，i表示子串开头位置，j表示子串结束位置
            for(int i=0;i<=n-len;i++){
                int j=i+len-1;
                //开始比较
                if(len==2&&s.charAt(i)==s.charAt(j)){
                    dp[i][j]=2;
                    max=2;
                    x=i;
                    y=j;
                }else{
                    if(s.charAt(i)==s.charAt(j)&&dp[i+1][j-1]!=0){
                        dp[i][j]=len;
                        max=len;
                        x=i;
                        y=j;
                    }
                }
            }

        }
       return s.substring(x,y+1);
   }
}

这种方法看来并不算太好，Your runtime beats 21.57 % of java submissions.

再用中心扩散法试试
Your runtime beats 93.63 % of java submissions

public class Solution {
    int left=0;
    int max=1;
    public String longestPalindrome(String s) {
        char[] cs=s.toCharArray();
        for(int i=0;i<cs.length;i++){
            findPailndromic(cs,i,i);
            findPailndromic(cs,i,i+1);
        }
        return s.substring(left,left+max);
    }
    public void findPailndromic(char[]cs,int i,int j){
        while(i>=0&&j<cs.length&&cs[i]==cs[j]){
            if(max<j-i+1){
                left=i;
                max=j-i+1;
            }
            i--;
            j++;
        }
    }
}