LeetCode_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.

　　分析：   DP 问题

Initial state:
table[i][i] =  true.
table[i][i+1] = (s[i]==s[i+1]);

State Change:
if s[i]==s[j], table[i][j]=table[i+1][j-1]

class Solution {
public:
    string longestPalindrome(string s) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int n = s.size();
        if(n < 2) return s;
        vector<vector<bool>> table(n, vector<bool>(n,false));
        
        //init length 1
        for(int i = 0; i< n; i++)
             table[i][i] = true;
             
        int len, maxlen = 1, maxStart = 0,i,j;
        for(len = 2; len <= n ; len ++)
        {
           for(i = 0; i< n - len +1 ; i++)
           { 
               j = i + len - 1;
           
              if(s[i] == s[j] &&len == 2)
                {
                      table[i][j] = true;
                     maxlen = len;
                     maxStart = i;
                }
                     
               else if (s[i] == s[j] && table[i+1][j-1])
                {
                    table[i][j] = true;
                    maxlen = len;
                    maxStart = i;
                }
                
           }
        }
        
           
        return s.substr(maxStart , maxlen);
    }
};

这里解释下为什么len ==2 要单独处理： 因为table[i][j]只有上三角的值有意义，即 j >= i ; 当len = 2 时，table[i+1][j-1] j-1= i+2-1-1 = i  即此时j-1< i+1 ; 所以要单独处理

reference :http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html

               http://www.geeksforgeeks.org/dynamic-programming-set-12-longest-palindromic-subsequence/