Shortest Palindrome

Given a string S, you are allowed to convert it to a palindrome by adding characters in front of it. Find and return the shortest palindrome you can find by performing this transformation.

For example:

Given "aacecaaa", return "aaacecaaa".

Given "abcd", return "dcbabcd".

Analyse: It asks us to get the longest palindrome starting from index 0. Suppose the longest palindrome is s_1, and the original string is s, remaining part is s_2 = s - s_1, then the result should be Reverse(s_2) + s.

For example, if the string is aaabbbccc, s_1 should be aa, s_2 is abbbccc, the result should be cccbbba|aaabbbccc

string   　　aaabbbccc

s_1 　　　　　　aa

s_2 　　　　abbbccc

result     cccbbba|aaabbbccc

　

Start from the back, check if s[0] == s[i] and if s[0...i] is palindrome. If so, compute the result.

Time limit exceeded. 

class Solution {
public:
    string shortestPalindrome(string s) {
        if (s.size() < 2) return s;
        // find the longest palindrome substring starting from s[0]
        int end = 0;
        for (int i = s.size() - 1; i >= 0; i--) {
            if (s[i] == s[0] && isPalindrome(s, 0, i)) {
                end = i;
                break;
            }
        }
        
        // insert [end + 1, s.size() - 1] in front of s in reverse order
        string result;
        for (int i = s.size() - 1; i > end; i--) 
            result += s[i];
        result += s;
        return result;
    }
private:
    bool isPalindrome(string s, int start, int end) {
        while (start < end) {
            if (s[start++] != s[end--]) return false;
        }
        return true;
    }
};