【回文】leetcode - Shortest Palindrome

题目：

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"

.

分析：

利用manacher算法进行求解，时间复杂度O(n)，空间复杂度O(n).

class Solution {
public:
    string shortestPalindrome(string s) {
        if(s.size()<=1)
            return s;
      
        string str(s.size()*2+1,'#');
        for(int i=0,j=1;i<s.size();++i,j+=2)
            str[j]=s[i];
        int res=1,id=1,size=str.size();
        vector<int> p(size,1);
        p[1]=2;
        for(int i=2;i<=size/2;++i)
        {
            int maxright=p[id]+id-1;
            if(i>maxright)
            {
                //注意检查越界
                while(i - p[i]>=0 && str[i+p[i]]==str[i-p[i]])
                    ++p[i];
            }
            else
            {
                int idleft=id-p[id]+1;
                int k=i-id,j=id-k,tmp=j-p[j]+1;//i和j关于id对称
                if(tmp>idleft)
                    p[i]=p[j];
                else if(tmp<idleft)
                    p[i]=p[id]-k; 
                else
                {
                     p[i]=p[j];
                     while(i - p[i]>=0 && str[i+p[i]]==str[i-p[i]])
                        ++p[i];
                }
                
            }
            if(p[i]+i>p[id]+id)
                id=i;
            if(i-p[i]+1==0)
                res=i;
        }
        
        if (res == s.size())
	    	return s;
    	else
	   {
		    string tmp = string(s.begin() + res, s.end());
	    	reverse(tmp.begin(), tmp.end());
	    	return tmp + s;
	    }
    }
};