public String shortestPalindrome(String s) {

String temp = s + "#" + new StringBuilder(s).reverse().toString();

int[] table = getTable(temp);

//get the maximum palin part in s starts from 0

return new StringBuilder(s.substring(table[table.length - 1])).reverse().toString() + s;

}

public int[] getTable(String s){

//get lookup table

int[] table = new int[s.length()];

//pointer that points to matched char in prefix part

int index = 0;

//skip index 0, we will not match a string with itself

for(int i = 1; i < s.length(); i++){

if(s.charAt(index) == s.charAt(i)){

//we can extend match in prefix and postfix

table[i] = table[i-1] + 1;

index ++;

}else{

//match failed, we try to match a shorter substring

//by assigning index to table[i-1], we will shorten the match string length, and jump to the

//prefix part that we used to match postfix ended at i - 1

index = table[i-1];

while(index > 0 && s.charAt(index) != s.charAt(i)){

//we will try to shorten the match string length until we revert to the beginning of match (index 1)

index = table[index-1];

}

//when we are here may either found a match char or we reach the boundary and still no luck

//so we need check char match

if(s.charAt(index) == s.charAt(i)){

//if match, then extend one char

index ++ ;

}

table[i] = index;

}

}

return table;

}