# Shortest Palindrome

To generate shortest palindorme, we first find the longest palindrome whose left is the start of string. For example, we have a string str, the longest palindrome we find is str[0..l], then the string this question is asked will be reverse(str[l..end]) + string[0..l].

To find such palindrome fast, we apply KMP algorithm and search pattern in the origin string reversely.

Let's say current position is i, to the next matching length is k. That means k characters after i is the same as the reverse of the first characters. When i meet k or i moves over k, we know that there is a palindrome prefix of s has been found. The first palindrome prefix

public class ShortestPalindrome {
int[] makeNext(char[] str) {
int [] next = new int[str.length];
next[0] = -1;

int l = -1, i = 0;

while (i < str.length - 1) {
if (l < 0 || str[l] == str[i]) {
next[++i] = ++l;
} else {
l = next[l];
}
}

return next;
}

public String shortestPalindrome(String s) {
if (s.length() < 2) return s;

char[] str = s.toCharArray();
int[] next = makeNext(str);

int i = str.length - 1, k = 0;

while (i > k) {
if (k < 0 || str[i] == str[k]) {
i--;
k++;
} else {
k = next[k];
}
}

int l = 0;

if (i == k) {
l = i * 2 + 1;
} else {
l = k * 2;
}

StringBuilder sbd = new StringBuilder();
sbd.append(s.substring(l));
sbd.reverse();
sbd.append(s);
return sbd.toString();
}
}