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public class Solution {
    public String shortestPalindrome(String s) {
        StringBuilder sb = new StringBuilder();
        sb.append(s).append('#').append(new StringBuilder(s).reverse());
        int longestPal = getPrefixFunction(sb.toString());
        StringBuilder res = new StringBuilder(s.substring(longestPal));
        res.reverse().append(s);
        return res.toString();
    }
    
    private int getPrefixFunction(String pattern) {
        int len = pattern.length();
        int[] pi = new int[len];
        pi[0] = 0;
        int matched = 0;
        for (int i = 1; i < len; i++) {
            while (matched > 0 && pattern.charAt(i) != pattern.charAt(matched)) {
                matched = pi[matched - 1];
            }
            if(pattern.charAt(i) == pattern.charAt(matched)) {
                matched++;
            }
            pi[i] = matched;
        }
        return pi[len - 1];
    }
}