# Java Solution using Manacher Algorithm

• This is my solution using Manacher Algorithm.

The Manacher Algorithm is used to find the longest palindromic substring, we can modify it to search to obtain the longest palindromic substring starting at index 0.

Once we have the longest palindrome starting at 0, we insert the remaining characters from the original string 1 by 1 at the head of the original string.

``````    public static String manacherize(String s) {
StringBuilder ms = new StringBuilder("^");
for(int i=0;i<s.length();i++) {
ms.append("#"+s.charAt(i));
}
ms.append("#\$");
return ms.toString();
}
public static String longestPalindromeStartingFrom0(String s) {
if(s.length()==0) return "";
String T = manacherize(s);
int[] P = new int[T.length()];
int C = 0;
int R = 0;
for(int i=1;i<T.length()-1;i++) {
int imirror = C-(i-C);
P[i] = (R > i) ? Math.min(R-i, P[imirror]) : 0;
while(T.charAt(i+1+P[i])==T.charAt(i-1-P[i])) {
P[i]++;
}
if(i+P[i]>R) {
C = i;
R = i + P[i];
}
}
int maxLen = 0;
int maxCenter = 0;
for(int i=1;i<P.length-1;i++) {
if(P[i]>maxLen && i-P[i]==1) {
maxLen = P[i];
maxCenter = i;
}
}
int start = (maxCenter-1-maxLen)/2;
return s.substring(start,start+maxLen);
}

public static String shortestPalindrome(String s) {
String pal = longestPalindromeStartingFrom0(s);
StringBuilder prefix = new StringBuilder();
for(int i=pal.length();i<s.length();i++) {
prefix.insert(0, s.charAt(i));
}
return prefix+s;
}
``````

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