Add Manacher’s Algorithm for Longest Palindromic Substring (#5462)

* Added Manacher Algorithm

* Formatted ManacherTest.java

* Formatted Manacher.java

* Refactor: Update Manacher's algorithm tests and improve readability

- Added parameterized tests for longestPalindrome, empty cases, complex cases, and sentence palindromes.
- Removed unnecessary comments for cleaner code.
- Renamed variable `p` to `palindromeLengths` for clarity based on code review feedback.

---------

Co-authored-by: Ionut Hodoroaga <ionut.hodoroaga20@gmail.com>

src/main/java/com/thealgorithms/strings/Manacher.java

@@ -0,0 +1,69 @@
+package com.thealgorithms.strings;
+
+/**
+ * Wikipedia: https://en.wikipedia.org/wiki/Longest_palindromic_substring#Manacher's_algorithm
+ */
+public final class Manacher {
+
+    private Manacher() {
+    }
+
+    /**
+     * Finds the longest palindromic substring using Manacher's Algorithm
+     *
+     * @param s The input string
+     * @return The longest palindromic substring in {@code s}
+     */
+    public static String longestPalindrome(String s) {
+        final String processedString = preprocess(s);
+        int[] palindromeLengths = new int[processedString.length()];
+        int center = 0;
+        int rightBoundary = 0;
+        int maxLen = 0;
+        int centerIndex = 0;
+
+        for (int i = 1; i < processedString.length() - 1; i++) {
+            int mirror = 2 * center - i;
+
+            if (i < rightBoundary) {
+                palindromeLengths[i] = Math.min(rightBoundary - i, palindromeLengths[mirror]);
+            }
+
+            while (processedString.charAt(i + 1 + palindromeLengths[i]) == processedString.charAt(i - 1 - palindromeLengths[i])) {
+                palindromeLengths[i]++;
+            }
+
+            if (i + palindromeLengths[i] > rightBoundary) {
+                center = i;
+                rightBoundary = i + palindromeLengths[i];
+            }
+
+            if (palindromeLengths[i] > maxLen) {
+                maxLen = palindromeLengths[i];
+                centerIndex = i;
+            }
+        }
+
+        final int start = (centerIndex - maxLen) / 2;
+        return s.substring(start, start + maxLen);
+    }
+
+    /**
+     * Preprocesses the input string by inserting a special character ('#') between each character
+     * and adding '^' at the start and '$' at the end to avoid boundary conditions.
+     *
+     * @param s The original string
+     * @return The preprocessed string with additional characters
+     */
+    private static String preprocess(String s) {
+        if (s.isEmpty()) {
+            return "^$";
+        }
+        StringBuilder sb = new StringBuilder("^");
+        for (char c : s.toCharArray()) {
+            sb.append('#').append(c);
+        }
+        sb.append("#$");
+        return sb.toString();
+    }
+}