Implement Manacher's Algorithm and Unit Tests for Longest Palindromic Substring

algorithms/strings/__init__.py

@@ -38,4 +38,5 @@
 from .atbash_cipher import *
 from .longest_palindromic_substring import *
 from .knuth_morris_pratt import *
-from .panagram import *
+from .panagram import *
+from .manacher import *

algorithms/strings/manacher.py

@@ -0,0 +1,39 @@
+"""
+Manacher's Algorithm to find the longest palindromic substring in linear time (O(n)).
+
+The algorithm transforms the string by inserting special characters (#) between
+characters to handle both odd and even length palindromes uniformly. Then it expands
+around each possible center to find the longest palindromic substring.
+"""
+
+def manacher(s):
+    # Transform the string to insert special characters between each character and at the start and end
+    t = '#' + '#'.join(s) + '#'
+    n = len(t)
+    p = [0] * n  # Array to store the length of the palindrome centered at each character
+    c = 0  # Current center
+    r = 0  # Right boundary of the current longest palindrome
+
+    for i in range(n):
+        mirror = 2 * c - i  # Mirror position of i with respect to center c
+
+        if i < r:
+            p[i] = min(r - i, p[mirror])  # Use the previously calculated palindrome length if possible
+
+        # Attempt to expand the palindrome centered at i
+        while i + p[i] + 1 < n and i - p[i] - 1 >= 0 and t[i + p[i] + 1] == t[i - p[i] - 1]:
+            p[i] += 1
+
+        # Update the center and right boundary if we've expanded beyond the current right boundary
+        if i + p[i] > r:
+            c = i
+            r = i + p[i]
+
+    # Find the maximum length palindrome
+    max_len = max(p)
+    center_index = p.index(max_len)
+
+    # Extract the original palindrome from the transformed string
+    start = (center_index - max_len) // 2
+    return s[start:start + max_len]
+

tests/test_strings.py

@@ -42,7 +42,8 @@
     longest_palindrome,
     knuth_morris_pratt,
     panagram,
-    fizzbuzz
+    fizzbuzz,
+    manacher
 )
 
 import unittest
@@ -728,5 +729,33 @@ def test_fizzbuzz(self):
         self.assertEqual(result, expected)
 
 
+class TestManacherAlgorithm(unittest.TestCase):
+    """Unit tests for the Manacher's Algorithm"""
+
+    def test_single_character(self):
+        self.assertEqual(manacher("a"), "a")
+
+    def test_even_length_palindrome(self):
+        self.assertEqual(manacher("abba"), "abba")
+
+    def test_odd_length_palindrome(self):
+        self.assertEqual(manacher("racecar"), "racecar")
+
+    def test_mixed_palindrome(self):
+        self.assertIn(manacher("babad"), ["aba", "bab"]) # There can be "bab" or "aba"
+
+    def test_no_palindrome(self):
+        self.assertEqual(manacher("abcde"), "a")  # The longest palindrome is just one character
+
+    def test_empty_string(self):
+        self.assertEqual(manacher(""), "")
+
+    def test_full_string_palindrome(self):
+        self.assertEqual(manacher("aaaa"), "aaaa")
+
+    def test_palindrome_with_special_characters(self):
+        self.assertEqual(manacher("a!b!a"), "a!b!a")
+
+
 if __name__ == "__main__":
     unittest.main()