feat: Add Manacher's Algorithm for finding the longest palindromic substring

docs/source/pydatastructs/strings/algorithms.rst

@@ -1,4 +1,5 @@
 Algorithms
 ==========
 
-.. autofunction:: pydatastructs.find
+.. autofunction:: pydatastructs.find
+.. autofunction:: pydatastructs.manacher

pydatastructs/strings/__init__.py

@@ -12,7 +12,8 @@
 __all__.extend(trie.__all__)
 
 from .algorithms import (
-    find
+    find,
+    manacher
 )
 
 __all__.extend(algorithms.__all__)

pydatastructs/strings/algorithms.py

@@ -4,7 +4,8 @@
     Backend, raise_if_backend_is_not_python)
 
 __all__ = [
-    'find'
+    'find',
+    'manacher'
 ]
 
 PRIME_NUMBER, MOD = 257, 1000000007
@@ -83,6 +84,57 @@ def find(text, query, algorithm, **kwargs):
         %(algorithm))
     return getattr(algorithms, func)(text, query)
 
+def manacher(text: str) -> str:
+    """
+    Finds the longest palindromic substring in the given text using Manacher's algorithm.
+
+    Parameters
+    ==========
+    text: str
+        The input string in which to find the longest palindromic substring.
+
+    Returns
+    =======
+    str
+        The longest palindromic substring found in the input text.
+
+    Examples
+    ========
+    >>> manacher("abacdfgdcaba")
+    'aba'
+    >>> manacher("forgeeksskeegfor")
+    'geeksskeeg'
+    """
+    if not text:
+        return ""
+
+    processed_text = "#" + "#".join(text) + "#"
+    n = len(processed_text)
+    lps = [0] * n
+    center = 0
+    right = 0
+    max_len = 0
+    max_center = 0
+
+    for i in range(n):
+        if i < right:
+            lps[i] = min(right - i, lps[2 * center - i])
+
+        while (i + lps[i] + 1 < n and i - lps[i] - 1 >= 0 and
+               processed_text[i + lps[i] + 1] == processed_text[i - lps[i] - 1]):
+            lps[i] += 1
+
+        if lps[i] > max_len:
+            max_len = lps[i]
+            max_center = i
+
+        if i + lps[i] > right:
+            center = i
+            right = i + lps[i]
+
+    start = (max_center - max_len) // 2
+    end = start + max_len
+    return text[start:end]
 
 def _knuth_morris_pratt(text, query):
     if len(text) == 0 or len(query) == 0:

pydatastructs/strings/tests/test_algorithms.py

@@ -1,4 +1,4 @@
-from pydatastructs.strings import find
+from pydatastructs.strings import find, manacher
 
 import random, string
 
@@ -14,6 +14,27 @@ def test_bm():
 def test_zf():
     _test_common_string_matching('z_function')
 
+def test_manacher():
+    """
+    Test cases for Manacher's Algorithm to find the longest palindromic substring.
+    """
+    test_cases = [
+        # (input_text, expected_longest_palindrome)
+        ("", ""),  # Empty string
+        ("a", "a"),  # Single character
+        ("abacdfgdcaba", "aba"),  # Odd-length palindrome
+        ("abba", "abba"),  # Even-length palindrome
+        ("forgeeksskeegfor", "geeksskeeg"),  # Long palindrome
+        ("abcde", "a"),  # No palindrome longer than 1
+        ("racecar", "racecar"),  # Full string is a palindrome
+        ("abacaba", "abacaba"),  # Overlapping palindromes
+        ("abacabacabb", "bacabacab"),  # Complex case
+    ]
+
+    for text, expected in test_cases:
+        result = manacher(text)
+        assert result == expected, f"Failed for input: {text}. Expected: {expected}, Got: {result}"
+
 def _test_common_string_matching(algorithm):
     true_text_pattern_dictionary = {
         "Knuth-Morris-Pratt": "-Morris-",