diff --git a/dynamic_programming/longest_palindromic_substring.py b/dynamic_programming/longest_palindromic_substring.py
new file mode 100644
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+++ b/dynamic_programming/longest_palindromic_substring.py
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+# reference :https://www.geeksforgeeks.org/dsa/longest-palindromic-substring/
+
+
+def longest_palindromic_substring(s: str) -> str:
+    """
+    This function returns longest palindromic substring in a string
+    using Dynamic Programming.
+
+    s : input string
+    >>> longest_palindromic_substring("babad")
+    'aba'
+    >>> longest_palindromic_substring("cbbd")
+    'bb'
+    >>> longest_palindromic_substring("a")
+    'a'
+    >>> longest_palindromic_substring("ac")
+    'a'
+    >>> longest_palindromic_substring("")
+    ''
+    """
+    n = len(s)
+
+    dp = [[False for i in range(n)] for j in range(n)]
+    start = 0
+    max_length = 1
+
+    for i in range(n):
+        dp[i][i] = True
+    # for length 2 palindrome check
+    for i in range(n - 1):
+        if s[i] == s[i + 1]:
+            dp[i][i + 1] = True
+            start = i
+            max_length = 2
+
+    # for length 3 and above
+    for length in range(3, n + 1):
+        for i in range(n - length + 1):
+            j = i + length - 1
+            if s[i] == s[j] and dp[i + 1][j - 1]:
+                dp[i][j] = True
+                start = i
+                max_length = length
+
+    return s[start : start + max_length]
+
+
+def manacher_algorithm(s: str) -> str:
+    """
+    This function returns the longest palindromic substring in a string
+    using Manacher's algorithm.
+
+    s : input string
+    t : transformed string
+    p : array to store length of palindrome radius around each center
+    c : center of the current rightmost palindrome
+    r : right edge of the current rightmost palindrome
+    n : length of transformed string
+
+    >>> longest_palindromic_substring("babad")
+    'aba'
+    >>> longest_palindromic_substring("cbbd")
+    'bb'
+    >>> longest_palindromic_substring("a")
+    'a'
+    >>> longest_palindromic_substring("ac")
+    'a'
+    >>> longest_palindromic_substring("")
+    ''
+    """
+    t = "^#" + "#".join(s) + "#$"
+    n = len(t)
+
+    p = [0] * n
+    c = 0
+    r = 0
+
+    for i in range(1, n - 1):
+        mirror = 2 * c - i
+        if i < r:
+            p[i] = min(r - i, p[mirror])
+        while t[i + (1 + p[i])] == t[i - (1 + p[i])]:
+            p[i] += 1
+        if i + p[i] > r:
+            c = i
+            r = i + p[i]
+
+    max_length = max(p)
+    max_center = p.index(max_length)
+    start = (max_center - max_length) // 2
+    return s[start : start + max_length]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()