longest palindromic substring

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 the longest palindromic substring in a string using dynamic programming
+    >>> 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
+    >>> 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()