Longest Palindromic Subsequence

dynamic_programming/longest_palindromic_subsequence.py

@@ -1,44 +1,53 @@
-"""
+def longest_palindromic_subsequence(input_string: str) -> int:
-author: Sanket Kittad
+    """
-Given a string s, find the longest palindromic subsequence's length in s.
+    Function to find the length of the longest palindromic subsequence
-Input: s = "bbbab"
+    in a given string using dynamic programming.
-Output: 4
+
-Explanation: One possible longest palindromic subsequence is "bbbb".
+    :param input_string: Input string
-Leetcode link: https://leetcode.com/problems/longest-palindromic-subsequence/description/
+    :return: Length of the longest palindromic subsequence
-"""
+
-
+    >>> longest_palindromic_subsequence("bbbab")
-
+    4
-def longest_palindromic_subsequence(input_string: str) -> int:
+    >>> longest_palindromic_subsequence("cbbd")
-    """
+    2
-    This function returns the longest palindromic subsequence in a string
+    >>> longest_palindromic_subsequence("")
-    >>> longest_palindromic_subsequence("bbbab")
+    0
-    4
+    >>> longest_palindromic_subsequence("a")
-    >>> longest_palindromic_subsequence("bbabcbcab")
+    1
-    7
+    >>> longest_palindromic_subsequence("abcd")
-    """
+    1
-    n = len(input_string)
+    >>> longest_palindromic_subsequence("agbdba")
-    rev = input_string[::-1]
+    5
-    m = len(rev)
+    """
-    dp = [[-1] * (m + 1) for i in range(n + 1)]
+    n = len(input_string)
-    for i in range(n + 1):
+
-        dp[i][0] = 0
+    # Base case: if string is empty, return 0
-    for i in range(m + 1):
+    if n == 0:
-        dp[0][i] = 0
+        return 0
-
+
-    # create and initialise dp array
+    # dp[i][j] will represent the length of the longest palindromic subsequence
-    for i in range(1, n + 1):
+    # within the substring input_string[i...j]
-        for j in range(1, m + 1):
+    dp = [[0] * n for _ in range(n)]
-            # If characters at i and j are the same
+
-            # include them in the palindromic subsequence
+    # Every single character is a palindrome of length 1
-            if input_string[i - 1] == rev[j - 1]:
+    for i in range(n):
-                dp[i][j] = 1 + dp[i - 1][j - 1]
+        dp[i][i] = 1
-            else:
+
-                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
+    # Build the DP table for substrings of increasing length
-
+    for length in range(2, n + 1):
-    return dp[n][m]
+        for i in range(n - length + 1):
-
+            j = i + length - 1
-
+            if input_string[i] == input_string[j]:
-if __name__ == "__main__":
+                dp[i][j] = dp[i + 1][j - 1] + 2
-    import doctest
+            else:
-
+                dp[i][j] = max(dp[i + 1][j], dp[i][j - 1])
-    doctest.testmod()
+
+    # The longest palindromic subsequence length for the full string is dp[0][n-1]
+    return dp[0][n - 1]
+
+
+# Example usage:
+if __name__ == "__main__":
+    input_string = "bbbab"
+    result = longest_palindromic_subsequence(input_string)
+    print(f"Length of Longest Palindromic Subsequence: {result}")