Added longest_palindromic_subsequence algorithm in Dynamic Programming with zero conflicts

dynamic_programming/longest_palindromic_subsequence.py

@@ -0,0 +1,72 @@
+"""
+LPS Problem Statement: Find the length of the longest palindromic subsequence
+in a given string. A palindromic subsequence is a sequence that reads the same
+forward and backward, but not necessarily continuous.
+
+Example: For the input "babad," the longest palindromic subsequence
+can be "bab" or "aba."
+"""
+
+
+def longest_palindromic_subsequence(s: str) -> tuple[int, str]:
+    """
+    Finds the length and the longest palindromic subsequence in a given string.
+
+    Parameters:
+        s (str): The input string.
+
+    Returns:
+        Tuple[int, str]: A tuple containing the length of the longest
+        palindromic subsequence and the subsequence itself.
+
+    Raises:
+        ValueError: If the input string is empty or None.
+
+    Example:
+        >>> longest_palindromic_subsequence("bbbab")
+        (4, 'bbbb')
+        >>> longest_palindromic_subsequence("babad")
+        (3, 'bab')
+        >>> longest_palindromic_subsequence("cbbd")
+        (2, 'bb')
+    """
+    if s is None or len(s) == 0:
+        raise ValueError("Input string cannot be empty or None")
+
+    n = len(s)
+    # Create a table to store results of subproblems
+    dp = [[0] * n for _ in range(n)]
+
+    for i in range(n):
+        dp[i][i] = 1
+
+    for cl in range(2, n + 1):
+        for i in range(n - cl + 1):
+            j = i + cl - 1
+            if s[i] == s[j] and cl == 2:
+                dp[i][j] = 2
+            elif s[i] == s[j]:
+                dp[i][j] = dp[i + 1][j - 1] + 2
+            else:
+                dp[i][j] = max(dp[i][j - 1], dp[i + 1][j])
+
+    # Reconstruct the Longest Palindromic Subsequence
+    i, j = 0, n - 1
+    lps = []
+    while i < n and j >= 0:
+        if s[i] == s[j]:
+            lps.append(s[i])
+            i += 1
+            j -= 1
+        elif i < j and dp[i][j - 1] >= dp[i + 1][j]:
+            j -= 1
+        else:
+            i += 1
+
+    return dp[0][n - 1], "".join(lps)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()