Longest Palindromic Subsequence

dynamic_programming/longest_palindromic_subsequence.py

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