Add greedy method for longest palindromic subsequence

greedy_method/greedy_longest_palindromic_subsequence.py

@@ -0,0 +1,65 @@
+"""
+The longest palindromic subsequence (LPS) is the longest
+subsequence in a string that is the same when reversed.
+A subsequence is not the same as a substring.
+Unlike substrings, the characters of subsequences are not required
+to occupy consecutive positions.
+
+Explanation:
+https://www.techiedelight.com/longest-palindromic-subsequence-using-dynamic-programming/
+"""
+
+
+def longest_palindromic_subsequence(
+    sequence: str, begin_substring: int, end_substring: int
+) -> int:
+    """Find the longest palindromic subsequence in a given string
+
+    :param sequence: The sequence to search in
+    :type sequence: str
+    :param i: The initial lower index bounding the search area
+    :type i: int
+    :param j: The initial upper index bounding the search area
+    :type j: int
+    :return: The length of the longest palindromic subsequence
+    :rtype: int
+
+    >>> longest_palindromic_subsequence("ABBDCACB", 0, 7)
+    5
+    >>> longest_palindromic_subsequence("nurses run", 0, 9)
+    9
+    >>> longest_palindromic_subsequence("Z", 0, 0)
+    1
+    """
+    # If the sequence only has one character, it is a palindrome
+    # This prevents a one-letter palindrome from being counted as 2
+    if begin_substring == end_substring:
+        return 1
+
+    # Base case: If i is greater than j you have gone too far
+    if begin_substring > end_substring:
+        return 0
+
+    # If the first character of the current string equals the last
+    if sequence[begin_substring] == sequence[end_substring]:
+        # Recur with the remaining substring
+        return (
+            longest_palindromic_subsequence(
+                sequence, begin_substring + 1, end_substring - 1
+            )
+            + 2
+        )
+
+    # If the first and last characters are NOT equal, then find the larger LPS between:
+    #   a.) the substring formed by removing the first character
+    #   b.) the substring formed by removing the last character
+    return max(
+        longest_palindromic_subsequence(sequence, begin_substring + 1, end_substring),
+        longest_palindromic_subsequence(sequence, begin_substring, end_substring - 1),
+    )
+
+
+if __name__ == "__main__":
+    sequence = input("Enter sequence string: ")
+    len_lps = longest_palindromic_subsequence(sequence, 0, len(sequence) - 1)
+    print(f'The length of the LPS in "{sequence}" is {len_lps}')