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 comproblemslongestpalindromicsubsequencedescription this function returns the longest palindromic subsequence in a string longestpalindromicsubsequencebbbab 4 longestpalindromicsubsequencebbabcbcab 7 create and initialise dp array if characters at i and j are the same include them in the palindromic subsequence this function returns the longest palindromic subsequence in a string longest_palindromic_subsequence bbbab 4 longest_palindromic_subsequence bbabcbcab 7 create and initialise dp array if characters at i and j are the same include them in the palindromic subsequence
def longest_palindromic_subsequence(input_string: str) -> int:
    
    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

    
    for i in range(1, n + 1):
        for j in range(1, m + 1):
            
            
            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()