#### Longest Palindromic Subsequence

```"""
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".
"""

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
for i in range(m + 1):
dp[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()
```  