Delete dynamic_programming/longest_palindromic_subsequence.py

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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}")