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Delete dynamic_programming/longest_palindromic_subsequence.py
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def longest_palindromic_subsequence(input_string: str) -> int:
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"""
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Function to find the length of the longest palindromic subsequence
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in a given string using dynamic programming.
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:param input_string: Input string
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:return: Length of the longest palindromic subsequence
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>>> longest_palindromic_subsequence("bbbab")
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4
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>>> longest_palindromic_subsequence("cbbd")
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2
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>>> longest_palindromic_subsequence("")
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0
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>>> longest_palindromic_subsequence("a")
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1
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>>> longest_palindromic_subsequence("abcd")
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1
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>>> longest_palindromic_subsequence("agbdba")
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5
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"""
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n = len(input_string)
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# Base case: if string is empty, return 0
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if n == 0:
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return 0
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# dp[i][j] will represent the length of the longest palindromic subsequence
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# within the substring input_string[i...j]
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dp = [[0] * n for _ in range(n)]
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# Every single character is a palindrome of length 1
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for i in range(n):
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dp[i][i] = 1
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# Build the DP table for substrings of increasing length
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for length in range(2, n + 1):
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for i in range(n - length + 1):
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j = i + length - 1
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if input_string[i] == input_string[j]:
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dp[i][j] = dp[i + 1][j - 1] + 2
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else:
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dp[i][j] = max(dp[i + 1][j], dp[i][j - 1])
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# The longest palindromic subsequence length for the full string is dp[0][n-1]
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return dp[0][n - 1]
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# Example usage:
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if __name__ == "__main__":
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input_string = "bbbab"
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result = longest_palindromic_subsequence(input_string)
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print(f"Length of Longest Palindromic Subsequence: {result}")
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