Adds new dynamic programming algorithm #2275
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| """ | ||
| Longest Palindromic Subsequence Problem: | ||
| Find the longest sequence of characters from a given input string that | ||
| is the same backwards and forwards | ||
| https://en.wikipedia.org/wiki/Longest_common_subsequence_problem | ||
| """ | ||
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| def longest_palindromic_subsequence(s: str, length: int) -> int: | ||
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| """ | ||
| Computes the longest Palindromic sequence of a string | ||
| :param s: str, the string we provide | ||
|
This conversation was marked as resolved
by kishan151999
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| :param length: int, the length of the string | ||
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This conversation was marked as resolved
by kishan151999
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| :return L[0][n - 1]: int, the length of the longest Palindromic subsequence | ||
| >>> longest_palindromic_subsequence("ABBCDABBC",9) | ||
| 5 | ||
| >>> longest_palindromic_subsequence("ABACCG",6) | ||
| 3 | ||
| >>> longest_palindromic_subsequence("55055901565109",14) | ||
| 9 | ||
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| """ | ||
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| # creating an array to store the values generated | ||
| dp_table = [[1 for i in range(length)] for i in range(length)] | ||
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| # Filling in the array created | ||
| for x in range(2, length + 1): | ||
| for y in range(length + 1 - x): | ||
| z = y + x - 1 | ||
| if s[y] == s[z] and x == 2: | ||
| dp_table[y][z] = 2 | ||
| elif s[y] == s[z]: | ||
| dp_table[y][z] = dp_table[y + 1][z - 1] + 2 | ||
| else: | ||
| dp_table[y][z] = max(dp_table[y][z - 1], dp_table[y + 1][z]) | ||
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| return dp_table[0][length - 1] | ||
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| if __name__ == "__main__": | ||
| test_case = "ABAC" | ||
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| len_of_test_case = len(test_case) | ||
| print( | ||
| "The longest palindromic subsequence is: " | ||
| + str(longest_palindromic_subsequence(test_case, len_of_test_case)) | ||
| ) | ||
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| import doctest | ||
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| doctest.testmod() | ||
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We should return the sequence, not the length of the sequence. The function is not named
length_of_the_longest_palindromic_subsequence()so I would not expect an int result.The caller can always call
len(result)if they want the length.