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67 lines
2.0 KiB
Python
67 lines
2.0 KiB
Python
class BoothsAlgorithm:
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"""
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Booth's Algorithm finds the lexicographically minimal rotation of a string.
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Time Complexity: O(n) - Linear time where n is the length of input string
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Space Complexity: O(n) - Linear space for failure function array
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For More Visit - https://en.wikipedia.org/wiki/Booth%27s_multiplication_algorithm
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"""
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def find_minimal_rotation(self, string: str) -> str:
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"""
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Find the lexicographically minimal rotation of the input string.
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Args:
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string (str): Input string to find minimal rotation.
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Returns:
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str: Lexicographically minimal rotation of the input string.
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Raises:
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ValueError: If the input is not a string or is empty.
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Examples:
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>>> ba = BoothsAlgorithm()
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>>> ba.find_minimal_rotation("baca")
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'abac'
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>>> ba.find_minimal_rotation("aaab")
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'aaab'
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>>> ba.find_minimal_rotation("abcd")
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'abcd'
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>>> ba.find_minimal_rotation("dcba")
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'adcb'
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>>> ba.find_minimal_rotation("aabaa")
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'aaaab'
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"""
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if not isinstance(string, str) or not string:
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raise ValueError("Input must be a non-empty string")
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n = len(string)
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s = string + string # Double the string to handle all rotations
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f = [-1] * (2 * n) # Initialize failure function array with twice the length
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k = 0 # Starting position of minimal rotation
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for j in range(1, 2 * n):
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sj = s[j]
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i = f[j - k - 1]
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while i != -1 and sj != s[k + i + 1]:
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if sj < s[k + i + 1]:
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k = j - i - 1
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i = f[i]
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if i == -1 and sj != s[k]:
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if sj < s[k]:
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k = j
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f[j - k] = -1
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else:
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f[j - k] = i + 1
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return s[k : k + n]
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if __name__ == "__main__":
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ba = BoothsAlgorithm()
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print(ba.find_minimal_rotation("bca")) # output is 'abc'
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