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https://github.com/TheAlgorithms/Python.git
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1608d75351
- Add more doctests and type checking to make sure only natural numbers are used - Simplified the algorithm slightly This new verison is also between 10-15% faster for really long sequences
44 lines
1.2 KiB
Python
44 lines
1.2 KiB
Python
from typing import List
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def collatz_sequence(n: int) -> List[int]:
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"""
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Collatz conjecture: start with any positive integer n. The next term is
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obtained as follows:
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If n term is even, the next term is: n / 2 .
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If n is odd, the next term is: 3 * n + 1.
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The conjecture states the sequence will always reach 1 for any starting value n.
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Example:
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>>> collatz_sequence(2.1)
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Traceback (most recent call last):
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...
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Exception: Sequence only defined for natural numbers
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>>> collatz_sequence(0)
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Traceback (most recent call last):
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...
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Exception: Sequence only defined for natural numbers
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>>> collatz_sequence(43)
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[43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1]
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"""
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if not isinstance(n, int) or n < 1:
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raise Exception("Sequence only defined for natural numbers")
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sequence = [n]
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while n != 1:
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n = 3 * n + 1 if n & 1 else n // 2
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sequence.append(n)
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return sequence
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def main():
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n = 43
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sequence = collatz_sequence(n)
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print(sequence)
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print(f"collatz sequence from {n} took {len(sequence)} steps.")
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if __name__ == "__main__":
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main()
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