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* Input for user choose his Collatz sequence
Now the user can tell the algorithm what number he wants to run on the Collatz Sequence.
* updating DIRECTORY.md
---------
Co-authored-by: Hugo Folloni <hugofollogua07@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
68 lines
2.5 KiB
Python
68 lines
2.5 KiB
Python
"""
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The Collatz conjecture is a famous unsolved problem in mathematics. Given a starting
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positive integer, define the following sequence:
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- If the current term n is even, then the next term is n/2.
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- If the current term n is odd, then the next term is 3n + 1.
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The conjecture claims that this sequence will always reach 1 for any starting number.
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Other names for this problem include the 3n + 1 problem, the Ulam conjecture, Kakutani's
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problem, the Thwaites conjecture, Hasse's algorithm, the Syracuse problem, and the
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hailstone sequence.
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Reference: https://en.wikipedia.org/wiki/Collatz_conjecture
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"""
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from __future__ import annotations
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from collections.abc import Generator
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def collatz_sequence(n: int) -> Generator[int, None, None]:
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"""
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Generate the Collatz sequence starting at n.
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>>> tuple(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 positive integers
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>>> tuple(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 positive integers
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>>> tuple(collatz_sequence(4))
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(4, 2, 1)
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>>> tuple(collatz_sequence(11))
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(11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1)
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>>> tuple(collatz_sequence(31)) # doctest: +NORMALIZE_WHITESPACE
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(31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137,
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412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593,
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1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425,
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1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644,
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1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732,
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866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53,
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160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1)
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>>> tuple(collatz_sequence(43)) # doctest: +NORMALIZE_WHITESPACE
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(43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26,
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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 positive integers")
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yield n
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while n != 1:
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if n % 2 == 0:
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n //= 2
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else:
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n = 3 * n + 1
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yield n
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def main():
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n = int(input("Your number: "))
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sequence = tuple(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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