maths/collatz_sequence.py · python/Python

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Python

maths

collatz_sequence.py

collatz_sequence.py 1.26 KB

from __future__ import annotations

def collatz_sequence(n: int) -> list[int]:
 """
 Collatz conjecture: start with any positive integer n. The next term is
 obtained as follows:
 If n term is even, the next term is: n / 2 .
 If n is odd, the next term is: 3 * n + 1.

The conjecture states the sequence will always reach 1 for any starting value n.
 Example:
 >>> collatz_sequence(2.1)
 Traceback (most recent call last):
 ...
 Exception: Sequence only defined for natural numbers
 >>> collatz_sequence(0)
 Traceback (most recent call last):
 ...
 Exception: Sequence only defined for natural numbers
 >>> collatz_sequence(43) # doctest: +NORMALIZE_WHITESPACE
 [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]
 """

if not isinstance(n, int) or n < 1:
 raise Exception("Sequence only defined for natural numbers")

sequence = [n]
 while n != 1:
 n = 3 * n + 1 if n & 1 else n // 2
 sequence.append(n)
 return sequence

def main():
 n = 43
 sequence = collatz_sequence(n)
 print(sequence)
 print(f"collatz sequence from {n} took {len(sequence)} steps.")

if __name__ == "__main__":
 main()

一键复制编辑原始数据按行查看历史

Christian Clauss 提交于 2020年09月23日 19:30 +08:00 . from future import annotations (#2464)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

from __future__ import annotations


def collatz_sequence(n: int) -> list[int]:
 """
 Collatz conjecture: start with any positive integer n. The next term is
 obtained as follows:
 If n term is even, the next term is: n / 2 .
 If n is odd, the next term is: 3 * n + 1.

 The conjecture states the sequence will always reach 1 for any starting value n.
 Example:
 >>> collatz_sequence(2.1)
 Traceback (most recent call last):
 ...
 Exception: Sequence only defined for natural numbers
 >>> collatz_sequence(0)
 Traceback (most recent call last):
 ...
 Exception: Sequence only defined for natural numbers
 >>> collatz_sequence(43) # doctest: +NORMALIZE_WHITESPACE
 [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]
 """

 if not isinstance(n, int) or n < 1:
 raise Exception("Sequence only defined for natural numbers")

 sequence = [n]
 while n != 1:
 n = 3 * n + 1 if n & 1 else n // 2
 sequence.append(n)
 return sequence


def main():
 n = 43
 sequence = collatz_sequence(n)
 print(sequence)
 print(f"collatz sequence from {n} took {len(sequence)} steps.")


if __name__ == "__main__":
 main()