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Remove duplicate implementation of Collatz sequence (#8836)
* updating DIRECTORY.md
* Remove duplicate implementation of Collatz sequence
* updating DIRECTORY.md
* Add suggestions from PR review
---------
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
This commit is contained in:
Tianyi Zheng
GitHub
parent
62dcbea943
commit
69f20033e5
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@ -522,7 +522,6 @@
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* [Xgboost Regressor](machine_learning/xgboost_regressor.py)
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## Maths
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* [3N Plus 1](maths/3n_plus_1.py)
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* [Abs](maths/abs.py)
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* [Add](maths/add.py)
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* [Addition Without Arithmetic](maths/addition_without_arithmetic.py)
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@ -1,151 +0,0 @@
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from __future__ import annotations
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def n31(a: int) -> tuple[list[int], int]:
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"""
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Returns the Collatz sequence and its length of any positive integer.
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>>> n31(4)
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([4, 2, 1], 3)
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"""
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if not isinstance(a, int):
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msg = f"Must be int, not {type(a).__name__}"
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raise TypeError(msg)
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if a < 1:
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msg = f"Given integer must be positive, not {a}"
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raise ValueError(msg)
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path = [a]
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while a != 1:
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if a % 2 == 0:
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a //= 2
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else:
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a = 3 * a + 1
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path.append(a)
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return path, len(path)
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def test_n31():
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"""
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>>> test_n31()
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"""
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assert n31(4) == ([4, 2, 1], 3)
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assert n31(11) == ([11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1], 15)
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assert n31(31) == (
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[
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31,
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94,
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47,
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142,
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71,
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214,
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107,
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322,
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161,
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484,
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242,
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121,
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364,
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182,
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91,
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274,
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137,
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412,
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206,
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103,
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310,
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155,
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466,
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233,
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700,
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350,
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175,
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526,
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263,
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790,
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395,
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1186,
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593,
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1780,
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890,
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445,
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1336,
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668,
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334,
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167,
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502,
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251,
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754,
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377,
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1132,
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566,
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283,
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850,
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425,
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1276,
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638,
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319,
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958,
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479,
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1438,
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719,
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2158,
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1079,
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3238,
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1619,
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4858,
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2429,
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7288,
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3644,
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1822,
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911,
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2734,
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1367,
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4102,
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2051,
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6154,
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3077,
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9232,
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4616,
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2308,
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1154,
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577,
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1732,
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866,
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433,
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1300,
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650,
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325,
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976,
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488,
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244,
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122,
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61,
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184,
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92,
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46,
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23,
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70,
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35,
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106,
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53,
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160,
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80,
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40,
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20,
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10,
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5,
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16,
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8,
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4,
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2,
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1,
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],
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107,
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)
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if __name__ == "__main__":
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num = 4
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path, length = n31(num)
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print(f"The Collatz sequence of {num} took {length} steps. \nPath: {path}")
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@ -1,43 +1,66 @@
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"""
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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) -> list[int]:
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def collatz_sequence(n: int) -> Generator[int, None, None]:
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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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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 natural numbers
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>>> collatz_sequence(0)
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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 natural numbers
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>>> collatz_sequence(43) # doctest: +NORMALIZE_WHITESPACE
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[43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7,
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22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1]
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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 natural numbers")
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raise Exception("Sequence only defined for positive integers")
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sequence = [n]
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yield 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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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 = 43
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sequence = collatz_sequence(n)
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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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print(f"Collatz sequence from {n} took {len(sequence)} steps.")
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if __name__ == "__main__":
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