From 69f20033e55ae62c337e2fb2146aea5fabf3e5a0 Mon Sep 17 00:00:00 2001 From: Tianyi Zheng Date: Mon, 26 Jun 2023 02:15:31 -0700 Subject: [PATCH] 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> --- DIRECTORY.md | 1 - maths/3n_plus_1.py | 151 -------------------------------------- maths/collatz_sequence.py | 69 +++++++++++------ 3 files changed, 46 insertions(+), 175 deletions(-) delete mode 100644 maths/3n_plus_1.py diff --git a/DIRECTORY.md b/DIRECTORY.md index 0c21b9537..1e0e450bc 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -522,7 +522,6 @@ * [Xgboost Regressor](machine_learning/xgboost_regressor.py) ## Maths - * [3N Plus 1](maths/3n_plus_1.py) * [Abs](maths/abs.py) * [Add](maths/add.py) * [Addition Without Arithmetic](maths/addition_without_arithmetic.py) diff --git a/maths/3n_plus_1.py b/maths/3n_plus_1.py deleted file mode 100644 index f9f6dfeb9..000000000 --- a/maths/3n_plus_1.py +++ /dev/null @@ -1,151 +0,0 @@ -from __future__ import annotations - - -def n31(a: int) -> tuple[list[int], int]: - """ - Returns the Collatz sequence and its length of any positive integer. - >>> n31(4) - ([4, 2, 1], 3) - """ - - if not isinstance(a, int): - msg = f"Must be int, not {type(a).__name__}" - raise TypeError(msg) - if a < 1: - msg = f"Given integer must be positive, not {a}" - raise ValueError(msg) - - path = [a] - while a != 1: - if a % 2 == 0: - a //= 2 - else: - a = 3 * a + 1 - path.append(a) - return path, len(path) - - -def test_n31(): - """ - >>> test_n31() - """ - assert n31(4) == ([4, 2, 1], 3) - assert n31(11) == ([11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1], 15) - assert n31(31) == ( - [ - 31, - 94, - 47, - 142, - 71, - 214, - 107, - 322, - 161, - 484, - 242, - 121, - 364, - 182, - 91, - 274, - 137, - 412, - 206, - 103, - 310, - 155, - 466, - 233, - 700, - 350, - 175, - 526, - 263, - 790, - 395, - 1186, - 593, - 1780, - 890, - 445, - 1336, - 668, - 334, - 167, - 502, - 251, - 754, - 377, - 1132, - 566, - 283, - 850, - 425, - 1276, - 638, - 319, - 958, - 479, - 1438, - 719, - 2158, - 1079, - 3238, - 1619, - 4858, - 2429, - 7288, - 3644, - 1822, - 911, - 2734, - 1367, - 4102, - 2051, - 6154, - 3077, - 9232, - 4616, - 2308, - 1154, - 577, - 1732, - 866, - 433, - 1300, - 650, - 325, - 976, - 488, - 244, - 122, - 61, - 184, - 92, - 46, - 23, - 70, - 35, - 106, - 53, - 160, - 80, - 40, - 20, - 10, - 5, - 16, - 8, - 4, - 2, - 1, - ], - 107, - ) - - -if __name__ == "__main__": - num = 4 - path, length = n31(num) - print(f"The Collatz sequence of {num} took {length} steps. \nPath: {path}") diff --git a/maths/collatz_sequence.py b/maths/collatz_sequence.py index 7b3636de6..4f3aa5582 100644 --- a/maths/collatz_sequence.py +++ b/maths/collatz_sequence.py @@ -1,43 +1,66 @@ +""" +The Collatz conjecture is a famous unsolved problem in mathematics. Given a starting +positive integer, define the following sequence: +- If the current term n is even, then the next term is n/2. +- If the current term n is odd, then the next term is 3n + 1. +The conjecture claims that this sequence will always reach 1 for any starting number. + +Other names for this problem include the 3n + 1 problem, the Ulam conjecture, Kakutani's +problem, the Thwaites conjecture, Hasse's algorithm, the Syracuse problem, and the +hailstone sequence. + +Reference: https://en.wikipedia.org/wiki/Collatz_conjecture +""" + from __future__ import annotations +from collections.abc import Generator -def collatz_sequence(n: int) -> list[int]: + +def collatz_sequence(n: int) -> Generator[int, None, None]: """ - 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) + Generate the Collatz sequence starting at n. + >>> tuple(collatz_sequence(2.1)) Traceback (most recent call last): ... - Exception: Sequence only defined for natural numbers - >>> collatz_sequence(0) + Exception: Sequence only defined for positive integers + >>> tuple(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] + Exception: Sequence only defined for positive integers + >>> tuple(collatz_sequence(4)) + (4, 2, 1) + >>> tuple(collatz_sequence(11)) + (11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1) + >>> tuple(collatz_sequence(31)) # doctest: +NORMALIZE_WHITESPACE + (31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, + 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, + 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, + 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, + 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, + 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, + 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1) + >>> tuple(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") + raise Exception("Sequence only defined for positive integers") - sequence = [n] + yield n while n != 1: - n = 3 * n + 1 if n & 1 else n // 2 - sequence.append(n) - return sequence + if n % 2 == 0: + n //= 2 + else: + n = 3 * n + 1 + yield n def main(): n = 43 - sequence = collatz_sequence(n) + sequence = tuple(collatz_sequence(n)) print(sequence) - print(f"collatz sequence from {n} took {len(sequence)} steps.") + print(f"Collatz sequence from {n} took {len(sequence)} steps.") if __name__ == "__main__":