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Remove duplicate implementation of Collatz sequence (#8836)

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* updating DIRECTORY.md

* Remove duplicate implementation of Collatz sequence

* updating DIRECTORY.md

* Add suggestions from PR review

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Tianyi Zheng 2023-06-26 02:15:31 -07:00 committed by GitHub
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1
DIRECTORY.md
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@ -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)

151
maths/3n_plus_1.py
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@ -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}")

69
maths/collatz_sequence.py
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@ -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__":