|
1 |
| -#!/usr/bin/env python3 |
2 |
| - |
3 |
| -# Recommended: Python 3.6+ |
4 |
| - |
5 |
| -""" |
6 |
| -Collatz Conjecture - Python |
7 |
| -
|
8 |
| -The Collatz conjecture, also known as the |
9 |
| -3x + 1 problem, is a mathematical conjecture |
10 |
| -concerning a certain sequence. This sequence |
11 |
| -operates on any input number in such a way |
12 |
| -hat the output will always reach 1. |
13 |
| -
|
14 |
| -The Collatz conjecture is most famous for |
15 |
| -harboring one of the unsolved problems in |
16 |
| -mathematics: does the Collatz sequence really |
17 |
| -reach 1 for all positive integers? |
18 |
| -
|
19 |
| -This program takes any input integer |
20 |
| -and performs a Collatz sequence on them. |
21 |
| -The expected behavior is that any number |
22 |
| -inputted will always reach a 4-2-1 loop. |
23 |
| -
|
24 |
| -Do note that Python is limited in terms of |
25 |
| -number size, so any enormous numbers may be |
26 |
| -interpreted as infinity, and therefore |
27 |
| -incalculable, by Python. This limitation |
28 |
| -was only observed in CPython, so other |
29 |
| -implementations may or may not differ. |
30 |
| -
|
31 |
| -11/24/2021 |
32 |
| -David Costell (DontEatThemCookies on GitHub) |
33 |
| -""" |
34 |
| - |
35 |
| -import math |
36 |
| - |
37 |
| -print("Collatz Conjecture") |
38 |
| -number = input('Enter a number to calculate: ') |
39 |
| -try: |
40 |
| - number = float(number) |
41 |
| -except: |
42 |
| - print('Error: Could not convert to integer.') |
43 |
| - print('Only integers/floats can be entered as input.') |
44 |
| - input() |
45 |
| - exit() |
46 |
| - |
47 |
| -# Checks to see if input is valid |
48 |
| -if number == 0: |
49 |
| - input('Error: Zero is not calculable. ') |
50 |
| - exit() |
51 |
| -if number < 0: |
52 |
| - input('Error: Negative numbers are not calculable. ') |
53 |
| - exit() |
54 |
| -if number == math.inf: |
55 |
| - input('Error: Infinity is not calculable.') |
56 |
| - exit() |
57 |
| - |
58 |
| -print('Number is', number) |
59 |
| -input('Press ENTER to begin.') |
60 |
| -print('BEGIN COLLATZ SEQUENCE') |
61 |
| - |
62 |
| -def modulo(): |
63 |
| - global number |
64 |
| - modulo = number % 2 # Modulo the number by 2 |
65 |
| - if modulo == 0: # If the result is 0, |
66 |
| - number = number / 2 # divide it by 2 |
67 |
| - else: # Otherwise, |
68 |
| - number = number * 3 + 1 # multiply by 3 and add 1 |
69 |
| - |
70 |
| -def final(): |
71 |
| - print('END COLLATZ SEQUENCE') |
72 |
| - print('Sequence has reached a 4-2-1 loop.') |
73 |
| - input() |
74 |
| - exit() |
75 |
| - |
76 |
| -while True: |
77 |
| - # Execute the sequence |
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| - modulo() |
79 |
| - print(number) |
80 |
| - if number == 1.0: |
81 |
| - break |
82 |
| - |
83 |
| -final() |
| 1 | +#!/usr/bin/env python3 |
| 2 | + |
| 3 | +# Recommended: Python 3.6+ |
| 4 | + |
| 5 | +""" |
| 6 | +Collatz Conjecture - Python |
| 7 | +
|
| 8 | +The Collatz conjecture, also known as the |
| 9 | +3x + 1 problem, is a mathematical conjecture |
| 10 | +concerning a certain sequence. This sequence |
| 11 | +operates on any input number in such a way |
| 12 | +that the output will always reach 1. |
| 13 | +
|
| 14 | +The Collatz conjecture is most famous for |
| 15 | +harboring one of the unsolved problems in |
| 16 | +mathematics: does the Collatz sequence really |
| 17 | +reach 1 for all positive integers? |
| 18 | +
|
| 19 | +This program takes any input integer |
| 20 | +and performs a Collatz sequence on them. |
| 21 | +The expected behavior is that any number |
| 22 | +inputted will always reach a 4-2-1 loop. |
| 23 | +
|
| 24 | +Do note that Python is limited in terms of |
| 25 | +number size, so any enormous numbers may be |
| 26 | +interpreted as infinity, and therefore |
| 27 | +incalculable, by Python. This limitation |
| 28 | +was only observed in CPython, so other |
| 29 | +implementations may or may not differ. |
| 30 | +
|
| 31 | +1/2/2022 - Revision 1 of Collatz-Conjecture |
| 32 | +David Costell (DontEatThemCookies on GitHub) |
| 33 | +""" |
| 34 | + |
| 35 | +import math |
| 36 | + |
| 37 | +print('Collatz Conjecture (Revised)\n') |
| 38 | + |
| 39 | +def main(): |
| 40 | + # Get the input |
| 41 | + number = input('Enter a number to calculate: ') |
| 42 | + try: |
| 43 | + number = float(number) |
| 44 | + except ValueError: |
| 45 | + print('Error: Could not convert to integer.') |
| 46 | + print('Only numbers (e.g. 42) can be entered as input.') |
| 47 | + main() |
| 48 | + |
| 49 | + # Prevent any invalid inputs |
| 50 | + if number <= 0: |
| 51 | + print('Error: Numbers zero and below are not calculable.') |
| 52 | + main() |
| 53 | + if number == math.inf: |
| 54 | + print('Error: Infinity is not calculable.') |
| 55 | + main() |
| 56 | + |
| 57 | + # Confirmation before beginning |
| 58 | + print('Number is:', number) |
| 59 | + input('Press ENTER to begin.') |
| 60 | + print('\nBEGIN COLLATZ SEQUENCE') |
| 61 | + |
| 62 | + def sequence(number: float) -> float: |
| 63 | + """ |
| 64 | + The core part of this program, |
| 65 | + it performs the operations of |
| 66 | + the Collatz sequence to the given |
| 67 | + number (parameter number). |
| 68 | + """ |
| 69 | + modulo = number % 2 # The number modulo'd by 2 |
| 70 | + if modulo == 0: # If the result is 0, |
| 71 | + number = number / 2 # divide it by 2 |
| 72 | + else: # Otherwise, |
| 73 | + number = 3 * number + 1 # multiply by 3 and add 1 (3x + 1) |
| 74 | + return number |
| 75 | + |
| 76 | + # Execute the sequence |
| 77 | + while True: |
| 78 | + number = sequence(number) |
| 79 | + print(round(number)) |
| 80 | + if number == 1.0: |
| 81 | + break |
| 82 | + |
| 83 | + print('END COLLATZ SEQUENCE') |
| 84 | + print('Sequence has reached a 4-2-1 loop.') |
| 85 | + exit(input('\nPress ENTER to exit.')) |
| 86 | + |
| 87 | +# Entry point of the program |
| 88 | +if __name__ == '__main__': |
| 89 | + main() |
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