|
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 |
78 | | - 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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