Collatz Conjecture in Python
Calculate the number of steps to reach 1 using the Collatz conjecture
exercism fetch python collatz-conjecture
The Collatz Conjecture or 3x+1 problem can be summarized as follows:
Take any positive integer n. If n is even, divide n by 2 to get n / 2. If n is odd, multiply n by 3 and add 1 to get 3n + 1. Repeat the process indefinitely. The conjecture states that no matter which number you start with, you will always reach 1 eventually.
Given a number n, return the number of steps required to reach 1.
Starting with n = 12, the steps would be as follows:
Resulting in 9 steps. So for input n = 12, the return value would be 9.
The Collatz Conjecture is only concerned with strictly positive integers, so your solution should raise a
ValueError with a meaningful message if given 0 or a negative integer.
Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.
To raise a message with an exception, just write it as an argument to the exception type. For example, instead of
raise Exception, you should write:
raise Exception("Meaningful message indicating the source of the error")
Running the tests
To run the tests, run the appropriate command below (why they are different):
- Python 2.7:
- Python 3.3+:
Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version):
python -m pytest collatz_conjecture_test.py
-v: enable verbose output
-x: stop running tests on first failure
--ff: run failures from previous test before running other test cases
For other options, see
python -m pytest -h
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An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem
Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.