Problem Set 2
=============

Write good, clean, elegant code.

Focus on good naming, functional decomposition and testing.

Writing auxiliary functions that simplify the task and/or add to the utility
of the function to be written is strongly encouraged.

1. Write a function that checks if the given integer argument is a prime.

**Python signature**

.. code-block:: Python

    def is_prime(n: int) -> bool:


2. Write a function to factorize a given positive integer. Use it to solve
   project Euler problem 3.

**C++ signature**

.. code-block:: C++

    vector<int> factorize(int a) {
        vector<int> factors;

        return factors;
    }


**Java signature**

.. code-block:: Java

    public List<Integer> factorize(int a) {
        List<Integer> factors = new ArrayList<>();

        return factors;
    }

3. Write a program to solve project Euler problem 1. Use different data structures,
   language constructs, and libraries and write at least three distinct solutions.


4. The famous Collatz-Kakutani-Ulam sequence aka the Collatz sequence aka the hailstone
   sequence is defined as follows:

    1. Start with any positive integer
    #. If the integer is even divide it by 2
    #. If the integer is odd multiple by 3 and add 1.
    #. Using the newly obtained number, repeat from step 2
    
    For example, starting number 7 gives you the sequence: 7, 22, 11, 34, 17, 52, 26, 13,
    40, 20, 10, 5, 16, 8, 4, 2, 1.

    If you try out a few more you will notice that all of them end in 4, 2, 1 (since
    applying the steps to 1 will repeat 4, 2, 1). Write a program that prints out
    the sequence for the given argument.

    Remember: the sequence includes the starting number and ends in 4, 2, 1