Sequence

using System;
using System.Collections.Generic;
using System.Linq;

public static class CollatzConjecture
{
    public static int Steps(int number)
    {
        if (number <= 0)
            throw new ArgumentOutOfRangeException(nameof(number));

        return Sequence(number).Count();
    }

    private static IEnumerable<int> Sequence(int number)
    {
        var currentNumber = number;

        while (currentNumber != 1)
        {
            if (currentNumber % 2 == 0)
                currentNumber = currentNumber / 2;
            else
                currentNumber = currentNumber * 3 + 1;

            yield return currentNumber;
        }
    }
}

The first step is to check the number parameter for validity:

if (number <= 0)
    throw new ArgumentOutOfRangeException(nameof(number));

In the second step, the Sequence() method is called with number as its argument. This method returns the sequence of numbers (IEnumerable<int>) that one gets by repeated application of the algorithm (excluding the number we start with). Then, we count the amount of numbers in that sequence to get the number of steps:

Let's examine the Sequence() method more closely. As a reminder, this is what the method looks like:

private static IEnumerable<int> Sequence(int number)
{
    var currentNumber = number;

    while (currentNumber != 1)
    {
        if (currentNumber % 2 == 0)
            currentNumber = currentNumber / 2;
        else
            currentNumber = currentNumber * 3 + 1;

        yield return currentNumber;
    }
}

First, we start out with assigning the number parameter to a currentNumber variable, which we'll use to keep track of where in the collatz conjecture sequence we currently are.

Then a while loop starts by checking whether the current number is not equal to 1; if it is, the method terminates:

while (currentNumber != 1)

Within the loop, we update the currentNumber based on the algorithm, re-assigning its value with its next value in the sequence.

if (currentNumber % 2 == 0)
    currentNumber = currentNumber / 2;
else
    currentNumber = currentNumber * 3 + 1;

Finally, we use a yield statement to yield the current number.

yield return currentNumber;

When a yield statement is written, the compiler transforms the method into a state machine that is suspended after each yield statement. Note that even though we are yield indidivual elements, what is returned from a caller's viewpoint is a sequence of elements.

Methods that use a yield statement are also lazy, which means that calling Sequence(number) by itself does not do anything. It is only when we call Count() on the sequence, that we're forcing iteration over the elements in the sequence.

Shortening

A ternary operator can be used instead of an if statement:

currentNumber = currentNumber % 2 == 0 ? currentNumber / 2 : currentNumber * 3 + 1;