Automatizing things

Repeating a command many times can be extremely annoying. Luckily, Julia can help us automatize things using loops, which are a way to repeat the same command, or list of commands many times. Here we will continue on playing with Fibonacci numbers, without having to manually evaluate the same command at the console many times.

The while loop

The while loop executes a statement as long as a given condition is verified. Let's use it to solve the exercise from the previous chapter: what is the largest Fibonacci smaller than 10000?

julia> fib, next_fib = 1, 2
(1, 2)

julia> while next_fib < 10000
       fib, next_fib = next_fib, fib+next_fib
       end

julia> fib, next_fib
(6765, 10946)

This simple program gave us the pair of Fibonacci around 10000 without any need to painfully iterate the command at the console. How did this happen? Let's look in detail at this program.

Julia first assinged the variables fib = 1 and next_fib = 2 and then checked the condition (a condition is a statement that returns either true or false, for example 3 < 4). In this case 2 < 1000 is true, so Julia executed fib, next_fib = next_fib, fib+next_fib. Now next_fib is 3, but still 3 < 10000, so Julia kept going. At some point next_fib became 10946 (the twentieth Fibonacci) and 10946 < 10000, so Julia stopped. How did I now it was the twentieth Fibonacci? I cheated a bit, and in my code I added a counter to track where I was in the Fibonacci sequence. I started with:

julia> fib, next_fib = 1, 2
(1, 2)

As next_fib == 2 is the second Fibonacci, I started my counter at 2:

julia> counter = 2

Then I added 1 to the counter at every iteration:

julia> while next_fib < 10000
       fib, next_fib = next_fib, fib+next_fib
       counter = counter + 1
       end

All that's left to do is inspecting the value of counter after the while loop has been executed:

julia> counter
20

which confirms that next_fib == 10946 is the twentieth Fibonacci.

julia> counter = counter + 1

julia> counter += 1

Exercises

1. (1346269, 2178309) is a Fibonacci pair. Now that you know while loops, can you find a smart way to go backward in the Fibonacci sequence?