Working with true and false

So far we have learnt how to stop a "looped" statement from going on forever, based on a condition. Now, we'll see how to execute single statements based on a condition and apply that to our study of the Fibonacci sequence.

Conditional statements

The simplest conditional statement has the form:

if condition
    command
end

meaning that command is to be executed only if condition is verified.

For example:

julia> x = 1000;

julia> if x > 100
       println("x is big")
       end
x is big

In this case x > 100 is true, so the command happened and we saw the result on the screen. If instead:

julia> x = 10;

julia> if x > 100
       println("x is big")
       end

nothing happens.

Else ?

In an if statement, we can specify a statement to be executed if the condition is not verified. For example:

julia> x = 10;

julia> if x > 100
       println("x is big")
       else
       println("x is small")
       end
x is small

There is a slightly more complex construct, elseif, to execute the command if the first condition is not verified but another is:

julia> x = 30;

julia> if x > 100
       println("x is big")
       elseif x > 20
       println("x is not so big")
       else
       println("x is small")
       end
x is not so big

Combining conditions

Note that conditions can be combined using the logical operators: and, or, not. In Julia they are written: &&, || and ! respectively. Can you figure out for which values:

julia> !(x > 20) && (x < 15)

returns true?

Choose one such x and run a celebratory:

julia> if !(x > 20) && (x < 15)
       println("I knew it!")
       end

Back to Fibonacci

Running an if statement in isolation is generally not very interesting, but we can combine it with things we have learnt already. In the last part of this post, we'll use the full extent of our knowledge to count how many Fibonacci numbers exist, smaller than 1000000 that are multiples of 7.

Intermezzo: checking divisibility

To see if a number is a multiple of another we can use the % (modulo) operator. a % b (reads: "a modulo b") gives the reminder of a when divided by b:

julia> 44 % 7
2

So "a is a multiple of b" is written a % b == 0 in Julia.

A you remember from the previous post there was a simple way to count the total number of Fibonacci smaller than 1000000 in Julia. First we start the Fibonacci sequence:

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 we add 1 to the counter at every iteration:

julia> while next_fib < 1000000
       fib, next_fib = next_fib, fib+next_fib
       counter += counter
       end

To only count those that are multiple of 7, we start our sequence as usual:

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

As there is no multiple of 7 in 1, 2, we start the counter from 0.

julia> counter = 0

Then we add 1 to the counter at every iteration but only if the Fibonacci is a multiple of 7:

julia> while next_fib < 1000000
       fib, next_fib = next_fib, fib+next_fib
       if next_fib % 7 == 0
       counter += 1
       end
       end

julia> counter
3

Exercises

1. What is the ratio of Fibonacci numbers smaller than 1000000 that is multiple of 7?
2. How many Fibonacci numbers between 10000 and 1000000 are multiple of 7?