Question

So I need a mathematical expression for the following loop, but I can’t seem to grasp it. I am assuming I am just missing something simple.

while a <= b
    a = a + a
end

Using an analysis, what would be the run time of this function?

Answer 1

The run time is dependent on the logarithm of b. In other words, the time complexity is O(log N).

You can see this if you start a at 1 and b at 256. Each time through the loop, a is doubled so that there are only nine iterations (would be eight if the condition was < b).

Each doubling of the b value will result in one extra iteration.

Of course, this is complexity analysis, the runtime depends on a host of other factors such as (almost certainly not an exhaustive list):

• how fast your machine is.
• what other things it has to do concurrently.
• initial value of a: a == 0 gives infinite run time, a == b + 1 gives you constant run time.