Question

Yesterday I applied for computer engineering master degree and it was the one of the their questions. I could not solve it so I was very curious.

...
i = 1;
while (i <= n)
{
    i = i * 2;
}
...

How many times will this while loop get executed, please give your answer as a formula. For ex: log n…

Thanks

Answer 1

On the x^th iteration of the loop, i equals 2^x (you can easily prove this by induction). Suppose the loop stops after X iterations, which means n < 2^X. This also means that on iteration X-1 the loop was still running and so 2^X-1 ≤ n. In other words :

2^X-1 ≤ n < 2^X

From there, finding X as a function of log₂(n) is easy.