Question

Given a C code

for(i=n,j=0 , i>0,i/=2 ,  j+=i)

What is the value of j after termination of for loop?

In the solution in my book, it starts with:

j=n+n/2 +n/4+....+log n terms.

Now I can understand how there are log n terms in the above series.

Any help appreciated, thanks.

Answer 1

It is log₂ n, that is the number of binary bits (or the rank of the highest 1 bit) in the binary representation of n

And you made a typo, you probably mean

 for(i=n,j=0 ; i>0 ;  (i/=2), (j+=i));

So you start with i==n then you halve it till 0 is reached (hence the log₂ n number of loops).