I am trying to prepare for a test comping up on run-time analysis. I have been hit with a for loop that is throwing me a bit. I am hoping someone can help me.
the loop is
for(j=1; j< n; j=j*2)
J is increasing at an increasing rate so it will be less than n/2 however I am having trouble concluding what exactly it will be.
In your loop, $j$ will take the values $1, 2, 4, 8, \dotsc, 2^k$ where $2^k<n$. You need to know how many times this will iterate. In other words, what will be the largest $k$ for which we have $2^k < n$? Take the log to the base 2 of each side of the inequality and you're asking what the largest $k$ will be for which $k<\log_2n$. What this means is that you're right in your comment: the loop will iterate no more than $\log_2n$ times.
