Time complexity analysis. choosing operator for counting number of times a line of code runs

Question

Analysing time complexity of this pseudocode. On the right my take on the number of times each line runs. I'm not sure whether to use log n , n log n , or simply n for the while-loop..please help

                                times
1 sum = 0                        1
2 i = 1                          1  
3 while i ≤ n                 log n + 1
4     for j = 1 to n           n log n
5     sum = sum + j            n log n
6 i = 2i                       log n
7 return sum                     1

this results in: 2 n log + 2log n + 4

and thereby : O(n log n)

is this correct ?

Answer 1

If your while loop is:

3 while i < n                 log n + 1
4     for j = 1 to n           n log n
5        sum = sum + j         n log n
6     i = 2i                   log n

Then yes, you are correct in calculating the complexity. The complexity of the code is indeedO(nlogn).

Edit:
Though I am curious what you are trying to do here. You are calculating the sum of 1st n elements logn times.

Hence the return value would be something like n*(n+1)/2 * logn