The answer
Because the variable grows exponentially, it reaches N in far fewer steps. Mathematically, it takes log2(N) steps, hence O(log N).
Time Complexity Analysis of Single Loops
Why is i *= 2 logarithmic?
More FAQs in Time Complexity Analysis of Single Loops
If the loop iterates from 0 to N incrementing by 1, the time complexity is strictly O(N) Linear Time.
No. Big O measures the worst-case scenario. Even if you break early in the best case, the worst case still requires checking all N elements, so it remains O(N).
O(N) + O(N) = O(2N). However, in Big O notation, we drop constants, so the final time complexity is still O(N).
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