How do you handle an O(N) loop followed by an O(log N) loop?
You add them: O(N + log N). Because linear time (N) grows much faster than logarithmic time (log N), N is dominant. The final complexity is just O(N).
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More FAQs in Analyzing Time Complexity of Multiple Consecutive Loops
You add their complexities together. O(N) + O(N) = O(2N), which is simplified by dropping the constant to O(N).
You multiply them only when one loop is nested completely inside the body of another loop.
If Loop A iterates over array size N, and Loop B iterates over array size M, the complexity is O(N + M). You cannot drop one because you don't know which is larger.
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