If an algorithm has a time complexity of O(n log n), what can you infer about its runtime as the input size doubles?
It remains constant
It increases exponentially
It increases slightly more than double
It increases by a factor of log n
Which notation is most useful when analyzing the average-case time complexity of an algorithm, considering all possible inputs?
Big Theta (Θ)
All notations are equally useful for average-case analysis.
Big-O (O)
Little-o (o)
Which of the following asymptotic notations represents the tightest upper bound on the growth of a function?
Big Omega (Ω)
What is the time complexity of the QuickSort algorithm in the worst-case scenario?
O(log n)
O(n)
O(n log n)
O(n^2)
Which of these Big-O notations represents the most efficient algorithm for large input sizes?
O(1)
How does profiling differ from benchmarking in the context of algorithm optimization?
Profiling is used for theoretical analysis, while benchmarking is used for real-world performance evaluation.
Profiling and benchmarking are essentially the same and can be used interchangeably.
Profiling focuses on measuring the memory usage of an algorithm, while benchmarking measures execution time.
Profiling identifies performance bottlenecks within an algorithm, while benchmarking compares different algorithms.
What is the time complexity of an algorithm with nested loops, where each loop iterates n times?
O(n^3)
What is the worst-case time complexity of the linear search algorithm?
Why is it crucial to consider real-world performance alongside theoretical time complexity analysis when designing algorithms?
Theoretical analysis is only relevant for academic purposes.
Real-world factors like hardware and data distribution can significantly impact performance.
Real-world performance is always better than theoretical predictions.
Theoretical analysis is sufficient for predicting real-world performance.
What is the best-case time complexity of the insertion sort algorithm?