Which of the following is the primary goal of benchmarking in the context of algorithm analysis?
Proving the correctness of an algorithm.
Determining the theoretical time complexity of an algorithm.
Identifying the best-case scenario for an algorithm's performance.
Measuring the actual execution time of an algorithm under specific conditions.
You have two algorithms for a task: Algorithm A has a time complexity of O(n log n), and Algorithm B has O(n^2). For which input size 'n' would Algorithm A likely start to outperform Algorithm B?
n = 10
n = 1000
It depends on the specific algorithms and their constant factors.
n = 100
What is the best-case time complexity of the insertion sort algorithm?
O(n log n)
O(n)
O(log n)
O(1)
In what scenario might an algorithm with a worse theoretical time complexity perform better in practice than one with a better complexity?
When the algorithm with worse complexity is implemented in a more efficient programming language.
When the algorithm with better complexity has a very large constant factor hidden in its Big O notation.
All of the above.
When the input data size is very small.
Which of the following asymptotic notations represents the tightest upper bound on the growth of a function?
Little-o (o)
Big Theta (Θ)
Big-O (O)
Big Omega (Ω)
Which of the following is a limitation of time complexity analysis?
It always provides the exact runtime of an algorithm
It can't be applied to algorithms with nested loops
It's only relevant for algorithms processing numerical data
It doesn't consider the hardware on which the algorithm will run
Which of the following typically represents the most inefficient time complexity for large input sizes?
O(n!)
O(n^2)
O(2^n)
Which of the following is NOT a valid reason for analyzing an algorithm's time complexity?
Understanding how an algorithm's runtime scales with input size
Comparing the efficiency of different algorithms for a given task
Determining the optimal programming language for an algorithm
Identifying potential performance bottlenecks
In the context of algorithm analysis, why are constant factors often ignored in asymptotic notations?
They are difficult to determine precisely and vary across different systems.
They are insignificant and have negligible impact on performance.
They become less relevant as the input size grows very large.
Which sorting algorithm has a time complexity of O(n^2) in its average and worst case?
Bubble Sort
Merge Sort
Quick Sort
Heap Sort