Which notation provides both an upper and lower bound on the growth of a function, implying the function grows at the same rate as the specified function?
Little-omega (ω)
Big Theta (Θ)
Big Omega (Ω)
Big-O (O)
Which of the following is the primary goal of benchmarking in the context of algorithm analysis?
Identifying the best-case scenario for an algorithm's performance.
Proving the correctness of an algorithm.
Measuring the actual execution time of an algorithm under specific conditions.
Determining the theoretical time complexity of an algorithm.
Which of the following is NOT a valid reason for analyzing an algorithm's time complexity?
Comparing the efficiency of different algorithms for a given task
Identifying potential performance bottlenecks
Determining the optimal programming language for an algorithm
Understanding how an algorithm's runtime scales with input size
Which time complexity is represented by an algorithm that iterates through a list of size n and performs a constant time operation in each iteration?
O(n^2)
O(n)
O(1)
O(log n)
In what scenario might an algorithm with a worse theoretical time complexity perform better in practice than one with a better complexity?
All of the above.
When the algorithm with worse complexity is implemented in a more efficient programming language.
When the input data size is very small.
When the algorithm with better complexity has a very large constant factor hidden in its Big O notation.
Which searching algorithm has a time complexity of O(log n) in the average case?
Jump Search
Interpolation Search
Linear Search
Binary Search
What is the time complexity of searching for an element in a sorted array using binary search?
O(n log n)
Which of the following is a limitation of time complexity analysis?
It's only relevant for algorithms processing numerical data
It can't be applied to algorithms with nested loops
It doesn't consider the hardware on which the algorithm will run
It always provides the exact runtime of an algorithm
Which sorting algorithm has a time complexity of O(n^2) in its average and worst case?
Merge Sort
Quick Sort
Heap Sort
Bubble Sort
Which of these Big-O notations represents the most efficient algorithm for large input sizes?