Consider an algorithm that iterates through a sorted array of size n. In the best-case scenario, the algorithm finds the desired element in the first comparison. What is the time complexity of this algorithm in the best case?
O(log n)
O(n)
O(n log n)
O(1)
Which of the following operations generally exhibits O(log n) time complexity in a balanced binary search tree?
Inserting a new element
Printing all elements in sorted order
Calculating the height of the tree
Finding the minimum element
You need to design an algorithm to solve a variation of the knapsack problem with a capacity C and N items. However, you can take multiple copies of the same item. Which algorithmic paradigm best addresses this scenario and provides an efficient solution?
Greedy Algorithm
Divide and Conquer
Depth First Search with Backtracking
Dynamic Programming with a 2D table
You are designing a data structure that supports two operations: 'insert' and 'find median'. 'Insert' adds an element in O(log n) time. Which of the following allows the 'find median' operation to also be achieved in O(log n) time?
A standard binary search tree
A self-balancing binary search tree
A sorted array
A hash table
Which of these is NOT a valid use of time complexity analysis?
Comparing the scalability of different algorithms as data size increases.
Identifying potential performance bottlenecks in a large codebase.
Choosing between different data structures for a specific task.
Determining the exact execution time of an algorithm on a given hardware.
You are comparing two sorting algorithms: Algorithm X with O(n log n) average-case complexity and Algorithm Y with O(n^2) worst-case complexity. In your benchmarks, Algorithm Y consistently outperforms Algorithm X. What is a PLAUSIBLE explanation for this observation?
Algorithm Y is inherently more efficient than Algorithm X for all input sizes and distributions.
The benchmark is flawed and does not accurately measure the execution time of the algorithms.
The input data, despite being randomly generated, consistently represents a special case where Algorithm Y excels.
The input data used in the benchmark always triggers the worst-case scenario for Algorithm X.
A randomized algorithm has a worst-case running time of O(n^2), but its expected running time is O(n log n). What does this imply about the algorithm's performance?
The algorithm always runs in O(n log n) time.
On average, the algorithm performs better than its worst-case bound.
The algorithm's running time is independent of the input.
The algorithm is unsuitable for practical use due to its unpredictable running time.
Which statement about benchmarking is TRUE?
Benchmarking focuses on measuring the execution time of an algorithm in a controlled environment.
Benchmarking is only useful for large-scale applications and not for smaller projects.
Benchmarking is primarily used for comparing the theoretical time complexity of different algorithms.
Benchmarking results are always generalizable across different hardware and software environments.
Which of the following statements about best-case, worst-case, and average-case analysis is FALSE?
Average-case analysis attempts to determine the average runtime over all possible inputs.
Worst-case analysis is typically the most important to consider when designing for performance-critical applications.
Best-case analysis considers the input that results in the algorithm's fastest possible execution.
Worst-case analysis always provides an upper bound on the algorithm's runtime for any input.
You have two algorithms, A and B, for the same problem. A has a time complexity of O(n log n) and Ω(n), while B has a time complexity of O(n^2) and Ω(log n). Which of the following statements is always true?
Algorithm A is faster than Algorithm B for all input sizes.
We cannot definitively compare the performance of the two algorithms based on the given information.
Algorithm A is faster than Algorithm B for sufficiently large input sizes.
Algorithm B is faster than Algorithm A for all input sizes.