What is the time complexity of inserting an element at the beginning of a dynamically sized array that needs to resize by doubling its capacity when full?
O(n)
O(1)
O(log n)
O(n log n)
You are designing a system to handle real-time stock market data. Which of the following time complexities would be LEAST desirable for an algorithm processing incoming price updates?
O(2^n)
Which of the following statements about best-case, worst-case, and average-case analysis is FALSE?
Worst-case analysis always provides an upper bound on the algorithm's runtime for any input.
Average-case analysis attempts to determine the average runtime over all possible inputs.
Best-case analysis considers the input that results in the algorithm's fastest possible execution.
Worst-case analysis is typically the most important to consider when designing for performance-critical applications.
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?
The benchmark is flawed and does not accurately measure the execution time of the algorithms.
The input data used in the benchmark always triggers the worst-case scenario for Algorithm X.
The input data, despite being randomly generated, consistently represents a special case where Algorithm Y excels.
Algorithm Y is inherently more efficient than Algorithm X for all input sizes and distributions.
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?
Why is time complexity generally considered more important than space complexity in algorithm analysis?
Modern computers have abundant memory, while efficient time utilization often remains a bottleneck.
Time complexity is always more difficult to analyze.
Space complexity cannot be expressed using Big-O notation.
Space complexity is irrelevant in modern computing.
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 B is faster than Algorithm A for all input sizes.
Algorithm A is faster than Algorithm B for sufficiently large input sizes.
Which of the following notations provides the tightest possible bound on the growth rate of an algorithm's running time?
Little-o (o)
Big-O (O)
Big-Omega (Ω)
Big-Theta (Θ)
Which of the following operations generally exhibits O(log n) time complexity in a balanced binary search tree?
Finding the minimum element
Inserting a new element
Calculating the height of the tree
Printing all elements in sorted order
Imagine you're optimizing a QuickSort algorithm for an array of size N. In the worst-case scenario, how does choosing a pivot element randomly impact the time complexity compared to always selecting the first element as the pivot?
Random pivot selection makes the worst-case time complexity unpredictable
Random pivot selection reduces the worst-case time complexity to O(N)
Random pivot selection changes the worst-case time complexity to O(N log N)
Random pivot selection has no impact on the worst-case time complexity, it remains O(N^2)