You need to choose an algorithm for a real-time system with strict timing constraints. Algorithm X has a time complexity of O(n log n) in the worst case and Θ(1) in the best case. Algorithm Y has a time complexity of Θ(n) in all cases. Which algorithm is a safer choice and why?
Neither algorithm is suitable for a real-time system.
Both algorithms are equally suitable for a real-time system.
Algorithm X, because its best-case complexity is excellent.
Algorithm Y, because its time complexity is consistent and predictable.
You are given a sorted array of n integers. You want to determine if there exists a pair of elements in the array that sum up to a specific target value. Which algorithm provides the most efficient time complexity?
Using a hash table to store seen elements
Nested loops to check all pairs
Sorting the array and then using binary search
Using two pointers, one at the beginning and one at the end of the array
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.
Algorithm A is faster than Algorithm B for sufficiently large input sizes.
Algorithm B is faster than Algorithm A for all input sizes.
We cannot definitively compare the performance of the two algorithms based on the given information.
Which of the following statements about best-case, worst-case, and average-case analysis is FALSE?
Worst-case analysis is typically the most important to consider when designing for performance-critical applications.
Worst-case analysis always provides an upper bound on the algorithm's runtime for any input.
Best-case analysis considers the input that results in the algorithm's fastest possible execution.
Average-case analysis attempts to determine the average runtime over all possible inputs.
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(1)
O(log n)
O(n)
O(n log n)
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?
Why is time complexity generally considered more important than space complexity in algorithm analysis?
Space complexity cannot be expressed using Big-O notation.
Space complexity is irrelevant in modern computing.
Modern computers have abundant memory, while efficient time utilization often remains a bottleneck.
Time complexity is always more difficult to analyze.
You need to find the smallest k elements in an unsorted array of size n. What is the most efficient time complexity achievable in the average case?
O(k^2)
O(n^2)
O(n + k log n)
Which of the following is the LEAST reliable indicator of an algorithm's real-world performance?
Worst-case time complexity
Average-case time complexity
Benchmarking results on different hardware configurations
Profiling results on a representative dataset
Consider a nested loop structure where the outer loop runs n times and the inner loop runs from 1 to i, where 'i' is the current iteration of the outer loop. What is the total number of iterations of the inner loop?
n(n+1)/2
n^2
n
log n