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.
Space complexity is irrelevant in modern computing.
Time complexity is always more difficult to analyze.
Space complexity cannot be expressed using Big-O notation.
When optimizing code for better time complexity, which approach will NOT always lead to improved real-world performance?
Caching frequently accessed data to avoid recomputation.
Replacing an O(n^2) algorithm with an O(n log n) algorithm.
Using a more complex data structure with better time complexity for certain operations.
Reducing the number of operations within loops.
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(1)
O(n)
O(log n)
O(2^n)
Which statement about benchmarking is TRUE?
Benchmarking is primarily used for comparing the theoretical time complexity of different algorithms.
Benchmarking results are always generalizable across different hardware and software environments.
Benchmarking is only useful for large-scale applications and not for smaller projects.
Benchmarking focuses on measuring the execution time of an algorithm in a controlled environment.
What is the time complexity of the following code snippet?
def mystery(n): if n <= 1: return 1 return mystery(n-1) + mystery(n-2)
O(n log n)
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 hash table
A sorted array
A self-balancing binary search tree
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 sufficiently large 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 all input sizes.
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 input data, despite being randomly generated, consistently represents a special case where Algorithm Y excels.
The benchmark is flawed and does not accurately measure the execution time of the algorithms.
Algorithm Y is inherently more efficient than Algorithm X for all input sizes and distributions.
The input data used in the benchmark always triggers the worst-case scenario for Algorithm X.
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?
Nested loops to check all pairs
Using a hash table to store seen elements
Using two pointers, one at the beginning and one at the end of the array
Sorting the array and then using binary search
Which of the following notations provides the tightest possible bound on the growth rate of an algorithm's running time?
Big-Theta (Θ)
Little-o (o)
Big-O (O)
Big-Omega (Ω)