Which of these is NOT a valid use of time complexity analysis?
Identifying potential performance bottlenecks in a large codebase.
Determining the exact execution time of an algorithm on a given hardware.
Comparing the scalability of different algorithms as data size increases.
Choosing between different data structures for a specific task.
Which of the following operations generally exhibits O(log n) time complexity in a balanced binary search tree?
Inserting a new element
Finding the minimum element
Calculating the height of the tree
Printing all elements in sorted order
A hash table using open addressing has a load factor of 0.8. What is the expected average-case time complexity for a successful search operation?
O(1)
O(n)
O(log n)
It depends on the hash function
Which of the following is the LEAST reliable indicator of an algorithm's real-world performance?
Average-case time complexity
Benchmarking results on different hardware configurations
Worst-case time complexity
Profiling results on a representative dataset
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(n^2)
O(k^2)
O(n + k log n)
O(n log n)
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.
Using a more complex data structure with better time complexity for certain operations.
Replacing an O(n^2) algorithm with an O(n log n) algorithm.
Reducing the number of operations within loops.
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?
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
log n
n^2
n(n+1)/2
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?
Dynamic Programming with a 2D table
Depth First Search with Backtracking
Divide and Conquer
Greedy Algorithm
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.
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.
Algorithm A is faster than Algorithm B for all input sizes.