A recursive function has a base case that executes in O(1) time. For each recursive step, it makes 3 recursive calls with input size n/2. What is the overall time complexity of this function?
O(n^2)
O(n log n)
O(n)
O(n^log_2(3))
Consider a social network graph with V users and E friendships. You want to find the shortest path between two users (A and B) in terms of friendship connections. What is the time complexity of the most efficient algorithm for this scenario in the worst-case?
O(V!) using brute-force depth-first search
O(E log V) using Dijkstra's Algorithm with a binary heap
O(V^2) using Floyd-Warshall Algorithm
O(V + E) using Breadth First Search
You are tasked with optimizing a critical function in a real-time trading system. Your theoretical analysis suggests Algorithm A (O(log n)) is superior to Algorithm B (O(n)). However, benchmarking reveals Algorithm B performs better for your typical data size. What is the MOST likely reason for this discrepancy?
The trading system's hardware is optimized for linear-time algorithms like Algorithm B.
Algorithm A's hidden constant factors are significantly larger than Algorithm B's, making it slower for smaller input sizes.
Benchmarking is flawed and does not accurately represent the real-world scenario.
Theoretical analysis is unreliable and cannot predict real-world performance.
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)
O(log n)
O(1)
An algorithm processes an input list of size n. It first performs an O(n log n) sorting operation. Then, for each element in the sorted list, it performs a nested loop iterating over all pairs of elements in the list. What is the overall time complexity of this algorithm?
O(n^3)
O(n^2 log n)
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?
It depends on the hash function
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?
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.
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.
Algorithm Y is inherently more efficient than Algorithm X for all input sizes and distributions.
The input data, despite being randomly generated, consistently represents a special case where Algorithm Y excels.
Consider a dynamic array implementation where resizing to double the capacity takes O(n) time. If we perform 'n' insertions sequentially, what is the amortized time complexity per insertion?