You need to design an algorithm that operates on a very large dataset. Which time complexity should you aim for to ensure reasonable performance?
O(n!)
O(n^3)
O(2^n)
O(log n)
What is the Big-O notation of an algorithm that iterates through an array of size 'n' twice in nested loops?
O(n^2)
O(n)
O(1)
Consider a binary search algorithm on a sorted array. In the worst-case scenario, how many comparisons are required to find a target element?
logâ‚‚(n) + 1
n
1
n/2
What is the time complexity of searching for an element in an unsorted array of size 'n' in the worst-case scenario?
What does it mean for an algorithm to have a time complexity of Θ(1)?
The runtime grows linearly with the input size.
The algorithm is guaranteed to be the fastest possible solution for the problem.
The algorithm's runtime is unpredictable and varies greatly with different inputs.
The runtime is constant and independent of the input size.
An algorithm processes an input of size 'n' by dividing it in half repeatedly until the size becomes 1. What is the most likely time complexity of this algorithm?
O(n log n)
Which of the following statements about the relationship between theoretical time complexity and real-world performance is FALSE?
An algorithm with better theoretical complexity will always outperform an algorithm with worse complexity in practice.
Hardware characteristics like CPU speed and cache size can influence the actual runtime of an algorithm.
Real-world data often exhibits patterns that can be exploited to improve performance beyond theoretical predictions.
Constant factors and lower-order terms ignored in Big O notation can significantly impact real-world performance.
Which of the following is NOT a common reason why real-world performance might differ from theoretical time complexity analysis?
Caching and data locality
The choice of algorithm used
The specific hardware being used
The programming language and compiler optimizations
Why is understanding time complexity crucial when comparing the efficiency of algorithms?
It allows us to analyze how the algorithm's runtime changes relative to the input size.
It helps determine the exact amount of memory an algorithm will use.
It provides a precise measurement of an algorithm's execution time in milliseconds.
It reveals the underlying hardware limitations that affect algorithm performance.
What is the time complexity of Dijkstra's algorithm for finding the shortest path in a graph with V vertices and E edges using an adjacency list and a priority queue?
O(E log V)
O(V + E)
O(V^2)
O(V log E)