What is the time complexity of the QuickSort algorithm in the worst-case scenario?
O(n^2)
O(n log n)
O(n)
O(log n)
What does it mean if an algorithm has a time complexity of Ω(n log n)?
It runs in at most n log n time.
It runs in exactly n log n time.
It runs in at least n log n time.
It has a logarithmic growth rate.
Why is understanding time complexity crucial in algorithm analysis?
To determine the exact execution time of an algorithm
To calculate the cost of developing an algorithm
To compare the aesthetic quality of different algorithms
To predict how the performance of an algorithm scales with larger inputs
Merge sort and heapsort are examples of sorting algorithms with which time complexity?
O(2^n)
Which of the following operations typically represents constant time complexity, O(1)?
Finding the smallest element in a sorted array
Searching for a specific value in an unsorted array
Inserting an element at the beginning of a linked list
Sorting an array using bubble sort
Which data structure, when used for searching, can potentially improve the time complexity from O(n) to O(log n)?
Linked List
Queue
Array
Binary Tree
Which of the following statements is TRUE regarding the trade-off between code optimization and readability?
Highly optimized code is always easier to read and maintain.
Code readability is irrelevant as long as the code achieves optimal performance.
There's no trade-off; optimal performance and readability always go hand-in-hand.
Excessive optimization can sometimes hinder code readability, making maintenance difficult.
Which notation is most useful when analyzing the average-case time complexity of an algorithm, considering all possible inputs?
All notations are equally useful for average-case analysis.
Big-O (O)
Little-o (o)
Big Theta (Θ)
How does profiling differ from benchmarking in the context of algorithm optimization?
Profiling identifies performance bottlenecks within an algorithm, while benchmarking compares different algorithms.
Profiling and benchmarking are essentially the same and can be used interchangeably.
Profiling is used for theoretical analysis, while benchmarking is used for real-world performance evaluation.
Profiling focuses on measuring the memory usage of an algorithm, while benchmarking measures execution time.
What is the time complexity of finding the Fibonacci number at position n using a recursive approach without memoization?