How does profiling differ from benchmarking in the context of algorithm optimization?
Profiling and benchmarking are essentially the same and can be used interchangeably.
Profiling identifies performance bottlenecks within an algorithm, while benchmarking compares different algorithms.
Profiling focuses on measuring the memory usage of an algorithm, while benchmarking measures execution time.
Profiling is used for theoretical analysis, while benchmarking is used for real-world performance evaluation.
Why is understanding time complexity crucial in algorithm analysis?
To compare the aesthetic quality of different algorithms
To predict how the performance of an algorithm scales with larger inputs
To calculate the cost of developing an algorithm
To determine the exact execution time of an algorithm
Merge sort and heapsort are examples of sorting algorithms with which time complexity?
O(n)
O(n^2)
O(n log n)
O(2^n)
What is the time complexity of finding the Fibonacci number at position n using a recursive approach without memoization?
O(log n)
Which of the following typically represents the most inefficient time complexity for large input sizes?
O(n!)
What is the primary focus of Big-O notation in time complexity analysis?
Expressing the exact number of operations an algorithm performs
Describing the upper bound of an algorithm's growth rate
Representing the lower bound of an algorithm's growth rate
Calculating the average-case runtime of an algorithm
Which sorting algorithm is generally considered the fastest for large datasets with an average time complexity of O(n log n)?
Merge Sort
Bubble Sort
Insertion Sort
Selection Sort
What is the time complexity of adding an element at the end of a dynamic array (ArrayList in Java, vector in C++) if there is enough capacity?
O(1)
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 Theta (Θ)
Big-O (O)
Little-o (o)
What does it mean if an algorithm has a time complexity of Ω(n log n)?
It runs in exactly n log n time.
It runs in at least n log n time.
It has a logarithmic growth rate.
It runs in at most n log n time.