A Level Computer Science OCR Practice Exam

What does O(n) signify in the context of algorithm complexity?

1. The algorithm runs in constant time

2. The algorithm scales linearly with the size of the input

3. The algorithm's performance degrades exponentially

4. The algorithm requires logarithmic operations

The correct answer is: The algorithm scales linearly with the size of the input

The notation O(n) is used in computer science to describe the time or space complexity of an algorithm in relation to the size of the input, denoted as n. When an algorithm is said to have a complexity of O(n), it indicates that the time or resources required by the algorithm increase linearly as the size of the input increases. This means that if you double the size of the input, the time taken by the algorithm would also approximately double. This linear relationship is beneficial as it is predictable and allows for efficient performance scaling for larger datasets. Other options describe different complexities: constant time complexity would be O(1), indicating no relationship to input size; exponential growth would be represented by O(2^n), showing very rapid increases in resource use; and logarithmic complexity, such as O(log n), would suggest a much slower increase. Thus, the choice that aligns with the linear scaling of algorithm complexity is indeed the correct one.