What does it mean if an algorithm has a time complexity of O(n)?

When an algorithm has a time complexity of O(n), it signifies that the algorithm's run time scales linearly with the size of the input. This means that as the amount of data (n) increases, the time it takes to execute the algorithm increases proportionally. For example, if you double the input size, the time taken to complete the algorithm also approximately doubles.

This linear relationship is essential in analyzing the efficiency of algorithms, as it helps predict how they will perform with varying sizes of input. Time complexities are used to classify algorithms based on their efficiency and scalability. In many scenarios, achieving linear time complexity is desirable, particularly in applications requiring efficiency with increasingly large datasets, as algorithms that operate in linear time can handle growth more effectively compared to those with higher complexities.

In contrast, time complexities characterized as constant time imply that the execution time does not depend on the input size, while exponential or logarithmic complexities would suggest different rates of growth that are not linear. Thus, B accurately captures the essence of O(n) time complexity.