What does time complexity measure?

Time complexity measures the time an algorithm takes to complete as a function of the size of its input. It provides an estimation of how the execution time will increase as the amount of data grows, which is essential when analyzing the efficiency of algorithms. This measurement often uses Big O notation to classify algorithms according to their worst-case or average-case run times based on their input size.

Understanding time complexity is crucial for selecting the most efficient algorithm for a given problem, especially when dealing with large inputs, as it helps predict resource usage without necessarily executing the algorithm. This approach allows software developers to plan and optimize their programs effectively.

The other options relate to important aspects of algorithms but do not correctly define time complexity. For instance, while memory usage is important to consider (which pertains to space complexity), it doesn't measure time. Similarly, speed of computer hardware is irrelevant to the algorithm's time complexity as it deals specifically with the algorithm itself. Finally, the relationship of time to cost, while potentially relevant in certain contexts, does not reflect the basic definition of time complexity.