What measures the efficiency of an algorithm during execution?

The efficiency of an algorithm during execution is measured by its time complexity and space complexity.

Time complexity refers to the computational complexity that describes the amount of time an algorithm takes to run as a function of the size of the input to the program. It is usually expressed using Big O notation, which describes the upper bound of the time complexity in the worst-case scenario. For example, a linear search algorithm has a time complexity of O(n), meaning the time it takes to execute increases linearly with the size of the input data set.

Space complexity, on the other hand, refers to the amount of memory an algorithm needs to run. It includes both the space needed by the input data and the additional space (or auxiliary space) required by the algorithm to execute. Like time complexity, space complexity is also expressed using Big O notation. For instance, an algorithm that sorts an array in-place (i.e., it doesn't require any additional space) has a space complexity of O(1), indicating that the space required does not change with the size of the input array.

In addition to time and space complexity, the efficiency of an algorithm can also be influenced by factors such as the programming language used, the hardware on which the algorithm is run, and the specific details of the input data. However, when comparing algorithms, we usually focus on time and space complexity because these are inherent to the algorithm itself, rather than being dependent on external factors.

In conclusion, understanding the efficiency of an algorithm is crucial in computer science. It helps in choosing the most appropriate algorithm for a given task, based on the resources available and the specific requirements of the task. By analysing the time and space complexity of different algorithms, we can make informed decisions about which algorithm to use in a particular situation.