Final answer:
The complexity of an algorithm should be expressed using both time complexity and space complexity to provide a complete picture of its efficiency. Time complexity refers to the execution time, while space complexity relates to the memory requirements of the algorithm.
Step-by-step explanation:
To express the complexity of an algorithm, you should use both time complexity and space complexity. Time complexity refers to the amount of time it takes to run an algorithm, often expressed as a function of the input size (for example, O(n), O(log n), etc.). Space complexity, on the other hand, represents the amount of memory space required by the algorithm, also as a function of the input size.
It's important to understand both these measures when evaluating an algorithm because they provide a more complete picture of the algorithm's efficiency. For instance, an algorithm might be really fast (excellent time complexity) but use up a lot of memory (poor space complexity), which might not be suitable for systems with limited memory resources.
When discussing algorithmic complexity, it is common to mention 'Big O' notation, which is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. It is a key concept in computational complexity theory used by more than 100 computer science courses worldwide to analyze algorithms' performance.