What are some advantages of incorporating algorithmic complexity in grading tests and assignments given to students?
Currently, students in 11th grade at my school are required in tests to write functions that should preform some operation (usually operations on data structures like
This works fairly well in terms of checking whether a student knows how to use those data structures.
However, it's not uncommon to see an answer that does, eventually, preform the required operation; and yet its complexity is $O(n^3)$ (no kidding. The specific case I'm thinking of is one where the student worked with the unsorted linked list of stacks1 in 3 nested for loops).
The students are required, after they write their functions, to also write the complexity of their solutions.
In a quest to improve the students' thinking skills, I thought that maybe we should give bonus points if the solutions are inventive and less complex than a head on approach. This means that if a student's function is $O(n)$ for a task that a direct assault would be of $O(n^2)$, they should get more points.
This can also apply to various assignments we can give them, in addition to the tests we already have (or maybe make the tests slightly easier and then add assignments).
The students are in a CS major, and they have experience with java, OOP, Data structures and basic calculations of complexity for various, simple, algorithms)
1We gave them some arbitrary way of comparing stacks (of Integers): The sum of elements.