How it works...

The std::vector provides the [] operator and the at function, and they basically do exactly the same job. The at function, however, performs additional bounds checks and throws an exception if the vector bounds are exceeded. This is super useful in situations like ours, but also makes the program a little bit slower.

Especially when doing numeric computations with indexed members which need to be really fast, it is advantageous to stick to [] indexed access. In any other situation, the at function helps uncovering bugs with usually negligible performance loss.