Describe the best way to store heat flow information for the surface of
a hollow box.
This could be done in a couple of ways. The first is to just make a 3D
array structure of the dimensions of the box and only fill in and
calculate the heat data on the outside elements. This wastes all the
memory for the elements in the middle, though. Depending on the size of
the box, this could be huge!
Another way to do it is to take the sides of the box apart. There would
be two of each shape: top & bottom, left & right, front & back.
The hard part would be calculating the heat flow at the edges as they would
have to map from one separate piece to another. But to save memory, it
could be done. Would this save memory? Well, we'd still want to store
these as a single 3D array, so it would waste space at the corners. We
could draw this out and calculate how much memory is wasted in the corner
regions vs how much memory was wasted with the interior of the box and set
up/solve the inequality.
Then the only question is, is overcoming the edge heat flow difficulty
worth it to save any memory the sides storage technique can? This has to
be answered by the individual/team implementing the solution.