Firstly, sorry for the vagueness of the title.
I don't know if there is a name for this sort of algorithm.
I am interested in finding out how this scenario could be implemented.
Say I have a matrix (columns and rows) where each "cell" can have one of two values ("on" and "off").
Each cell's "background" should also display a number that tells how many of the adjacent cells are "on".
For example, if every cell should be "on":
| A | B | C | A | B | C | |
|---|---|---|---|---|---|---|
| 4 | 6 | 4 | --> | on | on | on |
| 6 | 9 | 6 | on | on | on | |
| 4 | 6 | 4 | on | on | on |
This is pretty simple to implement. The question is: what's the minimal amount of tips I can have, and how can I implement this?
In this same example, it would be enough to have:
| A | B | C | A | B | C | |
|---|---|---|---|---|---|---|
| --> | on | on | on | |||
| 9 | on | on | on | |||
| on | on | on |
It can get trickier:
| A | B | C | A | B | C | |
|---|---|---|---|---|---|---|
| --> | on | ? | off | |||
| 4 | 1 | on | ? | off | ||
| on | ? | off |
In this last example, the matrix would be larger and have other hints that later on would help determine the remaining cells.
So how can this be achieved?