The problem is seemingly simple: given a sudoku board, how can that board be solved? There are many ways to solve the problem, but the one untilized here is the wave function collapse algorithm. This program is a command line executable written in Rust that can take an input board (in the format of a CSV) and output a new file containing the solved board.

The wave function collapse algorithm is an algorithm that has an intimidating name, but is quite tame from a programming perspective. The fundimental idea is a generation algorithm, which assumes that any unknown is just a combination of all the possible states it could be, at once. For example, if you have a sudoku row of: [5, 3, 9, 2, x, 1, 4, y, 6], where x and y are tiles that you don't know, the wave function collapse algorithm would say that instead of x and y simply be unknown, or having no value, x and y are considered to both be at the state 7 and 8 at once. Then if (for example) [4, y, 6] are in a square that already has 8 in it, the y's state is just 7, and it "collapses" into a single state of 7. Once y is at a single state, the origional list is now [5, 3, 9, 2, x, 1, 4, 7, 6], so x only has one possible state: 8, meaning that the entire row collapses into a solution: [5, 3, 9, 2, 8, 1, 4, 7, 6], and is solved.

Using Rust's Cargo Build tool, clone this repository, the run cargo build --release, which will output the compiled executable into target/release/sudoku_solve. To run it, simply put [path to executable] [path to board] [additional arguements]. For example: ./sudoku_solve board.csv -v -a. To view all arguements, run [path to executable] -h.

At the moment, due to the nature of algorithm in use, there are some limitations to what can be solved by the solver. For example, if, after all possible iterations, there are still tiles that cannot collapse, then there isn't anything that the algorithm can do. In this situation, the solver will spit out the unfinished board, and human intervention will be required. The --attempt-solve flag can be used to combat this, just not very effectively.

The config file is a proof of concept, displaying the ability for this project to have a config. It's written in JSON and currently provides a default output file name. The --config-dir command is provided to override the default configuration directory of a given operating system, such as Linux's ~/.config. It will initially look in for a sudoku_solve/config.json inside of a system's default configuration directory.

Much like the config file, Attempt-Solve is a proof of concept. It is highly unstable due to its nature, but if a board is not solvable with WFC, this flag can be raised to have the program guess a correct answer for one of the unknown tiles, and move on from there. This is unstable because there is no check as to whether or not the guessed answer is actually correct, and will often result in an error.