make the solver more generic
The solver is now not specific to Sudoku but pretty much any game where a set of square tiles needs to be filled according to a specific rule. Since it is not specific to Sudoku any more, it is a bit less performant, but that is not a big issue in my use case, so is fine.
This commit is contained in:
parent
4e1b5d7b05
commit
38157d7b5e
GPG key ID:
9EE6577A2A06F8F1
5 changed files with 388 additions and 166 deletions
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@ -6,3 +6,5 @@ edition = "2021"
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# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
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[dependencies]
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log = "*"
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simple_logger = "*"
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112
src/board.rs
Normal file
112
src/board.rs
Normal file
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@ -0,0 +1,112 @@
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use std::collections::HashMap;
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/**
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Contains the values on a given board as well as a bit of metadata.
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The actual tiles are stored in a `HashMap` to allow disparate data.
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*/
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#[derive(Clone, Debug)]
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pub struct Board {
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width: usize,
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height: usize,
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num_options: usize,
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tiles: HashMap<(usize, usize), usize>,
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}
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impl Board {
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/**
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Creates a new board.
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Panics if width or height are zero, or there are less than two options.
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*/
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pub fn new(width: usize, height: usize, num_options: usize) -> Self {
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assert!(width != 0);
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assert!(height != 0);
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assert!(num_options >= 2);
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Self {
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width,
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height,
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num_options,
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tiles: HashMap::new(),
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}
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}
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pub fn get_width(&self) -> usize {
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self.width
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}
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pub fn get_height(&self) -> usize {
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self.height
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}
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pub fn get_num_options(&self) -> usize {
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self.num_options
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}
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/**
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Set the value of a tile, or removes it if `None` is given.
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Returns the previous value or `None`.
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Panics if `x` or `y` are beyond the boards dimensions or `value` is greater or equal to `num_options`.
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*/
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pub fn set_tile(&mut self, x: usize, y: usize, value: Option<usize>) -> Option<usize> {
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assert!(x < self.width);
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assert!(y < self.height);
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if let Some(value) = value {
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assert!(value < self.num_options);
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self.tiles.insert((x, y), value)
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} else {
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self.tiles.remove(&(x, y))
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}
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}
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/**
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Get the value of a tile, or `None` if no value is known.
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Panics if `x` or `y` are beyond the boards dimensions.
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*/
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pub fn get_tile(&self, x: usize, y: usize) -> Option<usize> {
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assert!(x < self.width);
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assert!(y < self.height);
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self.tiles.get(&(x, y)).copied()
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}
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/**
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Get all the values of a column, in ascending y order.
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If a value in one row is not present, `None` is given instead.
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*/
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pub fn get_column(&self, x: usize) -> Vec<Option<usize>> {
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(0..self.height)
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.map(|y| self.tiles.get(&(x, y)).copied())
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.collect()
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}
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/**
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Get all the values of a row, in ascending x order.
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If a value in one column is not present, `None` is given instead.
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*/
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pub fn get_row(&self, y: usize) -> Vec<Option<usize>> {
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(0..self.width)
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.map(|x| self.tiles.get(&(x, y)).copied())
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.collect()
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}
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}
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impl std::fmt::Display for Board {
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fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
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for x in 0..self.width {
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for y in 0..self.height {
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if let Some(value) = self.tiles.get(&(x, y)) {
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write!(f, "{value}\t")?;
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} else {
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write!(f, "?\t")?;
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}
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}
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writeln!(f)?;
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}
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Ok(())
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}
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}
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118
src/constrain.rs
Normal file
118
src/constrain.rs
Normal file
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@ -0,0 +1,118 @@
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use crate::board::Board;
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use std::collections::HashMap;
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pub type BoardCheckFunction = dyn Fn(&Board) -> bool;
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/**
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Implementation of the actual solving algorithm.
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## Parameters
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* `board`: The (incomplete) board to be solved, which will be modified to contain the solution.
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* `check_fn`: A function that, given the board determines whether the board is valid, i.e. the rules of the game.
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## Return value
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Returns `true` if the board has been solved. The initial given `board` will have been modified to contain it.
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Returns `false` if the rules as defined by `check_fn` do not allow any valid solution of the initial board. The value of `board` may nevertheless have been modified.
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*/
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pub fn constrain_board(board: &mut Board, check_fn: &BoardCheckFunction) -> bool {
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_constrain_board(board, check_fn, None)
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}
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fn _constrain_board(
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board: &mut Board,
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check_fn: &BoardCheckFunction,
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hints: Option<HashMap<(usize, usize), Vec<usize>>>,
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) -> bool {
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let mut anything_changed = true;
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let mut memo = hints.unwrap_or_default();
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while anything_changed {
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anything_changed = false;
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for x in 0..board.get_width() {
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for y in 0..board.get_height() {
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if board.get_tile(x, y).is_some() {
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continue;
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}
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// Removing the item from the memo list since it will be replaced later
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// if it still makes sense to memoize for this tile and this avoids cloning.
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let mut valid = memo
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.remove(&(x, y))
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.unwrap_or_else(|| (0..board.get_num_options()).collect());
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log::trace!("valid {valid:?}");
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// only keep the options which result in a valid overall board
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valid.retain(|&opt| {
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board.set_tile(x, y, Some(opt));
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check_fn(&board)
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});
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log::trace!("still valid {valid:?}");
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match valid.len() {
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0 => {
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// invalid board
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board.set_tile(x, y, None);
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log::error!("no valid tiles at {x},{y}");
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return false;
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}
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1 => {
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// there is only one option
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board.set_tile(x, y, valid.pop());
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anything_changed = true;
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}
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_ => {
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// there are multiple options, restore the board for now and keep trying
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board.set_tile(x, y, None);
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memo.insert((x, y), valid);
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}
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}
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}
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}
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}
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// After this loop is done, it is guaranteed that memo contains only valid options
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// because all unfilled cells will have been checked.
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if memo.is_empty() {
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// There aren't any memoized values, this must mean that there are no empty fields
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// and we have already solved this board.
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log::debug!("solved (before recursion)");
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return true;
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}
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let old_board = board.clone();
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// find the coordinate with the least amount of possibilities
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let mut coords = memo
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.iter()
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.map(|(key, val)| (*key, val.len()))
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.collect::<Vec<_>>();
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coords.sort_unstable_by_key(|&t| t.1);
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// SAFTEY: can unwrap because `memo` is not empty, so coords will have
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// at least one entry
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let best_coord = coords.first().copied().unwrap().0;
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// SAFETY: can unwrap because we got this coordinate pair from memo
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let valid = memo.remove(&best_coord).unwrap();
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let (x, y) = best_coord;
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log::info!("starting recursion at {x},{y}");
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for opt in valid {
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*board = old_board.clone();
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board.set_tile(x, y, Some(opt));
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if _constrain_board(board, check_fn, Some(memo.clone())) {
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// TODO: figure out how to find multiple solutions
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log::debug!("solved (with recursion)");
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return true;
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}
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}
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// if we get here we tried all options and did not find one
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*board = old_board;
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log::error!("did not find a valid solution");
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false
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}
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207
src/main.rs
207
src/main.rs
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@ -1,169 +1,44 @@
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struct Board([u8; 9 * 9]);
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struct SuperBoard([bool; 9 * 9 * 9]);
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impl std::fmt::Display for Board {
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fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
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for i in 0..9 * 9 {
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if i % 9 > 0 {
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if i % 3 == 0 {
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write!(f, "|")?;
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} else {
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write!(f, " ")?;
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}
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} else if i > 0 && i % (9 * 3) == 0 {
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writeln!(f, "-----+-----+-----")?;
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}
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match self.0[i] {
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0 => {
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write!(f, " ")?;
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}
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n => {
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write!(f, "{n}")?;
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}
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}
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if i % 9 == 8 {
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writeln!(f)?;
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}
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}
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Ok(())
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}
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}
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impl std::fmt::Display for SuperBoard {
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fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
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for j in 0..9 * 9 * 9 {
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let col = j / 3 % 9;
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let row = j / (9 * 9);
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let n = j / 9 / 3 % 3 * 3 + j % 3;
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if j == 0 {
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// start of grid
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} else if j % 243 == 0 {
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writeln!(f, "-----------+-----------+-----------")?;
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} else if j % 81 == 0 {
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writeln!(f, "...........|...........|...........")?;
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} else if j % 27 == 0 {
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// start of line
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} else if j % 9 == 0 {
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write!(f, "|")?;
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} else if j % 3 == 0 {
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write!(f, ".")?;
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}
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let offset = n + (col * 9) + (row * 9 * 9);
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if self.0[offset] {
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write!(f, "{}", n + 1)?;
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} else {
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write!(f, " ")?;
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}
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if j % 27 == 26 {
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// end of line
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writeln!(f)?;
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}
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}
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Ok(())
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}
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}
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impl From<&Board> for SuperBoard {
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fn from(board: &Board) -> SuperBoard {
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let mut super_board = [false; 9 * 9 * 9];
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for (i, &cell) in board.0.iter().enumerate() {
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let super_i = i * 9;
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match cell {
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0 => {
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for i in 0..9 {
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super_board[super_i + i] = true;
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}
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}
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n => {
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super_board[super_i + n as usize - 1] = true;
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}
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}
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}
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SuperBoard(super_board)
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}
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}
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impl Board {
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fn constrain(&mut self) -> Result<SuperBoard, ()> {
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let mut collapsed = self
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.0
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.iter()
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.enumerate()
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.filter(|(_, &x)| x != 0)
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.map(|(i, _)| i)
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.collect::<Vec<_>>();
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let mut super_board = SuperBoard::from(&*self);
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while let Some(i) = collapsed.pop() {
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let value = self.0[i];
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assert!(value > 0);
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let offset = (value - 1) as usize;
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// column
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let col_start = i % 9;
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let row_start = i - col_start;
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let box_start = i / 27 * 27 + i % 9 / 3 * 3;
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let to_constrain = (col_start..81)
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.step_by(9)
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.chain((row_start..81).take(9))
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.chain((box_start..81).step_by(9).take(3).flat_map(|x| x..x + 3))
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.collect::<std::collections::HashSet<_>>();
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for j in to_constrain.into_iter() {
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if i == j {
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continue;
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}
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// safe to unwrap because none of the above can ever go outside the predefined bounds
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let x = &mut super_board.0[j * 9 + offset];
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if *x {
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*x = false;
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let cell = &super_board.0[(j * 9)..(j * 9 + 9)];
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match cell.iter().filter(|&&x| x).count() {
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0 => return Err(()),
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1 => {
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self.0[j] = cell
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.iter()
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.enumerate()
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.find(|(_, &x)| x)
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.map(|(i, _)| i + 1)
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.unwrap() as u8;
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if !collapsed.contains(&j) {
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collapsed.push(j);
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}
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}
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_ => (),
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}
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}
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}
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}
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Ok(super_board)
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}
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}
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pub mod board;
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mod constrain;
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mod rules;
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fn main() {
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let mut board = Board([
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0, 6, 0, /**/ 0, 0, 1, /**/ 0, 0, 3,
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8, 0, 0, /**/ 0, 0, 0, /**/ 0, 1, 9,
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5, 0, 2, /**/ 0, 7, 0, /**/ 8, 4, 0,
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/**********************************/
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4, 0, 6, /**/ 9, 0, 2, /**/ 3, 0, 5,
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0, 0, 0, /**/ 8, 0, 7, /**/ 0, 0, 0,
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1, 0, 7, /**/ 5, 0, 3, /**/ 4, 0, 8,
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/**********************************/
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0, 4, 1, /**/ 0, 9, 0, /**/ 5, 0, 2,
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9, 2, 0, /**/ 0, 0, 0, /**/ 0, 0, 7,
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6, 0, 0, /**/ 2, 0, 0, /**/ 0, 9, 0,
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]);
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board.constrain().unwrap();
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println!("{}", board);
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simple_logger::init_with_level(log::Level::Info).unwrap();
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let mut board = board::Board::new(9, 9, 9);
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board.set_tile(0, 1, Some(6 -1));
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board.set_tile(0, 2, Some(8 -1));
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board.set_tile(0, 4, Some(3 -1));
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board.set_tile(0, 7, Some(7 -1));
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board.set_tile(1, 0, Some(2 -1));
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board.set_tile(1, 3, Some(9 -1));
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board.set_tile(1, 6, Some(1 -1));
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board.set_tile(2, 1, Some(4 -1));
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board.set_tile(2, 4, Some(8 -1));
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board.set_tile(2, 5, Some(1 -1));
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board.set_tile(2, 8, Some(3 -1));
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board.set_tile(3, 2, Some(7 -1));
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board.set_tile(3, 6, Some(4 -1));
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board.set_tile(4, 3, Some(8 -1));
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board.set_tile(4, 4, Some(1 -1));
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board.set_tile(4, 5, Some(9 -1));
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board.set_tile(5, 2, Some(9 -1));
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board.set_tile(5, 6, Some(2 -1));
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board.set_tile(6, 0, Some(7 -1));
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board.set_tile(6, 3, Some(3 -1));
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board.set_tile(6, 4, Some(9 -1));
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board.set_tile(6, 7, Some(4 -1));
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board.set_tile(7, 2, Some(2 -1));
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board.set_tile(7, 5, Some(5 -1));
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board.set_tile(7, 8, Some(6 -1));
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board.set_tile(8, 1, Some(3 -1));
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board.set_tile(8, 4, Some(7 -1));
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board.set_tile(8, 6, Some(9 -1));
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board.set_tile(8, 7, Some(5 -1));
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|
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if constrain::constrain_board(&mut board, &rules::valid_board_sudoku) {
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println!("{board}");
|
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} else {
|
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eprintln!("could not solve board!");
|
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}
|
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}
|
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|
|
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115
src/rules.rs
Normal file
115
src/rules.rs
Normal file
|
|
@ -0,0 +1,115 @@
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use std::collections::HashSet;
|
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|
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use crate::board::Board;
|
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|
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/**
|
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Checks whether a board is valid according to the rules of the game
|
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"Unruly" from Simon Tathams Portable Puzzle Collection.
|
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|
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Only works on boards which have an even number of tiles in width and height,
|
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and which have only two options.
|
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*/
|
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pub fn valid_board_unruly(board: &Board) -> bool {
|
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debug_assert!(board.get_num_options() == 2);
|
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debug_assert!(board.get_width() % 2 == 0);
|
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debug_assert!(board.get_height() % 2 == 0);
|
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|
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fn valid_window(win: &[Option<usize>]) -> bool {
|
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win[0].zip(win[1]).map_or(true, |(x, y)| x != y)
|
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|| win[1].zip(win[2]).map_or(true, |(x, y)| x != y)
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}
|
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|
||||
// check each column and row:
|
||||
// * may only contain n/2 number of one option
|
||||
// * may not contain more than 2 consecutives
|
||||
for x in 0..board.get_width() {
|
||||
let col = board.get_column(x);
|
||||
for opt in [0, 1] {
|
||||
if col.iter().filter(|&&x| x == Some(opt)).count() > (board.get_width() / 2) {
|
||||
log::warn!("col {x} invalid: too many of {opt}");
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
if !col.windows(3).all(valid_window) {
|
||||
log::warn!("col {x} invalid: invalid window");
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
for y in 0..board.get_height() {
|
||||
let row = board.get_row(y);
|
||||
for opt in [0, 1] {
|
||||
if row.iter().filter(|&&x| x == Some(opt)).count() > (board.get_width() / 2) {
|
||||
log::warn!("row {y} invalid: too many of {opt}");
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
if !row.windows(3).all(valid_window) {
|
||||
log::warn!("row {y} invalid: invalid window");
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
true
|
||||
}
|
||||
|
||||
/**
|
||||
Checks whether a board is valid according to the rules of ordinary 9x9 Sudoku:
|
||||
Numbers must be unique in row, column and each 3x3 cell.
|
||||
*/
|
||||
pub fn valid_board_sudoku(board: &Board) -> bool {
|
||||
debug_assert!(board.get_num_options() == 9);
|
||||
debug_assert!(board.get_width() == 9);
|
||||
debug_assert!(board.get_height() == 9);
|
||||
|
||||
fn get_cell(board: &Board, start_x: usize, start_y: usize) -> Vec<Option<usize>> {
|
||||
(start_x..start_x + 3)
|
||||
.flat_map(|x| (start_y..start_y + 3).map(|y| (x, y)).collect::<Vec<_>>())
|
||||
.map(|(x, y)| board.get_tile(x, y))
|
||||
.collect()
|
||||
}
|
||||
|
||||
// check columns: must be unique
|
||||
for x in 0..9 {
|
||||
let mut set = HashSet::new();
|
||||
if !board
|
||||
.get_column(x)
|
||||
.iter()
|
||||
.filter_map(|&x| x)
|
||||
.all(|x| set.insert(x))
|
||||
{
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
// check rows: must be unique
|
||||
for y in 0..9 {
|
||||
let mut set = HashSet::new();
|
||||
if !board
|
||||
.get_row(y)
|
||||
.iter()
|
||||
.filter_map(|&x| x)
|
||||
.all(|x| set.insert(x))
|
||||
{
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
// check 3x3 cells: must be unique
|
||||
for x in [0,3,6] {
|
||||
for y in [0,3,6] {
|
||||
let mut set = HashSet::new();
|
||||
if !get_cell(board, x, y)
|
||||
.iter()
|
||||
.filter_map(|&x| x)
|
||||
.all(|x| set.insert(x))
|
||||
{
|
||||
return false;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
true
|
||||
}
|
||||
Loading…
Reference in a new issue