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//! This module is about strategic solving of Sudoku. In contrast to //! backtracking, this is often faster, but cannot solve all Sudoku. However, //! strategic backtracking is also possible, which still uses backtracking, but //! also uses strategies to reduce the search space. This is solely a //! performance optimization and offers no functional advantage over pure //! backtracking. For more information, view the [StrategicBacktrackingSolver]. //! //! This module contains the definition of the [Strategy] trait, which all //! strategies must implement, as well as the [SudokuInfo] struct, which wraps //! metadata about Sudoku that can be used by strategies to exchange //! information. //! //! `sudoku-variants` offers a small library of pre-defined strategies you can //! use. See the [impls] module for further details. //! //! # Defining difficulties using strategies //! //! Besides a performance optimization for backtracking, strategies also have //! the use of defining a difficulty level for generated Sudoku. This can be //! done by instantiating the [Reducer](crate::generator::Reducer) with a //! [StrategicSolver]. The resulting Sudoku is then guaranteed to be solveable //! by the provided strategy. As an example consider the following code, which //! generates a classic Sudoku that can be solved by solely looking for naked //! singles (see [NakedSingleStrategy]). //! //! ``` //! use sudoku_variants::constraint::DefaultConstraint; //! use sudoku_variants::generator::{Generator, Reducer}; //! use sudoku_variants::solver::{Solution, Solver}; //! use sudoku_variants::solver::strategy::{ //! NakedSingleStrategy, //! StrategicSolver //! }; //! //! // Generate the full Sudoku //! let mut generator = Generator::new_default(); //! let mut sudoku = generator.generate(3, 3, DefaultConstraint).unwrap(); //! let expected_solution = sudoku.grid().clone(); //! //! // Define the difficulty level by providing a not-so-powerful solver //! let solver = StrategicSolver::new(NakedSingleStrategy); //! //! // Reduce the Sudoku using the solver //! let mut reducer = Reducer::new(solver.clone(), rand::thread_rng()); //! reducer.reduce(&mut sudoku); //! //! // Test that the solver can in fact solve the Sudoku //! let actual_solution = solver.solve(&sudoku); //! assert_eq!(Solution::Unique(expected_solution), actual_solution); //! ``` //! //! # Implementing a custom strategy //! //! As an example let's define a strategy that puts a 1 in every cell without //! any other option. This is a subset of the [NakedSingleStrategy]. //! //! To do this, we must implement the [Strategy] trait, which only requires the //! [Strategy::apply] method. This method gets an instance of a [SudokuInfo] //! struct for the Sudoku at hand. We must then implement our logic to make //! deductions and if we can find something, that is, we can write in a digit //! or remove an option, we can modify the sudoku info. If we changed //! something, we must return true, and false otherwise. This indicates to the //! solvers whether it is useful to apply this strategy or other strategies //! again, since we may find something new. //! //! In our case, we can implement this method as follows: //! //! ``` //! use sudoku_variants::constraint::Constraint; //! use sudoku_variants::solver::strategy::{Strategy, SudokuInfo}; //! //! struct NakedOneStrategy; //! //! impl Strategy for NakedOneStrategy { //! fn apply(&self, sudoku_info: &mut SudokuInfo<impl Constraint + Clone>) //! -> bool { //! let size = sudoku_info.sudoku().grid().size(); //! let mut changed = false; //! //! // We must iterate over every cell. //! for row in 0..size { //! for column in 0..size { //! // The SudokuInfo struct stores which digits could go into //! // each cell. We can get that information with get_options. //! let options = //! sudoku_info.get_options(column, row).unwrap(); //! //! if options.len() == 1 && options.contains(1) { //! // Only a 1 can go into this cell! We found something! //! // We batch all changes using enter_cell_no_update for //! // performance reasons. //! sudoku_info.enter_cell_no_update(column, row, 1) //! .unwrap(); //! changed = true; //! } //! } //! } //! //! changed //! } //! } //! ``` use crate::Sudoku; use crate::constraint::Constraint; use crate::error::{SudokuError, SudokuResult}; use crate::util::USizeSet; pub mod impls; pub mod solvers; pub use impls::*; pub use solvers::*; /// Enriches a [Sudoku] with additional information about which numbers can go /// into the cells. This is analogous to the pencil markings a human player /// would make. It is used by [Strategies](Strategy) to communicate the results /// of logical reasoning. /// /// This struct already excludes options which violate the Sudoku's constraint, /// unless unprocessed changes have been made. #[derive(Clone)] pub struct SudokuInfo<C: Constraint + Clone> { sudoku: Sudoku<C>, cell_options: Vec<USizeSet>, enqueued_cells: Vec<(usize, usize, usize)>, up_to_date: bool } impl<C: Constraint + Clone> SudokuInfo<C> { /// Creates a new Sudok info for a [Sudoku]. The options for all cells that /// are empty in the provided Sudoku are all valid digits, and the options /// for cells which are filled in the Sudoku are only the digit in that /// cell. pub fn from_sudoku(sudoku: Sudoku<C>) -> SudokuInfo<C> { let size = sudoku.grid().size(); let mut cell_options = Vec::new(); for row in 0..size { for column in 0..size { let cell = sudoku.grid().get_cell(column, row).unwrap(); let options = match cell { Some(number) => USizeSet::singleton(1, size, number).unwrap(), None => { let mut options = USizeSet::new(1, size).unwrap(); for option in 1..=size { let is_valid = sudoku .is_valid_number(column, row, option) .unwrap(); if is_valid { options.insert(option).unwrap(); } } options } }; cell_options.push(options); } } SudokuInfo { sudoku, cell_options, enqueued_cells: Vec::new(), up_to_date: true } } fn verified_index(&self, column: usize, row: usize) -> SudokuResult<usize> { let size = self.size(); if column >= size || row >= size { Err(SudokuError::OutOfBounds) } else { Ok(crate::index(column, row, size)) } } /// Gets the content of the cell at the specified position. /// /// This is syntactic sugar for `x.sudoku().grid().get_cell(...)`. /// /// # Arguments /// /// * `column`: The column (x-coordinate) of the desired cell. Must be in /// the range `[0, size[`. /// * `row`: The row (y-coordinate) of the desired cell. Must be in the /// range `[0, size[`. /// /// # Errors /// /// If either `column` or `row` are not in the specified range. In that /// case, `SudokuError::OutOfBounds` is returned. pub fn get_cell(&self, column: usize, row: usize) -> SudokuResult<Option<usize>> { self.sudoku.grid().get_cell(column, row) } /// Enqueues a number to be assigned to the content of the cell at the /// specified position on the next update. If the cell is not empty at that /// point, the old number will be overwritten. /// /// In contrast with /// [enter_cell_no_update](SudokuInfo::enter_cell_no_update), this function /// never enters the number into the cell right away, so when querying the /// cell it will still look empty. This is done both for performance /// reasons and to preserve semantics of only applying a strategy once for /// strategies which may process the same cell more than once, which is /// important for the bounded backtracking strategies. To ensure that the /// state of this is up-to-date, i.e. the new cells are entered and the /// options are adapted to accomodate for them, call /// [invalidate](SudokuInfo::invalidate) after you are finished enqueueing /// changes. /// /// # Arguments /// /// * `column`: The column (x-coordinate) of the assigned cell. Must be in /// the range `[0, size[`. /// * `row`: The row (y-coordinate) of the assigned cell. Must be in the /// range `[0, size[`. /// * `number`: The number to assign to the specified cell. Must be in the /// range `[1, size]`. /// /// # Errors /// /// * `SudokuError::OutOfBounds` If either `column` or `row` are not in the /// specified range. /// * `SudokuError::InvalidNumber` If `number` is not in the specified /// range. pub fn enqueue_enter_cell(&mut self, column: usize, row: usize, number: usize) -> SudokuResult<()> { let size = self.sudoku.grid().size(); if column >= size || row >= size { return Err(SudokuError::InvalidDimensions); } if number < 1 || number > size { return Err(SudokuError::InvalidNumber); } self.enqueued_cells.push((column, row, number)); self.up_to_date = false; Ok(()) } /// Sets the content of the cell at the specified position to the given /// number. If the cell was not empty, the old number will be overwritten. /// /// In contrast with [enter_cell](SudokuInfo::enter_cell), this method does /// not remove cell options that are invalidated by the new digit. This is /// done for performance reasons to allow batching of multiple changes /// before updating the options. To ensure the cell options are up-to-date, /// call [invalidate](SudokuInfo::invalidate) after making any changes. /// /// # Arguments /// /// * `column`: The column (x-coordinate) of the assigned cell. Must be in /// the range `[0, size[`. /// * `row`: The row (y-coordinate) of the assigned cell. Must be in the /// range `[0, size[`. /// * `number`: The number to assign to the specified cell. Must be in the /// range `[1, size]`. /// /// # Errors /// /// * `SudokuError::OutOfBounds` If either `column` or `row` are not in the /// specified range. /// * `SudokuError::InvalidNumber` If `number` is not in the specified /// range. pub fn enter_cell_no_update(&mut self, column: usize, row: usize, number: usize) -> SudokuResult<()> { self.sudoku.grid_mut().set_cell(column, row, number)?; let options = self.get_options_mut(column, row).unwrap(); options.clear(); options.insert(number).unwrap(); self.up_to_date = false; Ok(()) } /// Sets the content of the cell at the specified position to the given /// number. If the cell was not empty, the old number will be overwritten. /// /// In contrast with /// [enter_cell_no_update](SudokuInfo::enter_cell_no_update), this method /// immediately removes all cell options that are invalidated by the new /// digit. /// /// # Arguments /// /// * `column`: The column (x-coordinate) of the assigned cell. Must be in /// the range `[0, size[`. /// * `row`: The row (y-coordinate) of the assigned cell. Must be in the /// range `[0, size[`. /// * `number`: The number to assign to the specified cell. Must be in the /// range `[1, size]`. /// /// # Errors /// /// * `SudokuError::OutOfBounds` If either `column` or `row` are not in the /// specified range. /// * `SudokuError::InvalidNumber` If `number` is not in the specified /// range. pub fn enter_cell(&mut self, column: usize, row: usize, number: usize) -> SudokuResult<()> { self.enter_cell_no_update(column, row, number)?; self.update(); Ok(()) } fn update(&mut self) { let size = self.size(); let mut options_to_remove = Vec::new(); let enqueued_cells: Vec<(usize, usize, usize)> = self.enqueued_cells.drain(..).collect(); for (column, row, number) in enqueued_cells { self.enter_cell_no_update(column, row, number).unwrap(); } for row in 0..size { for column in 0..size { let content = self.sudoku.grid().get_cell(column, row) .unwrap(); if content.is_some() { continue; } // TODO find a way to use get_options without triggering the // borrow checker let options = &mut self.cell_options[crate::index(column, row, size)]; options_to_remove.clear(); for option in options.iter() { let is_valid = self.sudoku .is_valid_number(column, row, option) .unwrap(); if !is_valid { options_to_remove.push(option); } } for &option_to_remove in options_to_remove.iter() { options.remove(option_to_remove).unwrap(); } } } self.up_to_date = true; } /// Removes all cell options that have been invalidated by digits entered /// using [enter_cell_no_update](SudokuInfo::enter_cell_no_update) which /// have not yet been processed. If there are no pending digits, nothing /// will be done. pub fn invalidate(&mut self) { if !self.up_to_date { self.update(); } } /// Gets a [USizeSet] of the possible digits that can be entered into the /// cell at the given position according to this grid info. /// /// Note that, because options are adapted to new digits lazily, this /// operation may require changes to this instance, namely if digits were /// changed since the last call to `get_options` or `get_options_mut`. This /// means a mutable reference to this instance is required. /// /// # Arguments /// /// * `column`: The column (x-coordinate) of the desired cell. Must be in /// the range `[0, size[`. /// * `row`: The row (y-coordinate) of the desired cell. Must be in the /// range `[0, size[`. /// /// # Errors /// /// If either `column` or `row` are not in the specified range. In that /// case, `SudokuError::OutOfBounds` is returned. pub fn get_options(&self, column: usize, row: usize) -> SudokuResult<&USizeSet> { let index = self.verified_index(column, row)?; Ok(&self.cell_options[index]) } /// Gets a mutable reference to the [USizeSet] that tracks the possible /// digits that can be entered into the cell at the given position /// according to this grid info. /// /// Note that, because options are adapted to new digits lazily, this /// operation may require changes to this instance, namely if digits were /// changed since the last call to `get_options` or `get_options_mut`. /// /// # Arguments /// /// * `column`: The column (x-coordinate) of the desired cell. Must be in /// the range `[0, size[`. /// * `row`: The row (y-coordinate) of the desired cell. Must be in the /// range `[0, size[`. /// /// # Errors /// /// If either `column` or `row` are not in the specified range. In that /// case, `SudokuError::OutOfBounds` is returned. pub fn get_options_mut(&mut self, column: usize, row: usize) -> SudokuResult<&mut USizeSet> { let index = self.verified_index(column, row)?; Ok(&mut self.cell_options[index]) } /// Gets the total size of the grid for which this instance tracks /// information on one axis (horizontally or vertically). Since grids are /// always squares, this is guaranteed to be valid for both axes. pub fn size(&self) -> usize { self.sudoku.grid().size() } /// Gets a read-only reference to the vector storing the options for every /// cell in a [USizeSet]. The cells are in eft-to-right, top-to-bottom /// order, where rows are together. pub fn cell_options(&self) -> &Vec<USizeSet> { &self.cell_options } /// Gets a mutable reference to the vector storing the options for every /// cell in a [USizeSet]. The cells are in left-to-right, top-to-bottom /// order, where rows are together. pub fn cell_options_mut(&mut self) -> &mut Vec<USizeSet> { &mut self.cell_options } /// Gets the width (number of columns) of one sub-block of the Sudoku. To /// ensure a square grid, this is also the number of blocks that compose /// the grid vertically. /// /// This is syntactic sugar for `x.sudoku().grid().block_width()`. pub fn block_width(&self) -> usize { self.sudoku.grid().block_width() } /// Gets the height (number of rows) of one sub-block of the Sudoku. To /// ensure a square grid, this is also the number of blocks that compose /// the grid horizontally. /// /// This is syntactic sugar for `x.sudoku().grid().block_height()`. pub fn block_height(&self) -> usize { self.sudoku.grid().block_height() } /// Assigns the content of another grid info to this one, that is, after /// the operation this grid info will equal `other`. The dimensions must be /// equivalent. /// /// # Errors /// /// If `other` has different dimensions to this instance. In that case, /// `SudokuError::InvalidDimensions` is returned. pub fn assign(&mut self, other: &SudokuInfo<C>) -> SudokuResult<()> { self.sudoku.grid_mut().assign(other.sudoku.grid())?; for i in 0..self.cell_options.len() { self.cell_options[i] = other.cell_options[i].clone(); } Ok(()) } /// Gets the [Sudoku] for which this Sudoku info stores additional /// information. pub fn sudoku(&self) -> &Sudoku<C> { &self.sudoku } /// Gets a mutable reference to the [Sudoku] for which this Sudoku info /// stores additional information. pub fn sudoku_mut(&mut self) -> &mut Sudoku<C> { &mut self.sudoku } fn op(&mut self, other: &SudokuInfo<C>, single_op: impl Fn((&mut Option<usize>, &mut USizeSet), (&Option<usize>, &USizeSet)) -> bool) -> SudokuResult<bool> { if self.block_width() != other.block_width() || self.block_height() != other.block_height() { return Err(SudokuError::InvalidDimensions); } let mut changed = false; let iter = (&mut self.sudoku).grid_mut().cells_mut().iter_mut() .zip((&mut self.cell_options).iter_mut()) .zip(other.sudoku().grid().cells().iter() .zip(other.cell_options().iter())); for (self_info, other_info) in iter { changed |= single_op(self_info, other_info); } if changed { self.update(); } Ok(changed) } /// Intersects this Sudoku info with the given other one, implying that all /// information of both is correct. All cells that are filled in in either /// will be written in the result and only options that are present in both /// will be retained. Note that contradictions (different digits in this /// and the other Sudoku info) will result in the cell being cleared and /// all options being removed. pub fn intersect_assign(&mut self, other: &SudokuInfo<C>) -> SudokuResult<bool> { self.op(other, |(self_cell, self_options), (other_cell, other_options)| { let cells_changed = if let Some(number) = other_cell { let old_number = self_cell.replace(*number); if Some(*number) == old_number { false } else { if old_number.is_some() { self_options.clear(); self_cell.take(); } true } } else { false }; let options_changed = self_options.intersect_assign(other_options).unwrap(); cells_changed || options_changed }) } /// Unifies this Sudoku info with the given other one, implying that all /// information of both *could* be correct. Options present in at least one /// will be put in the result and digits are only retained if they are /// present in both (unless the other does not have any options for that /// cell). Note that contradictions (different digits in this /// and the other Sudoku info) will result in the cell being cleared and /// both numbers being put in the option set. pub fn union_assign(&mut self, other: &SudokuInfo<C>) -> SudokuResult<bool> { self.op(other, |(self_cell, self_options), (other_cell, other_options)| { let content_changed = if let Some(self_number) = self_cell { if &Some(*self_number) == other_cell || other_options.is_empty() { false } else { self_cell.take(); true } } else if self_options.is_empty() { *self_cell = *other_cell; self_cell.is_some() } else { false }; let options_changed = self_options.union_assign(other_options).unwrap(); content_changed || options_changed }) } } impl<C: Constraint + Clone> PartialEq for SudokuInfo<C> { fn eq(&self, other: &Self) -> bool { if self.sudoku().grid() != other.sudoku().grid() { false } else if !self.up_to_date { let mut lhs = self.clone(); lhs.update(); lhs.eq(other) } else if !other.up_to_date { let mut other = other.clone(); other.update(); self.eq(&other) } else { self.cell_options() == other.cell_options() } } } /// A trait for strategies, which use logical reasoning to restrict the /// possibilities of a Sudoku. pub trait Strategy { /// Applies this strategy to the given Sudoku. The strategy may rely on and /// modify the information in the given `sudoku_info`. This instance is /// given to other strategies that participate in the solution and/or /// future iterations of the same strategy. It can thus be used to /// communicate insights. /// /// This method shall return `true` if and only if something has changed, /// that is, a digit has been entered or an option has been removed. fn apply(&self, sudoku_info: &mut SudokuInfo<impl Constraint + Clone>) -> bool; } #[cfg(test)] mod tests { use super::*; use crate::Sudoku; use crate::constraint::DefaultConstraint; #[test] fn sudoku_info_equality() { let sudoku = Sudoku::parse("2x2;\ ,1, ,4,\ ,2,3, ,\ , , ,2,\ , , , ", DefaultConstraint).unwrap(); let mut si1 = SudokuInfo::from_sudoku(sudoku.clone()); let mut si2 = SudokuInfo::from_sudoku(sudoku); assert!(si1 == si2); si1.enter_cell_no_update(3, 1, 1).unwrap(); assert!(si1 != si2); si2.enter_cell_no_update(3, 1, 1).unwrap(); assert!(si1 == si2); si1.update(); assert!(si1 == si2); si2.update(); assert!(si1 == si2); si1.get_options_mut(0, 3).unwrap().remove(1).unwrap(); assert!(si1 != si2); } fn get_different_sudoku_infos() -> (SudokuInfo<DefaultConstraint>, SudokuInfo<DefaultConstraint>) { let sudoku = Sudoku::parse("2x2;\ ,1, ,4,\ ,2,3, ,\ , , ,2,\ , , , ", DefaultConstraint).unwrap(); let mut si1 = SudokuInfo::from_sudoku(sudoku.clone()); let mut si2 = SudokuInfo::from_sudoku(sudoku); si1.enter_cell(2, 0, 2).unwrap(); si1.enter_cell(3, 1, 1).unwrap(); si2.enter_cell(3, 1, 1).unwrap(); si1.get_options_mut(0, 3).unwrap().remove(1).unwrap(); si2.get_options_mut(0, 3).unwrap().remove(1).unwrap(); si2.get_options_mut(1, 3).unwrap().remove(3).unwrap(); (si1, si2) } #[test] fn sudoku_info_union() { let (mut si1, si2) = get_different_sudoku_infos(); assert!(si1.union_assign(&si2).unwrap()); assert_eq!(None, si1.get_cell(2, 0).unwrap()); assert_eq!(Some(1), si1.get_cell(3, 1).unwrap()); assert!(!si1.get_options(0, 3).unwrap().contains(1)); assert!(si1.get_options(1, 3).unwrap().contains(3)); } #[test] fn sudoku_info_intersect() { let (mut si1, si2) = get_different_sudoku_infos(); assert!(si1.intersect_assign(&si2).unwrap()); assert_eq!(Some(2), si1.get_cell(2, 0).unwrap()); assert_eq!(Some(1), si1.get_cell(3, 1).unwrap()); assert!(!si1.get_options(0, 3).unwrap().contains(1)); assert!(!si1.get_options(1, 3).unwrap().contains(3)); } #[test] fn sudoku_info_operation_err() { let sudoku1 = Sudoku::parse("1x2;1,2,2,1", DefaultConstraint).unwrap(); let sudoku2 = Sudoku::parse("2x1;1,2,2,1", DefaultConstraint).unwrap(); let mut si1 = SudokuInfo::from_sudoku(sudoku1); let si2 = SudokuInfo::from_sudoku(sudoku2); assert_eq!(Err(SudokuError::InvalidDimensions), si1.union_assign(&si2)); assert_eq!(Err(SudokuError::InvalidDimensions), si1.intersect_assign(&si2)); } }