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//! Sudoku solving routines.
#[cfg(test)]
mod tests;
use std::iter::FusedIterator;
use super::board::*;
use bit_iter::BitIter;
/// Test whether a sudoku board state obeys the contraints of the game.
///
/// The constraints are:
///
/// * No digit 1-9 is repeated in any given row, column or square.
/// * Every cell contains a value from 0-9 inclusive.
///
/// Note that zeroes repesent unfilled cells, and do not count as duplicates.
///
/// ## Example
///
/// A board with a duplicate in the first column:
///
/// ```rust
/// # fn main() {
/// # use sudoku_solver::*;
/// let mut board = Board::from(&[[0u8; BOARD_SIZE]; BOARD_SIZE]);
/// board.set_cell(0, 0, 9);
/// board.set_cell(0, 5, 9);
///
/// assert!(!valid(&board));
/// # }
/// ```
pub fn valid(b: &Board) -> bool {
const PRECALC_MASKS: [u64; BOARD_SIZE + 1] = [
0x00_0000_0001,
0x00_0000_0010,
0x00_0000_0100,
0x00_0000_1000,
0x00_0001_0000,
0x00_0010_0000,
0x00_0100_0000,
0x00_1000_0000,
0x01_0000_0000,
0x10_0000_0000,
];
for y in 0..BOARD_SIZE {
for x in 0..BOARD_SIZE {
if b.get_cell(x, y) > 9 {
return false;
}
}
}
// Check rows.
for y in 0..BOARD_SIZE {
let mut acc = 0;
for x in 0..BOARD_SIZE {
acc += PRECALC_MASKS[b.get_cell(x, y) as usize];
}
if (acc & 0xee_eeee_eee0) != 0 {
return false;
}
}
// Check columns.
for x in 0..BOARD_SIZE {
let mut acc = 0;
for y in 0..BOARD_SIZE {
acc += PRECALC_MASKS[b.get_cell(x, y) as usize];
}
if (acc & 0xee_eeee_eee0) != 0 {
return false;
}
}
// Check squares.
for square in 0..BOARD_SIZE {
let mut acc = 0;
let x = SQUARE_SIZE * (square % SQUARE_SIZE);
let y = SQUARE_SIZE * (square / SQUARE_SIZE);
for i in 0..BOARD_SIZE {
acc += PRECALC_MASKS[b.get_cell(x + (i % 3), y + (i / 3)) as usize];
}
if (acc & 0xee_eeee_eee0) != 0 {
return false;
}
}
true
}
fn valid_choices_for_cell(b: &Board, x: usize, y: usize) -> u16 {
let mut cs = 0b00_0000_0001;
let xs = SQUARE_SIZE * (x / SQUARE_SIZE);
let ys = SQUARE_SIZE * (y / SQUARE_SIZE);
// Generate a mask of already-used values.
for i in 0..BOARD_SIZE {
cs |= b.get_cell_as_mask(x, i);
cs |= b.get_cell_as_mask(i, y);
cs |= b.get_cell_as_mask(xs + (i % 3), ys + (i / 3));
}
// Invert the mask to indicate which choices are still available.
cs ^ 0b11_1111_1111u16
}
fn cell_with_fewest_candidates(b: &Board) -> Option<(usize, usize, u16)> {
let mut min_x = 0;
let mut min_y = 0;
let mut min_candidates = 0;
let mut min_count = BOARD_SIZE + 1;
// Find the cell with the least number of possible valid values.
for y in 0..BOARD_SIZE {
for x in 0..BOARD_SIZE {
if b.get_cell_as_mask(x, y) == 1 {
let cs = valid_choices_for_cell(b, x, y);
if cs == 0 {
// No valid choices for this empty cell, so we need to backtrack.
return None;
}
let count = cs.count_ones() as usize;
if count == 1 {
// Can't do better than this.
return Some((x, y, cs));
} else if count < min_count {
min_x = x;
min_y = y;
min_candidates = cs;
min_count = count;
}
}
}
}
Some((min_x, min_y, min_candidates))
}
/// Solve a sudoku puzzle.
///
/// Returns an `Option<Board>` which is either `None`, if no solution could be found, or a `Some`
/// variant wrapping the first solution found.
///
/// ## Example
///
/// ```rust
/// # fn main() {
/// # use sudoku_solver::*;
/// let board = Board::from(&[
/// [0, 0, 0, 2, 6, 0, 7, 0, 1], // row 1
/// [6, 8, 0, 0, 7, 0, 0, 9, 0], // row 2
/// [1, 9, 0, 0, 0, 4, 5, 0, 0], // row 3
/// [8, 2, 0, 1, 0, 0, 0, 4, 0], // row 4
/// [0, 0, 4, 6, 0, 2, 9, 0, 0], // row 5
/// [0, 5, 0, 0, 0, 3, 0, 2, 8], // row 6
/// [0, 0, 9, 3, 0, 0, 0, 7, 4], // row 7
/// [0, 4, 0, 0, 5, 0, 0, 3, 6], // row 8
/// [7, 0, 3, 0, 1, 8, 0, 0, 0], // row 9
/// ]);
///
/// assert!(solve(&board).is_some());
/// # }
/// ```
pub fn solve(b: &Board) -> Option<Board> {
SolutionIter::new(b).next()
}
/// An iterator which produces the set of solutions to a sudoku-style puzzle.
///
/// Strictly speaking, sudokus should have only one solution. However, it is possible to construct
/// sudoku-style puzzles with multiple solutions. `SolutionIter` provides a means of generating
/// such solutions lazily.
///
/// ## Example
///
/// ```rust
/// # fn main() {
/// # use sudoku_solver::*;
/// let mut solutions = SolutionIter::new(&Board::from(&[
/// [9, 0, 6, 0, 7, 0, 4, 0, 3], // row 1
/// [0, 0, 0, 4, 0, 0, 2, 0, 0], // row 2
/// [0, 7, 0, 0, 2, 3, 0, 1, 0], // row 3
/// [5, 0, 0, 0, 0, 0, 1, 0, 0], // row 4
/// [0, 4, 0, 2, 0, 8, 0, 6, 0], // row 5
/// [0, 0, 3, 0, 0, 0, 0, 0, 5], // row 6
/// [0, 3, 0, 7, 0, 0, 0, 5, 0], // row 7
/// [0, 0, 7, 0, 0, 5, 0, 0, 0], // row 8
/// [4, 0, 5, 0, 1, 0, 7, 0, 8], // row 9
/// ]));
///
/// assert_eq!(solutions.next(), Some(Board::from(&[
/// [9, 2, 6, 5, 7, 1, 4, 8, 3], // row 1
/// [3, 5, 1, 4, 8, 6, 2, 7, 9], // row 2
/// [8, 7, 4, 9, 2, 3, 5, 1, 6], // row 3
/// [5, 8, 2, 3, 6, 7, 1, 9, 4], // row 4
/// [1, 4, 9, 2, 5, 8, 3, 6, 7], // row 5
/// [7, 6, 3, 1, 4, 9, 8, 2, 5], // row 6
/// [2, 3, 8, 7, 9, 4, 6, 5, 1], // row 7
/// [6, 1, 7, 8, 3, 5, 9, 4, 2], // row 8
/// [4, 9, 5, 6, 1, 2, 7, 3, 8], // row 9
/// ])));
///
/// assert_eq!(solutions.next(), Some(Board::from(&[
/// [9, 2, 6, 5, 7, 1, 4, 8, 3], // row 1
/// [3, 5, 1, 4, 8, 6, 2, 7, 9], // row 2
/// [8, 7, 4, 9, 2, 3, 5, 1, 6], // row 3
/// [5, 8, 2, 3, 6, 7, 1, 9, 4], // row 4
/// [1, 4, 9, 2, 5, 8, 3, 6, 7], // row 5
/// [7, 6, 3, 1, 9, 4, 8, 2, 5], // row 6
/// [2, 3, 8, 7, 4, 9, 6, 5, 1], // row 7
/// [6, 1, 7, 8, 3, 5, 9, 4, 2], // row 8
/// [4, 9, 5, 6, 1, 2, 7, 3, 8], // row 9
/// ])));
///
/// assert_eq!(solutions.next(), None);
/// # }
/// ```
#[derive(Debug)]
pub struct SolutionIter {
first: bool,
board: Board,
stack: Vec<(usize, usize, BitIter<u16>)>,
}
impl SolutionIter {
/// Construct a `SolutionIter` value from a [`Board`].
///
/// ## Example
///
/// ```rust
/// # fn main() {
/// # use sudoku_solver::*;
/// let board = Board::from(&[
/// [9, 0, 6, 0, 7, 0, 4, 0, 3], // row 1
/// [0, 0, 0, 4, 0, 0, 2, 0, 0], // row 2
/// [0, 7, 0, 0, 2, 3, 0, 1, 0], // row 3
/// [5, 0, 0, 0, 0, 0, 1, 0, 0], // row 4
/// [0, 4, 0, 2, 0, 8, 0, 6, 0], // row 5
/// [0, 0, 3, 0, 0, 0, 0, 0, 5], // row 6
/// [0, 3, 0, 7, 0, 0, 0, 5, 0], // row 7
/// [0, 0, 7, 0, 0, 5, 0, 0, 0], // row 8
/// [4, 0, 5, 0, 1, 0, 7, 0, 8], // row 9
/// ]);
///
/// let solutions = SolutionIter::new(&board);
///
/// assert_eq!(solutions.count(), 2);
/// # }
/// ```
pub fn new(board: &Board) -> Self {
Self {
first: true,
board: *board,
stack: Vec::with_capacity(BOARD_SIZE * BOARD_SIZE),
}
}
}
/// `From` implementation for `SolutionIter`.
impl From<Board> for SolutionIter {
fn from(board: Board) -> Self {
Self::new(&board)
}
}
/// `Iterator` implementation for `SolutionIter`.
impl Iterator for SolutionIter {
type Item = Board;
fn next(&mut self) -> Option<Self::Item> {
if self.first {
self.first = false;
if valid(&self.board) {
if let Some((x, y, values)) = cell_with_fewest_candidates(&self.board) {
if values == 0 {
return Some(self.board);
}
self.stack.push((x, y, values.into()));
}
}
}
if let Some((mut x, mut y, mut values)) = self.stack.pop() {
loop {
if let Some(value) = values.next() {
self.board.set_cell(x, y, value as u8);
if let Some(cs) = cell_with_fewest_candidates(&self.board) {
self.stack.push((x, y, values));
if cs.2 == 0 {
return Some(self.board);
}
x = cs.0;
y = cs.1;
values = cs.2.into();
}
} else {
self.board.set_cell(x, y, 0);
if let Some(cs) = self.stack.pop() {
x = cs.0;
y = cs.1;
values = cs.2;
} else {
return None;
}
}
}
} else {
None
}
}
}
/// `FusedIterator` implementation for `SolutionIter`.
impl FusedIterator for SolutionIter {}