kangalio/sudoku-solver.rs

## sudoku-solver.rs
#![allow(clippy::needless_range_loop)]

trait MyItertools: Iterator + Sized {
    /// This function will yield the iterator's next item, but only if that item is the only item
    fn into_single(mut self) -> Option<Self::Item> {
        let first_item = self.next()?;
        if self.next().is_some() {
            None
        } else {
            Some(first_item)
        }
    }
}
impl<I: Iterator> MyItertools for I {}

fn offset_pos(x: usize, y: usize, offset_x: isize, offset_y: isize) -> Option<(usize, usize)> {
    Some((offset(x, offset_x)?, offset(y, offset_y)?))
}

fn offset(number: usize, offset: isize) -> Option<usize> {
    let new_number = number as isize + offset;
    if new_number >= 0 && new_number < 9 {
        Some(new_number as usize)
    } else {
        None
    }
}

/// Converts coordinates into human readable form: (0, 0) => A1, (2, 4) => C5
fn cell_name(x: usize, y: usize) -> impl std::fmt::Display {
    struct CellName { x: usize, y: usize };
    impl std::fmt::Display for CellName {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            write!(f, "{}{}",
                std::char::from_u32(b'A' as u32 + self.x as u32).unwrap(),
                std::char::from_u32(b'1' as u32 + self.y as u32).unwrap(),
            )
        }
    }
    CellName { x, y }
}

fn indent(depth: u32) -> impl std::fmt::Display {
    struct Indent { depth: u32 }
    impl std::fmt::Display for Indent {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            for _ in 0..self.depth {
                f.write_str("  ")?;
            }
            Ok(())
        }
    }
    Indent { depth }
}

/// Stores all the possible numbers for this cell
#[derive(Debug, Clone)]
struct CellState {
    possibilities: u16,
}

impl Default for CellState {
    fn default() -> Self {
        Self::completely_uncertain()
    }
}

impl CellState {
    fn completely_uncertain() -> Self {
        Self { possibilities: 0b111111111 }
    }

    fn certain(number: usize) -> Self {
        Self { possibilities: 1 << number }
    }

    /// Returns false if the given number was already eliminated
    fn eliminate(&mut self, number: usize) -> bool {
        let prev = self.possibilities;
        self.possibilities &= !(1 << number);
        self.possibilities != prev
    }

    fn could_contain(&self, number: usize) -> bool {
        self.possibilities & (1 << number) > 0
    }

    fn is_certain(&self) -> bool {
        self.possibilities.count_ones() == 1
    }

    fn is_impossible(&self) -> bool {
        self.possibilities.count_ones() == 0
    }

    /// If this cell is certain, return the number of the cell
    fn get_certain(&self) -> Option<usize> {
        if self.is_certain() {
            Some(self.possibilities.trailing_zeros() as usize)
        } else {
            None
        }
    }
}

struct UniqueRegion {
    pub name: &'static str,
    pub cells: [(usize, usize); 9],
}

#[derive(Default, Clone)]
struct SudokuState {
    pub cells: [[CellState; 9]; 9],
}

impl SudokuState {
    pub const UNIQUE_REGIONS: [UniqueRegion; 27] = {
        macro_rules! cells {
            (3x3, $name:literal, $x:expr, $y:expr) => { UniqueRegion { name: concat!($name, " block"), cells: [
                ($x, $y), ($x + 1, $y), ($x + 2, $y),
                ($x, $y + 1), ($x + 1, $y + 1), ($x + 2, $y + 1),
                ($x, $y + 2), ($x + 1, $y + 2), ($x + 2, $y + 2),
            ] } };
            (row, $name:literal, $y:expr) => { UniqueRegion { name: concat!("row ", $name), cells: [
                (0, $y), (1, $y), (2, $y),
                (3, $y), (4, $y), (5, $y),
                (6, $y), (7, $y), (8, $y),
            ] } };
            (column, $name:literal, $x:expr) => { UniqueRegion { name: concat!("column ", $name), cells: [
                ($x, 0), ($x, 1), ($x, 2),
                ($x, 3), ($x, 4), ($x, 5),
                ($x, 6), ($x, 7), ($x, 8),
            ] } };
        }
        [
            cells!(3x3, "top left", 0, 0), cells!(3x3, "top", 3, 0), cells!(3x3, "top right", 6, 0),
            cells!(3x3, "left", 0, 3), cells!(3x3, "center", 3, 3), cells!(3x3, "right", 6, 3),
            cells!(3x3, "bottom left", 0, 6), cells!(3x3, "bottom", 3, 6), cells!(3x3, "bottom right", 6, 6),
            cells!(row, "1", 0), cells!(row, "2", 1), cells!(row, "3", 2),
            cells!(row, "4", 3), cells!(row, "5", 4), cells!(row, "6", 5),
            cells!(row, "7", 6), cells!(row, "8", 7), cells!(row, "9", 8),
            cells!(column, "A", 0), cells!(column, "B", 1), cells!(column, "C", 2),
            cells!(column, "D", 3), cells!(column, "E", 4), cells!(column, "F", 5),
            cells!(column, "G", 6), cells!(column, "H", 7), cells!(column, "I", 8),
        ]
    };

    pub fn set_certain(&mut self,
        certain_x: usize,
        certain_y: usize,
        number: usize,
        explain: bool,
        depth: u32,
    ) {
        let mut eliminate = |x: usize, y: usize, number_to_eliminate, reason| {
            if x == certain_x && y == certain_y { return; }
            if self.cells[x][y].eliminate(number_to_eliminate) {
                if explain { println!("{}{} = {}, so {} ({}) can't be {}",
                    indent(depth),
                    cell_name(certain_x, certain_y),
                    number + 1,
                    cell_name(x, y),
                    reason,
                    number_to_eliminate + 1,
                ); }

                if let Some(new_certain_number_by_elimination) = self.cells[x][y].get_certain() {
                    if explain { println!("{}Therefore, {} can only be {}",
                        indent(depth),
                        cell_name(x, y),
                        new_certain_number_by_elimination + 1,
                    ); }

                    self.set_certain(x, y, new_certain_number_by_elimination, explain, depth + 1);
                }
            }
        };

        // eliminate same row
        for x in 0..9 {
            eliminate(x, certain_y, number, "same row");
        }

        // eliminate same column
        for y in 0..9 {
            eliminate(certain_x, y, number, "same column");
        }

        // eliminate 3x3 block
        for x in (certain_x / 3 * 3)..(certain_x / 3 * 3 + 3) {
            for y in (certain_y / 3 * 3)..(certain_y / 3 * 3 + 3) {
                eliminate(x, y, number, "same block");
            }
        }

        // eliminate surrounding 16 cells
        for &(offset_x, offset_y) in &[
            // 8 neighboring cells
            (-1, 1), (0, 1), (1, 1), (1, 0), (1, -1), (0, -1), (-1, -1), (-1, 0),
            // 8 cells reachable by chess knight move
            (-1, 2), (1, 2), (2, 1), (2, -1), (1, -2), (-1, -2), (-2, -1), (-2, 1),
        ] {
            if let Some((x, y)) = offset_pos(certain_x, certain_y, offset_x, offset_y) {
                eliminate(x, y, number, "near cell");
            }
        }

        // eliminate neighboring numbers in directly neighboring cells
        for &(offset_x, offset_y) in &[(0, 1), (1, 0), (0, -1), (-1, 0)] {
            if let Some((x, y)) = offset_pos(certain_x, certain_y, offset_x, offset_y) {
                if let Some(number_increment) = offset(number, 1) {
                    eliminate(x, y, number_increment, "direct neighbor");
                }
                if let Some(number_decrement) = offset(number, -1) {
                    eliminate(x, y, number_decrement, "direct neighbor");
                }
            }
        }

        self.cells[certain_x][certain_y] = CellState::certain(number);
    }

    pub fn is_impossible(&self, explain: bool) -> bool {
        for x in 0..9 {
            for y in 0..9 {
                if self.cells[x][y].is_impossible() {
                    if explain { println!("{} has no valid value anymore!", cell_name(x, y)); }
                    return true;
                }
            }
        }
        false
    }
}

impl std::fmt::Debug for SudokuState {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        writeln!(f, "     A     B     C     D     E     F     G     H     I   ")?;
        for y in 0..9 {
            let separator_char = if y % 3 == 0 { '=' } else { '-' };
            write!(f, "  ")?;
            for _ in 0..9 {
                write!(f, "+{0}{0}{0}{0}{0}", separator_char)?;
            }
            writeln!(f, "+")?;

            write!(f, "  ")?;
            for x in 0..9 {
                write!(f, "{}", if x % 3 == 0 { "‖" } else { "|" })?;
                write!(f, "{} ", if self.cells[x][y].could_contain(0) { "1" } else { " " })?;
                write!(f, "{} ", if self.cells[x][y].could_contain(1) { "2" } else { " " })?;
                write!(f, "{}", if self.cells[x][y].could_contain(2) { "3" } else { " " })?;
            }
            writeln!(f, "‖")?;

            write!(f, "{} ", y + 1)?;
            for x in 0..9 {
                write!(f, "{}", if x % 3 == 0 { "‖" } else { "|" })?;
                write!(f, "{}", if self.cells[x][y].could_contain(3) { "4" } else { " " })?;
                write!(f, " {}", if self.cells[x][y].could_contain(4) { "5" } else { " " })?;
                write!(f, " {}", if self.cells[x][y].could_contain(5) { "6" } else { " " })?;
            }
            writeln!(f, "‖")?;

            write!(f, "  ")?;
            for x in 0..9 {
                write!(f, "{}", if x % 3 == 0 { "‖" } else { "|" })?;
                write!(f, "{}", if self.cells[x][y].could_contain(6) { "7" } else { " " })?;
                write!(f, " {}", if self.cells[x][y].could_contain(7) { "8" } else { " " })?;
                write!(f, " {}", if self.cells[x][y].could_contain(8) { "9" } else { " " })?;
            }
            writeln!(f, "‖")?;
        }
        write!(f, "  +=====+=====+=====+=====+=====+=====+=====+=====+=====+")?;

        Ok(())
    }
}

fn try_out_field_state(
    field: SudokuState,
    handle_solution: &mut dyn FnMut(SudokuState),
    depth: u32
) {
    let explain = true;

    fn applicable_cells<'a>(
        field: &'a SudokuState,
        region: &'a UniqueRegion,
        number: usize
    ) -> impl Iterator<Item = (usize, usize)> + 'a {
        region.cells.iter().cloned().filter(move |&(cell_x, cell_y)| {
            field.cells[cell_x][cell_y].could_contain(number)
                && !field.cells[cell_x][cell_y].is_certain()
        })
    }

    // find the unique region (column, row or 3x3 block) with the fewest number of possible cells
    // for a given number
    let mut low_hanging_region: Option<(_, _, _)> = None;
    for region in &SudokuState::UNIQUE_REGIONS {
        for number in 0..9 {
            // Number of cells in this region that could contain `number`
            let num_applicable_cells = applicable_cells(&field, region, number).count();
            if num_applicable_cells == 0 { continue; }
            if low_hanging_region.map_or(true, |r| num_applicable_cells < r.0) {
                low_hanging_region = Some((num_applicable_cells, region, number));
            }
        }
    }

    // Unwrap the low hanging region's parts, or call the solution callback and return if no region
    // was found with anything left to do
    let (num_applicable_cells, region, number) = match low_hanging_region {
        Some(x) => x,
        None => { handle_solution(field); return },
    };

    let mut try_with_cell_set_to = |cell_x, cell_y, number| {
        let mut field = field.clone();
        field.set_certain(cell_x, cell_y, number, explain, 0);
        if field.is_impossible(explain) {
            // Setting this field causes a cell to have no valid possible value anymore, so this
            // permutation is a dead end
            return;
        }

        if explain { println!("The field now looks like this:\n{:?}", field); }

        try_out_field_state(field, handle_solution, depth + 1);
    };

    if explain {
        println!("{:?}", field);
        if num_applicable_cells == 1 {
            // UNWRAP: num_applicable_cells is one, so this iterator can only have one element
            let (cell_x, cell_y) = applicable_cells(&field, region, number).into_single().unwrap();
            println!("Only {0} can contain the {1} in {2} => {0} must be {1}",
                cell_name(cell_x, cell_y), number + 1, region.name
            );
        } else {
            println!("Multiple cells could contain the {} in {}",
                number + 1, region.name
            );
        }
    }

    for (cell_x, cell_y) in applicable_cells(&field, region, number) {
        if explain && num_applicable_cells > 1 {
            println!("Assuming that {} houses the {} in {}",
                cell_name(cell_x, cell_y), number + 1, region.name
            );
        }

        try_with_cell_set_to(cell_x, cell_y, number);
    }

    if explain {
        println!("Done checking all {} cells that could contain the {} in {}",
            num_applicable_cells, number + 1, region.name
        );
    }
}

fn main() {
    let mut field = SudokuState::default();
    field.set_certain(2, 4, 0, false, 0);
    field.set_certain(6, 5, 1, false, 0);

    println!("Calculating solutions:");
    try_out_field_state(field, &mut |f| println!("{:?}", f), 0);
}
	#![allow(clippy::needless_range_loop)]

	trait MyItertools: Iterator + Sized {
	/// This function will yield the iterator's next item, but only if that item is the only item
	fn into_single(mut self) -> Option<Self::Item> {
	let first_item = self.next()?;
	if self.next().is_some() {
	None
	} else {
	Some(first_item)
	}
	}
	}
	impl<I: Iterator> MyItertools for I {}

	fn offset_pos(x: usize, y: usize, offset_x: isize, offset_y: isize) -> Option<(usize, usize)> {
	Some((offset(x, offset_x)?, offset(y, offset_y)?))
	}

	fn offset(number: usize, offset: isize) -> Option<usize> {
	let new_number = number as isize + offset;
	if new_number >= 0 && new_number < 9 {
	Some(new_number as usize)
	} else {
	None
	}
	}

	/// Converts coordinates into human readable form: (0, 0) => A1, (2, 4) => C5
	fn cell_name(x: usize, y: usize) -> impl std::fmt::Display {
	struct CellName { x: usize, y: usize };
	impl std::fmt::Display for CellName {
	fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
	write!(f, "{}{}",
	std::char::from_u32(b'A' as u32 + self.x as u32).unwrap(),
	std::char::from_u32(b'1' as u32 + self.y as u32).unwrap(),
	)
	}
	}
	CellName { x, y }
	}

	fn indent(depth: u32) -> impl std::fmt::Display {
	struct Indent { depth: u32 }
	impl std::fmt::Display for Indent {
	fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
	for _ in 0..self.depth {
	f.write_str(" ")?;
	}
	Ok(())
	}
	}
	Indent { depth }
	}

	/// Stores all the possible numbers for this cell
	#[derive(Debug, Clone)]
	struct CellState {
	possibilities: u16,
	}

	impl Default for CellState {
	fn default() -> Self {
	Self::completely_uncertain()
	}
	}

	impl CellState {
	fn completely_uncertain() -> Self {
	Self { possibilities: 0b111111111 }
	}

	fn certain(number: usize) -> Self {
	Self { possibilities: 1 << number }
	}

	/// Returns false if the given number was already eliminated
	fn eliminate(&mut self, number: usize) -> bool {
	let prev = self.possibilities;
	self.possibilities &= !(1 << number);
	self.possibilities != prev
	}

	fn could_contain(&self, number: usize) -> bool {
	self.possibilities & (1 << number) > 0
	}

	fn is_certain(&self) -> bool {
	self.possibilities.count_ones() == 1
	}

	fn is_impossible(&self) -> bool {
	self.possibilities.count_ones() == 0
	}

	/// If this cell is certain, return the number of the cell
	fn get_certain(&self) -> Option<usize> {
	if self.is_certain() {
	Some(self.possibilities.trailing_zeros() as usize)
	} else {
	None
	}
	}
	}

	struct UniqueRegion {
	pub name: &'static str,
	pub cells: [(usize, usize); 9],
	}

	#[derive(Default, Clone)]
	struct SudokuState {
	pub cells: [[CellState; 9]; 9],
	}

	impl SudokuState {
	pub const UNIQUE_REGIONS: [UniqueRegion; 27] = {
	macro_rules! cells {
	(3x3, $name:literal, $x:expr, $y:expr) => { UniqueRegion { name: concat!($name, " block"), cells: [
	($x, $y), ($x + 1, $y), ($x + 2, $y),
	($x, $y + 1), ($x + 1, $y + 1), ($x + 2, $y + 1),
	($x, $y + 2), ($x + 1, $y + 2), ($x + 2, $y + 2),
	] } };
	(row, $name:literal, $y:expr) => { UniqueRegion { name: concat!("row ", $name), cells: [
	(0, $y), (1, $y), (2, $y),
	(3, $y), (4, $y), (5, $y),
	(6, $y), (7, $y), (8, $y),
	] } };
	(column, $name:literal, $x:expr) => { UniqueRegion { name: concat!("column ", $name), cells: [
	($x, 0), ($x, 1), ($x, 2),
	($x, 3), ($x, 4), ($x, 5),
	($x, 6), ($x, 7), ($x, 8),
	] } };
	}
	[
	cells!(3x3, "top left", 0, 0), cells!(3x3, "top", 3, 0), cells!(3x3, "top right", 6, 0),
	cells!(3x3, "left", 0, 3), cells!(3x3, "center", 3, 3), cells!(3x3, "right", 6, 3),
	cells!(3x3, "bottom left", 0, 6), cells!(3x3, "bottom", 3, 6), cells!(3x3, "bottom right", 6, 6),
	cells!(row, "1", 0), cells!(row, "2", 1), cells!(row, "3", 2),
	cells!(row, "4", 3), cells!(row, "5", 4), cells!(row, "6", 5),
	cells!(row, "7", 6), cells!(row, "8", 7), cells!(row, "9", 8),
	cells!(column, "A", 0), cells!(column, "B", 1), cells!(column, "C", 2),
	cells!(column, "D", 3), cells!(column, "E", 4), cells!(column, "F", 5),
	cells!(column, "G", 6), cells!(column, "H", 7), cells!(column, "I", 8),
	]
	};

	pub fn set_certain(&mut self,
	certain_x: usize,
	certain_y: usize,
	number: usize,
	explain: bool,
	depth: u32,
	) {
	let mut eliminate = \|x: usize, y: usize, number_to_eliminate, reason\| {
	if x == certain_x && y == certain_y { return; }
	if self.cells[x][y].eliminate(number_to_eliminate) {
	if explain { println!("{}{} = {}, so {} ({}) can't be {}",
	indent(depth),
	cell_name(certain_x, certain_y),
	number + 1,
	cell_name(x, y),
	reason,
	number_to_eliminate + 1,
	); }

	if let Some(new_certain_number_by_elimination) = self.cells[x][y].get_certain() {
	if explain { println!("{}Therefore, {} can only be {}",
	indent(depth),
	cell_name(x, y),
	new_certain_number_by_elimination + 1,
	); }

	self.set_certain(x, y, new_certain_number_by_elimination, explain, depth + 1);
	}
	}
	};

	// eliminate same row
	for x in 0..9 {
	eliminate(x, certain_y, number, "same row");
	}

	// eliminate same column
	for y in 0..9 {
	eliminate(certain_x, y, number, "same column");
	}

	// eliminate 3x3 block
	for x in (certain_x / 3 * 3)..(certain_x / 3 * 3 + 3) {
	for y in (certain_y / 3 * 3)..(certain_y / 3 * 3 + 3) {
	eliminate(x, y, number, "same block");
	}
	}

	// eliminate surrounding 16 cells
	for &(offset_x, offset_y) in &[
	// 8 neighboring cells
	(-1, 1), (0, 1), (1, 1), (1, 0), (1, -1), (0, -1), (-1, -1), (-1, 0),
	// 8 cells reachable by chess knight move
	(-1, 2), (1, 2), (2, 1), (2, -1), (1, -2), (-1, -2), (-2, -1), (-2, 1),
	] {
	if let Some((x, y)) = offset_pos(certain_x, certain_y, offset_x, offset_y) {
	eliminate(x, y, number, "near cell");
	}
	}

	// eliminate neighboring numbers in directly neighboring cells
	for &(offset_x, offset_y) in &[(0, 1), (1, 0), (0, -1), (-1, 0)] {
	if let Some((x, y)) = offset_pos(certain_x, certain_y, offset_x, offset_y) {
	if let Some(number_increment) = offset(number, 1) {
	eliminate(x, y, number_increment, "direct neighbor");
	}
	if let Some(number_decrement) = offset(number, -1) {
	eliminate(x, y, number_decrement, "direct neighbor");
	}
	}
	}

	self.cells[certain_x][certain_y] = CellState::certain(number);
	}

	pub fn is_impossible(&self, explain: bool) -> bool {
	for x in 0..9 {
	for y in 0..9 {
	if self.cells[x][y].is_impossible() {
	if explain { println!("{} has no valid value anymore!", cell_name(x, y)); }
	return true;
	}
	}
	}
	false
	}
	}

	impl std::fmt::Debug for SudokuState {
	fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
	writeln!(f, " A B C D E F G H I ")?;
	for y in 0..9 {
	let separator_char = if y % 3 == 0 { '=' } else { '-' };
	write!(f, " ")?;
	for _ in 0..9 {
	write!(f, "+{0}{0}{0}{0}{0}", separator_char)?;
	}
	writeln!(f, "+")?;

	write!(f, " ")?;
	for x in 0..9 {
	write!(f, "{}", if x % 3 == 0 { "‖" } else { "\|" })?;
	write!(f, "{} ", if self.cells[x][y].could_contain(0) { "1" } else { " " })?;
	write!(f, "{} ", if self.cells[x][y].could_contain(1) { "2" } else { " " })?;
	write!(f, "{}", if self.cells[x][y].could_contain(2) { "3" } else { " " })?;
	}
	writeln!(f, "‖")?;

	write!(f, "{} ", y + 1)?;
	for x in 0..9 {
	write!(f, "{}", if x % 3 == 0 { "‖" } else { "\|" })?;
	write!(f, "{}", if self.cells[x][y].could_contain(3) { "4" } else { " " })?;
	write!(f, " {}", if self.cells[x][y].could_contain(4) { "5" } else { " " })?;
	write!(f, " {}", if self.cells[x][y].could_contain(5) { "6" } else { " " })?;
	}
	writeln!(f, "‖")?;

	write!(f, " ")?;
	for x in 0..9 {
	write!(f, "{}", if x % 3 == 0 { "‖" } else { "\|" })?;
	write!(f, "{}", if self.cells[x][y].could_contain(6) { "7" } else { " " })?;
	write!(f, " {}", if self.cells[x][y].could_contain(7) { "8" } else { " " })?;
	write!(f, " {}", if self.cells[x][y].could_contain(8) { "9" } else { " " })?;
	}
	writeln!(f, "‖")?;
	}
	write!(f, " +=====+=====+=====+=====+=====+=====+=====+=====+=====+")?;

	Ok(())
	}
	}

	fn try_out_field_state(
	field: SudokuState,
	handle_solution: &mut dyn FnMut(SudokuState),
	depth: u32
	) {
	let explain = true;

	fn applicable_cells<'a>(
	field: &'a SudokuState,
	region: &'a UniqueRegion,
	number: usize
	) -> impl Iterator<Item = (usize, usize)> + 'a {
	region.cells.iter().cloned().filter(move \|&(cell_x, cell_y)\| {
	field.cells[cell_x][cell_y].could_contain(number)
	&& !field.cells[cell_x][cell_y].is_certain()
	})
	}

	// find the unique region (column, row or 3x3 block) with the fewest number of possible cells
	// for a given number
	let mut low_hanging_region: Option<(_, _, _)> = None;
	for region in &SudokuState::UNIQUE_REGIONS {
	for number in 0..9 {
	// Number of cells in this region that could contain `number`
	let num_applicable_cells = applicable_cells(&field, region, number).count();
	if num_applicable_cells == 0 { continue; }
	if low_hanging_region.map_or(true, \|r\| num_applicable_cells < r.0) {
	low_hanging_region = Some((num_applicable_cells, region, number));
	}
	}
	}

	// Unwrap the low hanging region's parts, or call the solution callback and return if no region
	// was found with anything left to do
	let (num_applicable_cells, region, number) = match low_hanging_region {
	Some(x) => x,
	None => { handle_solution(field); return },
	};

	let mut try_with_cell_set_to = \|cell_x, cell_y, number\| {
	let mut field = field.clone();
	field.set_certain(cell_x, cell_y, number, explain, 0);
	if field.is_impossible(explain) {
	// Setting this field causes a cell to have no valid possible value anymore, so this
	// permutation is a dead end
	return;
	}

	if explain { println!("The field now looks like this:\n{:?}", field); }

	try_out_field_state(field, handle_solution, depth + 1);
	};

	if explain {
	println!("{:?}", field);
	if num_applicable_cells == 1 {
	// UNWRAP: num_applicable_cells is one, so this iterator can only have one element
	let (cell_x, cell_y) = applicable_cells(&field, region, number).into_single().unwrap();
	println!("Only {0} can contain the {1} in {2} => {0} must be {1}",
	cell_name(cell_x, cell_y), number + 1, region.name
	);
	} else {
	println!("Multiple cells could contain the {} in {}",
	number + 1, region.name
	);
	}
	}

	for (cell_x, cell_y) in applicable_cells(&field, region, number) {
	if explain && num_applicable_cells > 1 {
	println!("Assuming that {} houses the {} in {}",
	cell_name(cell_x, cell_y), number + 1, region.name
	);
	}

	try_with_cell_set_to(cell_x, cell_y, number);
	}

	if explain {
	println!("Done checking all {} cells that could contain the {} in {}",
	num_applicable_cells, number + 1, region.name
	);
	}
	}

	fn main() {
	let mut field = SudokuState::default();
	field.set_certain(2, 4, 0, false, 0);
	field.set_certain(6, 5, 1, false, 0);

	println!("Calculating solutions:");
	try_out_field_state(field, &mut \|f\| println!("{:?}", f), 0);
	}