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Implement Rat in Maze Path Finder (#730)
* feat: implement Rat in Maze * ref: rewrite tests using macro * chore(docs): add `rat_in_maze` to `DIRECTORY.md` * fix: fix clippy issues * chore(ref): update implementation - Remove bad comments - Add some tests * ref: handle improper maze * ref: change `maze` representation from `Vec<Vec<usize>>` to `Vec<Vec<bool>>` * ref: refactor maze cell validation for clarity and efficiency * ref: refactor rat in maze implementation - Add custom errors to handle various exception cases: empty maze, non-rectangle maze, start out of maze bound - Add edge tests to handle various types of maze * ref: update implementation - Add `maze_with_going_back` test - Add explaination of why return this solution and not the other one when multiple path exist in maze --------- Co-authored-by: Piotr Idzik <[email protected]>
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‎DIRECTORY.md

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* [N Queens](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/n_queens.rs)
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* [Parentheses Generator](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/parentheses_generator.rs)
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* [Permutations](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/permutations.rs)
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* [Rat in Maze](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/rat_in_maze.rs)
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* [Sudoku](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/sudoku.rs)
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* Big Integer
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* [Fast Factorial](https://github.com/TheAlgorithms/Rust/blob/master/src/big_integer/fast_factorial.rs)

‎src/backtracking/mod.rs

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mod n_queens;
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mod parentheses_generator;
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mod permutations;
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mod rat_in_maze;
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mod sudoku;
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pub use all_combination_of_size_k::generate_all_combinations;
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pub use knight_tour::find_knight_tour;
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pub use n_queens::n_queens_solver;
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pub use parentheses_generator::generate_parentheses;
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pub use permutations::permute;
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pub use rat_in_maze::find_path_in_maze;
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pub use sudoku::sudoku_solver;

‎src/backtracking/rat_in_maze.rs

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//! This module contains the implementation of the Rat in Maze problem.
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//!
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//! The Rat in Maze problem is a classic algorithmic problem where the
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//! objective is to find a path from the starting position to the exit
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//! position in a maze.
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/// Enum representing various errors that can occur while working with mazes.
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#[derive(Debug, PartialEq, Eq)]
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pub enum MazeError {
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/// Indicates that the maze is empty (zero rows).
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EmptyMaze,
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/// Indicates that the starting position is out of bounds.
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OutOfBoundPos,
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/// Indicates an improper representation of the maze (e.g., non-rectangular maze).
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ImproperMazeRepr,
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}
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/// Finds a path through the maze starting from the specified position.
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///
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/// # Arguments
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///
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/// * `maze` - The maze represented as a vector of vectors where each
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/// inner vector represents a row in the maze grid.
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/// * `start_x` - The x-coordinate of the starting position.
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/// * `start_y` - The y-coordinate of the starting position.
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///
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/// # Returns
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///
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/// A `Result` where:
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/// - `Ok(Some(solution))` if a path is found and contains the solution matrix.
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/// - `Ok(None)` if no path is found.
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/// - `Err(MazeError)` for various error conditions such as out-of-bound start position or improper maze representation.
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///
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/// # Solution Selection
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///
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/// The function returns the first successful path it discovers based on the predefined order of moves.
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/// The order of moves is defined in the `MOVES` constant of the `Maze` struct.
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///
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/// The backtracking algorithm explores each direction in this order. If multiple solutions exist,
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/// the algorithm returns the first path it finds according to this sequence. It recursively explores
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/// each direction, marks valid moves, and backtracks if necessary, ensuring that the solution is found
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/// efficiently and consistently.
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pub fn find_path_in_maze(
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maze: &[Vec<bool>],
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start_x: usize,
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start_y: usize,
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) -> Result<Option<Vec<Vec<bool>>>, MazeError> {
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if maze.is_empty() {
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return Err(MazeError::EmptyMaze);
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}
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// Validate start position
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if start_x >= maze.len() || start_y >= maze[0].len() {
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return Err(MazeError::OutOfBoundPos);
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}
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// Validate maze representation (if necessary)
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if maze.iter().any(|row| row.len() != maze[0].len()) {
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return Err(MazeError::ImproperMazeRepr);
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}
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// If validations pass, proceed with finding the path
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let mut maze_instance = Maze::new(maze.to_owned());
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Ok(maze_instance.find_path(start_x, start_y))
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}
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/// Represents a maze.
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struct Maze {
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maze: Vec<Vec<bool>>,
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}
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impl Maze {
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/// Represents possible moves in the maze.
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const MOVES: [(isize, isize); 4] = [(0, 1), (1, 0), (0, -1), (-1, 0)];
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/// Constructs a new Maze instance.
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/// # Arguments
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///
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/// * `maze` - The maze represented as a vector of vectors where each
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/// inner vector represents a row in the maze grid.
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///
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/// # Returns
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///
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/// A new Maze instance.
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fn new(maze: Vec<Vec<bool>>) -> Self {
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Maze { maze }
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}
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/// Returns the width of the maze.
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///
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/// # Returns
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///
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/// The width of the maze.
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fn width(&self) -> usize {
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self.maze[0].len()
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}
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/// Returns the height of the maze.
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///
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/// # Returns
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///
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/// The height of the maze.
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fn height(&self) -> usize {
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self.maze.len()
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}
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/// Finds a path through the maze starting from the specified position.
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///
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/// # Arguments
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///
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/// * `start_x` - The x-coordinate of the starting position.
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/// * `start_y` - The y-coordinate of the starting position.
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///
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/// # Returns
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///
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/// A solution matrix if a path is found or None if not found.
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fn find_path(&mut self, start_x: usize, start_y: usize) -> Option<Vec<Vec<bool>>> {
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let mut solution = vec![vec![false; self.width()]; self.height()];
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if self.solve(start_x as isize, start_y as isize, &mut solution) {
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Some(solution)
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} else {
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None
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}
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}
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/// Recursively solves the Rat in Maze problem using backtracking.
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///
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/// # Arguments
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///
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/// * `x` - The current x-coordinate.
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/// * `y` - The current y-coordinate.
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/// * `solution` - The current solution matrix.
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///
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/// # Returns
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///
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/// A boolean indicating whether a solution was found.
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fn solve(&self, x: isize, y: isize, solution: &mut [Vec<bool>]) -> bool {
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if x == (self.height() as isize - 1) && y == (self.width() as isize - 1) {
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solution[x as usize][y as usize] = true;
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return true;
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}
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if self.is_valid(x, y, solution) {
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solution[x as usize][y as usize] = true;
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for &(dx, dy) in &Self::MOVES {
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if self.solve(x + dx, y + dy, solution) {
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return true;
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}
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}
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// If none of the directions lead to the solution, backtrack
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solution[x as usize][y as usize] = false;
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return false;
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}
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false
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}
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/// Checks if a given position is valid in the maze.
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///
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/// # Arguments
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///
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/// * `x` - The x-coordinate of the position.
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/// * `y` - The y-coordinate of the position.
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/// * `solution` - The current solution matrix.
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///
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/// # Returns
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///
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/// A boolean indicating whether the position is valid.
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fn is_valid(&self, x: isize, y: isize, solution: &[Vec<bool>]) -> bool {
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x >= 0
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&& y >= 0
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&& x < self.height() as isize
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&& y < self.width() as isize
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&& self.maze[x as usize][y as usize]
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&& !solution[x as usize][y as usize]
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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macro_rules! test_find_path_in_maze {
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($($name:ident: $start_x:expr, $start_y:expr, $maze:expr, $expected:expr,)*) => {
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$(
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#[test]
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fn $name() {
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let solution = find_path_in_maze($maze, $start_x, $start_y);
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assert_eq!(solution, $expected);
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if let Ok(Some(expected_solution)) = &solution {
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assert_eq!(expected_solution[$start_x][$start_y], true);
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}
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}
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)*
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}
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}
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test_find_path_in_maze! {
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maze_with_solution_5x5: 0, 0, &[
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vec![true, false, true, false, false],
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vec![true, true, false, true, false],
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vec![false, true, true, true, false],
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vec![false, false, false, true, true],
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vec![false, true, false, false, true],
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], Ok(Some(vec![
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vec![true, false, false, false, false],
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vec![true, true, false, false, false],
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vec![false, true, true, true, false],
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vec![false, false, false, true, true],
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vec![false, false, false, false, true],
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])),
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maze_with_solution_6x6: 0, 0, &[
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vec![true, false, true, false, true, false],
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vec![true, true, false, true, false, true],
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vec![false, true, true, true, true, false],
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vec![false, false, false, true, true, true],
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vec![false, true, false, false, true, false],
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vec![true, true, true, true, true, true],
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], Ok(Some(vec![
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vec![true, false, false, false, false, false],
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vec![true, true, false, false, false, false],
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vec![false, true, true, true, true, false],
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vec![false, false, false, false, true, false],
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vec![false, false, false, false, true, false],
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vec![false, false, false, false, true, true],
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])),
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maze_with_solution_8x8: 0, 0, &[
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vec![true, false, false, false, false, false, false, true],
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vec![true, true, false, true, true, true, false, false],
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vec![false, true, true, true, false, false, false, false],
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vec![false, false, false, true, false, true, true, false],
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vec![false, true, false, true, true, true, false, true],
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vec![true, false, true, false, false, true, true, true],
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vec![false, false, true, true, true, false, true, true],
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vec![true, true, true, false, true, true, true, true],
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], Ok(Some(vec![
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vec![true, false, false, false, false, false, false, false],
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vec![true, true, false, false, false, false, false, false],
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vec![false, true, true, true, false, false, false, false],
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vec![false, false, false, true, false, false, false, false],
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vec![false, false, false, true, true, true, false, false],
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vec![false, false, false, false, false, true, true, true],
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vec![false, false, false, false, false, false, false, true],
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vec![false, false, false, false, false, false, false, true],
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])),
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maze_without_solution_4x4: 0, 0, &[
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vec![true, false, false, false],
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vec![true, true, false, false],
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vec![false, false, true, false],
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vec![false, false, false, true],
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], Ok(None::<Vec<Vec<bool>>>),
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maze_with_solution_3x4: 0, 0, &[
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vec![true, false, true, true],
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vec![true, true, true, false],
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vec![false, true, true, true],
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], Ok(Some(vec![
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vec![true, false, false, false],
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vec![true, true, true, false],
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vec![false, false, true, true],
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])),
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maze_without_solution_3x4: 0, 0, &[
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vec![true, false, true, true],
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vec![true, false, true, false],
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vec![false, true, false, true],
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], Ok(None::<Vec<Vec<bool>>>),
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improper_maze_representation: 0, 0, &[
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vec![true],
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vec![true, true],
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vec![true, true, true],
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vec![true, true, true, true]
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], Err(MazeError::ImproperMazeRepr),
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out_of_bound_start: 0, 3, &[
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vec![true, false, true],
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vec![true, true],
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vec![false, true, true],
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], Err(MazeError::OutOfBoundPos),
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empty_maze: 0, 0, &[], Err(MazeError::EmptyMaze),
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maze_with_single_cell: 0, 0, &[
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vec![true],
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], Ok(Some(vec![
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vec![true]
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])),
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maze_with_one_row_and_multiple_columns: 0, 0, &[
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vec![true, false, true, true, false]
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], Ok(None::<Vec<Vec<bool>>>),
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maze_with_multiple_rows_and_one_column: 0, 0, &[
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vec![true],
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vec![true],
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vec![false],
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vec![true],
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], Ok(None::<Vec<Vec<bool>>>),
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maze_with_walls_surrounding_border: 0, 0, &[
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vec![false, false, false],
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vec![false, true, false],
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vec![false, false, false],
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], Ok(None::<Vec<Vec<bool>>>),
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maze_with_no_walls: 0, 0, &[
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vec![true, true, true],
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vec![true, true, true],
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vec![true, true, true],
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], Ok(Some(vec![
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vec![true, true, true],
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vec![false, false, true],
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vec![false, false, true],
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])),
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maze_with_going_back: 0, 0, &[
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vec![true, true, true, true, true, true],
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vec![false, false, false, true, false, true],
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vec![true, true, true, true, false, false],
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vec![true, false, false, false, false, false],
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vec![true, false, false, false, true, true],
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vec![true, false, true, true, true, false],
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vec![true, false, true , false, true, false],
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vec![true, true, true, false, true, true],
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], Ok(Some(vec![
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vec![true, true, true, true, false, false],
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vec![false, false, false, true, false, false],
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vec![true, true, true, true, false, false],
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vec![true, false, false, false, false, false],
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vec![true, false, false, false, false, false],
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vec![true, false, true, true, true, false],
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vec![true, false, true , false, true, false],
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vec![true, true, true, false, true, true],
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])),
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}
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}

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