Code shared from the Rust Playground

playground.rs

// Compile with: rustc -C opt-level=3 -C target-cpu=native

struct Board {
    squares: Vec<bool>,
    side: usize,
}

impl Board {
    fn new(side: usize) -> Self {
        Self {
            squares: vec![false; side * side],
            side,
        }
    }

    fn toggle_piece(&mut self, i: usize, j: usize) {
        self.squares[i * self.side + j] = !self.squares[i * self.side + j];
    }

    fn has_been_visited(&self, i: usize, j: usize) -> bool {
        self.squares[i * self.side + j]
    }
}

fn robot_paths(n: usize) -> usize {
    fn robot_paths(board: &mut Board, i: usize, j: usize) -> usize {
        if i == board.side - 1 && j == board.side - 1 {
            return 1;
        }
        board.toggle_piece(i, j);

        let mut result = 0;
        for &(s0, s1) in [(0, 1), (1, 0), (-1, 0), (0, -1)].iter() {
            let i = (i as isize).wrapping_add(s0) as usize;
            let j = (j as isize).wrapping_add(s1) as usize;
            if i < board.side && j < board.side && !board.has_been_visited(i, j) {
                result += robot_paths(board, i, j);
            }
        }
        board.toggle_piece(i, j);
        result
    }

    robot_paths(&mut Board::new(n), 0, 0)
}

fn main() {
    println!("{:?}", robot_paths(6));
}