Rat in a Maze Problem in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if the rat can move to the cell (x, y) inside the maze boundaries.

DSA Rust

fn is_safe(x: i32, y: i32, n: usize) -> bool {
    x >= 0 && y >= 0 && (x as usize) < n && (y as usize) < n && [1]
}

Drag options to blanks, or click blank then click option'

Atrue

Bfalse

Cx < n as i32

Dy < n as i32

Attempts:

3 left

💡 Hint

Common Mistakes

Returning false instead of true.

Checking only one boundary condition.

The function checks if the coordinates are within bounds and the cell is safe. Returning true means the cell is safe to move.

2fill in blank

medium

Complete the code to mark the current cell (x, y) as part of the solution path.

DSA Rust

fn solve_maze_util(maze: &Vec<Vec<i32>>, x: usize, y: usize, solution: &mut Vec<Vec<i32>>, n: usize) -> bool {
    if x == n - 1 && y == n - 1 {
        solution[x][y] = [1];
        return true;
    }
    if is_safe(x as i32, y as i32, n) {
        solution[x][y] = 1;
        // rest of the code
    }
    false
}

Drag options to blanks, or click blank then click option'

A1

B0

C-1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Marking the cell with 0 which means no path.

Using negative numbers which are invalid here.

Marking the cell with 1 means it is part of the path.

3fill in blank

hard

Fix the error in the recursive call to move right in the maze.

DSA Rust

if solve_maze_util(maze, x, y + 1, solution, n) [1] {
    return true;
}

Drag options to blanks, or click blank then click option'

A== false

B!= true

C= true

D== true

Attempts:

3 left

💡 Hint

Common Mistakes

Using assignment '=' instead of comparison '=='.

Checking for false instead of true.

The recursive call returns a boolean. We check if it is true to continue the path.

4fill in blank

hard

Fill both blanks to backtrack by unmarking the current cell and returning false.

DSA Rust

solution[x][y] = [1];
return [2];

Drag options to blanks, or click blank then click option'

A0

Btrue

Cfalse

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Returning true after backtracking.

Not unmarking the cell.

Backtracking means unmarking the cell with 0 and returning false to try other paths.

5fill in blank

hard

Fill all three blanks to complete the main solve_maze function that initializes the solution matrix and calls the utility function.

DSA Rust

fn solve_maze(maze: &Vec<Vec<i32>>) -> Vec<Vec<i32>> {
    let n = maze.len();
    let mut solution = vec![vec![[1]; n]; n];
    if solve_maze_util([2], 0, 0, &mut solution, n) {
        return [3];
    }
    vec![vec![0; n]; n]
}

Drag options to blanks, or click blank then click option'

A0

Bmaze

Csolution.clone()

Dsolution

Attempts:

3 left

💡 Hint

Common Mistakes

Forgetting to use `.clone()` when returning solution.

Initializing with wrong value instead of 0.

Passing wrong argument to solve_maze_util.

Initialize the solution matrix with 0s, pass the maze reference to the utility function, and return a clone of the solution if a path is found.

Practice

1. What is the main goal of the Rat in a Maze problem in data structures?

easy

A. Find a path from the start to the destination in a maze

B. Count the total number of cells in the maze

C. Calculate the shortest distance between two points in a graph

D. Sort the maze cells in ascending order

Solution

1. Step 1: Understand the problem goal

   The Rat in a Maze problem asks to find a path from the start cell (usually top-left) to the destination cell (usually bottom-right) in a maze represented by a grid.

2. Step 2: Identify the correct goal

   The goal is not counting cells, sorting, or shortest distance but finding a valid path through allowed cells.

3. Final Answer:

   Find a path from the start to the destination in a maze -> Option A

4. Quick Check:

   Goal = Find path [OK]

Hint: Focus on pathfinding, not counting or sorting [OK]

Common Mistakes:

• Confusing pathfinding with counting cells
• Thinking it finds shortest path always
• Mixing it with sorting or graph distance problems

2. Which of the following Rust function signatures is correct for a recursive function solving the Rat in a Maze problem?

easy

A. fn solve_maze(maze: Vec<i32>, x: usize, y: usize) -> Vec<(usize, usize)>

B. fn solve_maze(maze: Vec, x: i32, y: i32) -> i32

C. fn solve_maze(maze: &mut Vec<i32>, x: usize, y: usize) -> bool

D. fn solve_maze(maze: &Vec, x: usize, y: usize, path: &mut Vec<(usize, usize)>) -> bool

Solution

1. Step 1: Check parameter types for maze and coordinates

   The maze is a 2D grid, so it should be a reference to a vector of vectors of integers (&Vec). Coordinates are usize for indexing.

2. Step 2: Check return type and path parameter

   The function returns bool to indicate success and uses a mutable path vector to store the route.

3. Final Answer:

   fn solve_maze(maze: &Vec, x: usize, y: usize, path: &mut Vec<(usize, usize)>) -> bool -> Option D

4. Quick Check:

   Correct signature uses references and bool return [OK]

Hint: Use references for maze and bool return for success [OK]

Common Mistakes:

• Passing maze by value causing unnecessary copying
• Using wrong coordinate types (i32 instead of usize)
• Returning wrong types like i32 or Vec instead of bool

3. Given the following Rust code snippet for Rat in a Maze, what will be printed?

fn main() {
    let maze = vec![
        vec![1, 0, 0, 0],
        vec![1, 1, 0, 1],
        vec![0, 1, 0, 0],
        vec![1, 1, 1, 1],
    ];
    let mut path = Vec::new();
    if solve_maze(&maze, 0, 0, &mut path) {
        println!("Path found: {:?}", path);
    } else {
        println!("No path found");
    }
}

fn solve_maze(maze: &Vec, x: usize, y: usize, path: &mut Vec<(usize, usize)>) -> bool {
    let n = maze.len();
    if x == n - 1 && y == n - 1 {
        path.push((x, y));
        return true;
    }
    if x < n && y < n && maze[x][y] == 1 {
        path.push((x, y));
        if x + 1 < n && solve_maze(maze, x + 1, y, path) {
            return true;
        }
        if y + 1 < n && solve_maze(maze, x, y + 1, path) {
            return true;
        }
        path.pop();
    }
    false
}

medium

A. Path found: [(0, 0), (1, 0), (1, 1), (2, 1), (3, 1), (3, 2), (3, 3)]

B. Path found: [(0, 0), (0, 1), (1, 1), (2, 1), (3, 1), (3, 2), (3, 3)]

C. No path found

D. Path found: [(0, 0), (1, 0), (2, 0), (3, 0), (3, 1), (3, 2), (3, 3)]

Solution

1. Step 1: Trace the recursive calls from (0,0)

   Start at (0,0) which is 1 (allowed). Try moving down to (1,0) which is 1, then (2,0) is 0 (blocked), so backtrack. Then try right from (1,0) to (1,1) which is 1.

2. Step 2: Continue path to destination

   From (1,1), down to (2,1) is 1, then down to (3,1) is 1, right to (3,2) is 1, and right to (3,3) is 1 (destination). Path is [(0,0),(1,0),(1,1),(2,1),(3,1),(3,2),(3,3)].

3. Final Answer:

   Path found: [(0, 0), (1, 0), (1, 1), (2, 1), (3, 1), (3, 2), (3, 3)] -> Option A

4. Quick Check:

   Recursive path = Path found: [(0, 0), (1, 0), (1, 1), (2, 1), (3, 1), (3, 2), (3, 3)] [OK]

Hint: Follow down then right moves recursively [OK]

Common Mistakes:

• Assuming path goes right first instead of down
• Not backtracking correctly on blocked cells
• Confusing coordinates order in path

4. Identify the bug in this Rust code snippet for Rat in a Maze and select the fix:

fn solve_maze(maze: &Vec, x: usize, y: usize, path: &mut Vec<(usize, usize)>) -> bool {
    let n = maze.len();
    if x == n - 1 && y == n - 1 {
        path.push((x, y));
        return true;
    }
    if x < n && y < n && maze[x][y] == 1 {
        path.push((x, y));
        if solve_maze(maze, x + 1, y, path) {
            return true;
        }
        if solve_maze(maze, x, y + 1, path) {
            return true;
        }
        path.pop();
    }
    false
}

medium

A. Change maze parameter to mutable reference

B. Remove path.pop() to keep all visited cells

C. Add boundary checks before recursive calls to avoid out-of-bounds

D. Return i32 instead of bool for success

Solution

1. Step 1: Analyze recursive calls for boundary safety

   The recursive calls use x+1 and y+1 without checking if they exceed maze size, risking out-of-bounds panic.

2. Step 2: Fix by adding boundary checks before recursion

   Adding checks like x + 1 < n and y + 1 < n before calling solve_maze prevents invalid indexing.

3. Final Answer:

   Add boundary checks before recursive calls to avoid out-of-bounds -> Option C

4. Quick Check:

   Boundary checks prevent panic [OK]

Hint: Always check indices before recursive calls [OK]

Common Mistakes:

• Ignoring index bounds causing runtime panic
• Changing maze to mutable unnecessarily
• Removing path.pop() causing wrong paths

5. You want to modify the Rat in a Maze solution in Rust to find all possible paths from start to finish instead of just one. Which approach is best?

hard

A. Use a queue to perform breadth-first search and return the shortest path only

B. Return a vector of paths and explore all possible moves recursively without stopping at first success

C. Stop recursion as soon as one path is found to save time

D. Modify the maze to mark visited cells permanently to avoid revisiting

Solution

1. Step 1: Understand requirement to find all paths

   Finding all paths means exploring every possible route without stopping at the first success.

2. Step 2: Use recursion to explore all moves and collect paths

   Return a vector of paths and do not return early. Backtrack properly to explore all options.

3. Final Answer:

   Return a vector of paths and explore all possible moves recursively without stopping at first success -> Option B

4. Quick Check:

   Explore all paths recursively [OK]

Hint: Collect all paths, don't stop at first success [OK]

Common Mistakes:

• Stopping recursion early losing other paths
• Using BFS only for shortest path, not all paths
• Marking visited permanently blocking other paths