Rat in a Maze Problem in DSA Rust - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal in the Rat in a Maze problem?

To find a path from the start point (usually top-left) to the destination (usually bottom-right) in a maze represented by a grid, moving only through allowed cells.

beginner

Which algorithmic technique is commonly used to solve the Rat in a Maze problem?

Backtracking, which tries possible paths and backtracks when a path leads to a dead end.

beginner

In the Rat in a Maze problem, what does a cell value of 0 usually represent?

A blocked cell where the rat cannot move.

intermediate

Why do we mark cells as visited during the Rat in a Maze solution?

To avoid revisiting the same cell and getting stuck in infinite loops.

advanced

What is the time complexity of the Rat in a Maze problem using backtracking on an N x N grid?

O(2^(N^2)) in the worst case, because each cell can be either part of the path or not, leading to exponential possibilities.

In the Rat in a Maze problem, which moves are typically allowed?

A Only Right and Down

B Up, Down, Left, Right

C Diagonal moves only

D Any direction including diagonal

The rat can move up, down, left, or right, but not diagonally.

What does backtracking do when it hits a dead end in the maze?

A Marks the cell as part of the path anyway

B Stops and returns failure immediately

C Tries a different path by going back to the previous cell

D Skips the cell and moves forward

Backtracking goes back to the previous cell to try a different path.

What data structure is commonly used to keep track of the path in the Rat in a Maze problem?

A Stack or recursion call stack

B Queue

C Hash map

D Linked list

Backtracking uses recursion which implicitly uses a call stack to keep track of the path.

If the maze is represented by a 2D array, what does a value of 1 usually mean?

A Destination point

B Blocked cell

C Start point

D Open cell where the rat can move

A value of 1 means the cell is open and the rat can move through it.

What is the base case in the recursive solution of the Rat in a Maze problem?

A When the rat reaches the destination cell

B When the rat hits a blocked cell

C When all cells are visited

D When the rat moves out of the maze

The base case is when the rat reaches the destination cell successfully.

Explain how backtracking helps solve the Rat in a Maze problem.

Think about trying moves and undoing them if they don't lead to success.

Describe the role of the maze grid and what the values inside it represent in the Rat in a Maze problem.

Consider how the rat knows where it can move.

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