Rat in a Maze Problem in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if the rat can move to the next cell inside the maze boundaries.

DSA C++

bool isSafe(int x, int y, int n) {
    return (x >= 0 && y >= 0 && x < [1] && y < n);
}

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

An

Bn-1

Cn+1

D2*n

Attempts:

3 left

💡 Hint

Common Mistakes

Using n-1 instead of n in the boundary check.

Not checking for negative indices.

The maze size is n x n, so valid indices are from 0 to n-1. We check if x and y are less than n to stay inside boundaries.

2fill in blank

medium

Complete the code to mark the current cell as part of the solution path.

DSA C++

void solveMazeUtil(int maze[][[1]], int x, int y, int n, int sol[][[1]]) {
    sol[x][y] = 1;
    // rest of the code
}

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

Ax

Bn

Cy

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using x or y as the array size dimension.

Using a fixed size like 1.

The maze and solution arrays are n x n, so the second dimension must be n.

3fill in blank

hard

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

DSA C++

if (solveMazeUtil(maze, x, y + 1, n, sol)) {
    return [1];
}

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

Atrue

Bfalse

Csol[x+1][y]

Dmaze[x+1][y]

Attempts:

3 left

💡 Hint

Common Mistakes

Returning false instead of true.

Returning the maze or solution cell value.

If the recursive call returns true, we return true to indicate the path is found.

4fill in blank

hard

Fill both blanks to check if the next cell is safe and open for the rat to move.

DSA C++

if (isSafe(x + [1], y + [2], n) && maze[x + [1]][y + [2]] == 1) {
    if (solveMazeUtil(maze, x + [1], y + [2], n, sol)) {
        return true;
    }
}

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

A1

B0

C-1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 for x increment or 0 for y increment.

Using negative increments incorrectly.

To move right, keep x the same (0) and increase y by 1.

5fill in blank

hard

Fill all three blanks to backtrack by unmarking the current cell and return false.

DSA C++

sol[x][y] = [1];
return [2];
// End of function returns [3] if no path found

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

A0

Bfalse

Ctrue

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting solution cell to 1 instead of 0.

Returning true instead of false.

Backtracking means unmarking the cell (0) and returning false to indicate failure.

Practice

1. What is the main goal of the Rat in a Maze Problem in Data Structures & Algorithms?

easy

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

B. Count the number of walls 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 context

   The Rat in a Maze problem involves navigating a maze represented by a grid to find a path from the start cell to the destination cell.

2. Step 2: Identify the main objective

   The main objective is to find a valid path through open cells (usually marked as 1) from the start to the end point.

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 walls
• Thinking it's about sorting cells
• Assuming it's about shortest distance always

2. Which of the following is the correct way to declare a 2D maze array of size 4x4 in C++?

easy

A. int maze[4][4];

B. int maze(4,4);

C. int maze[4,4];

D. int maze{4,4};

Solution

1. Step 1: Recall C++ array declaration syntax

   In C++, a 2D array is declared using square brackets for each dimension, like int maze[4][4];.

2. Step 2: Analyze each option

   int maze[4][4]; uses correct syntax. int maze(4,4); uses parentheses which is invalid for arrays. int maze[4,4]; uses comma inside brackets which is incorrect. int maze{4,4}; uses braces which is invalid for declaration.

3. Final Answer:

   int maze[4][4]; -> Option A

4. Quick Check:

   2D array = int maze[4][4]; [OK]

Hint: Use square brackets for array dimensions [OK]

Common Mistakes:

• Using parentheses instead of brackets
• Using commas inside brackets
• Using braces for declaration

3. Consider the following C++ code snippet for a 2x2 maze where 1 means open path and 0 means blocked:

int maze[2][2] = {{1, 0}, {1, 1}};
bool solveMaze(int maze[2][2], int x, int y) {
  if (x == 1 && y == 1) return true;
  if (x < 0 || y < 0 || x >= 2 || y >= 2 || maze[x][y] == 0) return false;
  if (solveMaze(maze, x + 1, y)) return true;
  if (solveMaze(maze, x, y + 1)) return true;
  return false;
}
int main() {
  bool result = solveMaze(maze, 0, 0);
  std::cout << (result ? "Path Found" : "No Path") << std::endl;
  return 0;
}

What will be the output when this program runs?

medium

A. Runtime Error

B. No Path

C. Compilation Error

D. Path Found

Solution

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

   At (0,0), maze[0][0] = 1 (open). Try moving down to (1,0): maze[1][0] = 1 (open). From (1,0), try moving down to (2,0) invalid, then right to (1,1): maze[1][1] = 1 (open) and is destination.

2. Step 2: Confirm path existence

   Since (1,1) is reached, function returns true and prints "Path Found".

3. Final Answer:

   Path Found -> Option D

4. Quick Check:

   Valid path exists = Path Found [OK]

Hint: Follow recursion down and right moves [OK]

Common Mistakes:

• Ignoring boundary checks
• Assuming no path due to blocked cell
• Confusing indices order

4. The following code snippet is intended to solve the Rat in a Maze problem but has a bug:

bool solveMaze(int maze[3][3], int x, int y) {
  if (x == 2 && y == 2) return true;
  if (x > 2 || y > 2 || maze[x][y] == 0) return false;
  if (solveMaze(maze, x + 1, y)) return true;
  if (solveMaze(maze, x, y + 1)) return true;
  return false;
}

What is the bug in this code?

medium

A. Missing check for negative indices

B. No check for maze boundaries less than zero

C. No check for visited cells causing infinite recursion

D. Incorrect base case coordinates

Solution

1. Step 1: Analyze boundary and base case checks

   The code checks if x or y are greater than 2 and if the cell is blocked. It returns true if destination (2,2) is reached.

2. Step 2: Identify missing visited check

   There is no mechanism to mark visited cells, so the recursion can revisit the same cells repeatedly, causing infinite recursion or stack overflow.

3. Final Answer:

   No check for visited cells causing infinite recursion -> Option C

4. Quick Check:

   Visited check missing = Infinite recursion [OK]

Hint: Always mark visited cells to avoid loops [OK]

Common Mistakes:

• Ignoring visited cells check
• Assuming boundary checks cover all cases
• Confusing base case with boundary

5. Given a 4x4 maze represented as:

int maze[4][4] = {
  {1, 0, 0, 0},
  {1, 1, 0, 1},
  {0, 1, 0, 0},
  {1, 1, 1, 1}
};

Write a function to find one path from (0,0) to (3,3) moving only right or down. Which of the following describes the correct approach?

hard

A. Use depth-first search but only move left and up

B. Use backtracking to explore right and down moves, marking visited cells to avoid cycles

C. Use breadth-first search without marking visited cells

D. Use a greedy approach always moving right first without backtracking

Solution

1. Step 1: Understand movement constraints and maze structure

   The rat can move only right or down. The maze has blocked cells (0) and open cells (1). We need to find a path from top-left to bottom-right.

2. Step 2: Choose correct algorithm approach

   Backtracking explores all possible paths by moving right or down, marking visited cells to avoid revisiting and infinite loops. Greedy or BFS without visited checks can fail or loop.

3. Final Answer:

   Use backtracking to explore right and down moves, marking visited cells to avoid cycles -> Option B

4. Quick Check:

   Backtracking + visited = Correct approach [OK]

Hint: Backtrack with visited marks for safe pathfinding [OK]

Common Mistakes:

• Using greedy without backtracking
• Ignoring visited cells causing loops
• Moving in wrong directions