I ask ChatGPT to explain the mouse in the maze problem

Me:

function buildMaze(size) {
  const maze = [];
  for (let i = 0; i < size; i++) {
    maze[i] = [];
    for (let j = 0; j < size; j++) {
      maze[i][j] = Math.random() > 0.3 ? 1 : 0;
    }
  }
  maze[0][0] = 1;
  maze[maze.length - 1][maze.length - 1] = 1;

  return maze;
}

const maze = buildMaze(4);

maze.forEach((row) => console.log(row));

function isSafe(maze, x, y) {
  const n = maze.length;
  if (x >= 0 && y >= 0 && x < n && y < n && maze[x][y] !== 0) {
    return true;
  }
  return false;
}

function findPath(maze, x, y, solution) {
  const n = maze.length;
  if (x === n - 1 && y === n - 1) {
    solution[x][y] = 1;
    return true;
  }
  if (isSafe(maze, x, y) === true) {
    solution[x][y] = 1;
    if (findPath(maze, x + 1, y, solution)) {
      return true;
    }
    if (findPath(maze, x, y + 1, solution)) {
      return true;
    }
    solution[x][y] = 0;
    return false;
  }
  return false;
}

function ratInAMaze(maze) {
  const solution = [];
  for (let i = 0; i < maze.length; i++) {
    solution[i] = [];
    for (let j = 0; j < maze[i].length; j++) {
      solution[i][j] = 0;
    }
  }
  if (findPath(maze, 0, 0, solution) === true) {
    return solution;
  }
  return "NO PATH FOUND";
}

console.log("-----------------");

const ans = ratInAMaze(maze);

if (typeof ans === "object") ans.forEach((row) => console.log(row));
else console.log(ans);

this is the log:

[ 1, 1, 1, 1 ]
[ 1, 1, 1, 0 ]
[ 0, 1, 1, 1 ]
[ 1, 1, 1, 1 ]
-----------------
[ 1, 0, 0, 0 ]
[ 1, 1, 0, 0 ]
[ 0, 1, 0, 0 ]
[ 0, 1, 1, 1 ]

Does the log output make sense to you?

ChatGPT:

Yes, the output makes sense based on how your maze is generated and solved.

Breakdown: Maze Generation (buildMaze)

Your function creates a random 4x4 maze with 1s (open path) and 0s (walls). The starting position (0,0) and the goal position (n-1, n-1) are always set to 1 (open). The generated maze in the log:

[ 1, 1, 1, 1 ]
[ 1, 1, 1, 0 ]
[ 0, 1, 1, 1 ]
[ 1, 1, 1, 1 ]

This means there are mostly open paths (1), except for a 0 in the second row and another in the third row. Pathfinding (ratInAMaze)

The findPath function explores the maze recursively: It tries moving right (x, y+1) first. If right doesn't work, it tries moving down (x+1, y). If a move doesn't lead to the goal, it backtracks (resets the cell to 0). The final solution matrix:

[ 1, 0, 0, 0 ]
[ 1, 1, 0, 0 ]
[ 0, 1, 0, 0 ]
[ 0, 1, 1, 1 ]

This solution follows a downward and then rightward approach. The path found: (0,0) -> (1,0) -> (1,1) -> (2,1) -> (3,1) -> (3,2) -> (3,3)

Me:

i wonder why the solution didn't go down on [0][2] first, then all the way to [3][2], and [3][3], i guess it has to do with how the callstack is form?

ChatGPT

You're exactly right! The behavior of the solution is determined by recursion and the call stack.

Why Didn't the Solution Go Down from [0][2] First? Your findPath function follows this order of movement:

1. Move Right (x, y+1)
2. Move Down (x+1, y)
3. If neither works, backtrack (reset the cell and return false).

This means it prioritizes moving right first, which influences how the call stack is formed.

How the Call Stack Forms: Step-by-Step Execution:

1. Start at (0,0) → Open path → Mark solution[0][0] = 1
2. Try moving right to (0,1) → Open path → Mark solution[0][1] = 1
3. Try moving right to (0,2) → Open path → Mark solution[0][2] = 1
4. Try moving right to (0,3) → Open path → Mark solution[0][3] = 1
5. Try moving right to (0,4) (out of bounds) → Backtrack
6. Try moving down to (1,3) → Blocked (0) → Backtrack
7. Backtrack further to (0,2), (0,1), then (0,0) (since right didn't work)
8. Now, it tries moving down instead:
   • Move down to (1,0) → Open path → Mark solution[1][0] = 1
   • Try moving right to (1,1) → Open path → Mark solution[1][1] = 1
   • Try moving right to (1,2) → Blocked (0) → Backtrack
   • Try moving down to (2,1) → Open path → Continue down to (3,1), then right to (3,2), and finally (3,3)

Key Takeaway:

The function always tries moving right first. The call stack remembers previous decisions, so if moving right doesn't work, it backtracks and tries moving down. Since (0,2) didn't work in its first recursive attempt, it never revisits that path after backtracking. If you wanted the solution to go down first, you could swap the movement order:

if (findPath(maze, x + 1, y, solution)) {
  // Try Down First
  return true;
}
if (findPath(maze, x, y + 1, solution)) {
  // Then Right
  return true;
}

This would favor a downward-first search instead.

Does that explanation make sense?

Me:

i still don't get that, in the first attempt, 01 -> 02 -> 03 -> 13, why it only try to go down from 03, and found it not work, then backtrack all the way back to 00, instead not exploring 12 from 02.

ChatGPT:

Great question! The reason the algorithm doesn't explore (1,2) from (0,2) before backtracking all the way is because of how recursive calls are stacked and undone.

Let's Break it Down:

Your function tries moving right first, then down. This means when it explores a path, it commits to moving right as long as possible before trying any downward moves.

1. Start at (0,0)

   • Mark solution[0][0] = 1
   • Try Right → (0,1)

2. Move to (0,1)

   • Mark solution[0][1] = 1
   • Try Right → (0,2)

3. Move to (0,2)

   • Mark solution[0][2] = 1
   • Try Right → (0,3)

4. Move to (0,3)

   • Mark solution[0][3] = 1
   • Try Right → (0,4) (out of bounds, fails)
   • Try Down → (1,3) (wall, fails)
   • Backtrack to (0,2)
   • Undo solution[0][3] = 0

5. Back at (0,2), why doesn't it try (1,2)?

   • Because it has already "committed" to moving right first
   • The function returns false for (0,3), meaning this entire path was a failure.
   • Backtrack further to (0,1)
   • Undo solution[0][2] = 0

6. Back at (0,1), why not try (1,1) now?

   • Because we are still unwinding failed paths.
   • The function has to return false all the way back to the first failed choice.
   • Backtrack further to (0,0)
   • Undo solution[0][1] = 0

7. Back at (0,0), now try (1,0)

   • This path works, so it proceeds downwards and eventually finds the correct path.

Key Takeaways

• Recursion is depth-first: It fully commits to the first choice (right) before trying alternatives.
• Backtracking undoes the entire failed decision: Since the decision to go right from (0,2) failed, the algorithm doesn't go back and try downward moves from (0,2).
• Once a function call returns false, it doesn't revisit previous choices: (0,2) was only explored because (0,1) chose to move right. Once (0,3) failed, it never goes back to check downward moves from (0,2).

Me:

Now explain this case, why now at 0,2, it didn't backtrack all the way back to 0,0, but move down??

[ 1, 1, 1, 1 ]
[ 1, 0, 1, 0 ]
[ 0, 0, 1, 1 ]
[ 1, 1, 1, 1 ]
-----------------
[ 1, 1, 1, 0 ]
[ 0, 0, 1, 0 ]
[ 0, 0, 1, 0 ]
[ 0, 0, 1, 1 ]

ChatGPT

Great question! Let's focus on why at (0,2), the algorithm decided to move down instead of backtracking all the way to (0,0).

Key Difference: Why (0,2) → (1,2) Instead of Full Backtrack?

The main reason is that not all paths from (0,2) were exhausted yet.

When the algorithm reached (0,3), it tried:

1. Moving right ((0,4)) → Failed (out of bounds).
2. Moving down ((1,3)) → Failed (wall).
3. No other moves left, so it backtracked to (0,2).

But now, at (0,2), it hasn't yet tried moving down to (1,2).

This is the key difference! The algorithm only fully backtracks when all possible moves from a position have been attempted and failed.

Comparing the Two Cases

Let's go case by case and analyze why backtracking behaves differently.

📌 First Case (Full Backtrack to (0,0))

Maze:

[ 1, 1, 1, 1 ]
[ 1, 1, 1, 0 ]
[ 0, 1, 1, 1 ]
[ 1, 1, 1, 1 ]

Solution Found:

[ 1, 0, 0, 0 ]
[ 1, 1, 0, 0 ]
[ 0, 1, 0, 0 ]
[ 0, 1, 1, 1 ]

Step-by-step Execution

1. (0,0) → (0,1) → (0,2) → (0,3)
2. Fails at (0,3):
   • Right (0,4): Out of bounds ❌
   • Down (1,3): Blocked (0) ❌
   • No moves left → Backtrack to (0,2)
3. Back at (0,2):
   • Right (0,3): Already failed ❌
   • No untried moves left → Backtrack to (0,1)
4. Back at (0,1):
   • Right (0,2): Already failed ❌
   • No untried moves left → Backtrack to (0,0)
5. Back at (0,0), try down instead ((1,0)), leading to a different path.

🛠 Why Full Backtrack Happened

• When the function backtracked to (0,2), it had no remaining moves (right already failed, and it never tried down because it wasn't open).
• This forced it to continue unwinding the stack until it reached (0,0), where a new path (down) was discovered.

📌 Second Case (Moves Down at (0,2))

Maze:

[ 1, 1, 1, 1 ]
[ 1, 0, 1, 0 ]
[ 0, 0, 1, 1 ]
[ 1, 1, 1, 1 ]

Solution Found:

[ 1, 1, 1, 0 ]
[ 0, 0, 1, 0 ]
[ 0, 0, 1, 0 ]
[ 0, 0, 1, 1 ]

Step-by-step Execution

1. (0,0) → (0,1) → (0,2) → (0,3)
2. Fails at (0,3):
   • Right (0,4): Out of bounds ❌
   • Down (1,3): Blocked (0) ❌
   • No moves left → Backtrack to (0,2)
3. Back at (0,2):
   • Right (0,3): Already failed ❌
   • Down (1,2) is open! ✅ → Move down instead of backtracking further.
4. Continues down from (1,2), leading to the final solution.

🛠 Why It Didn't Fully Backtrack This Time

• When it backtracked to (0,2), there was still a move left to try ((1,2)).
• Since it could still explore a new path, it didn't have to continue unwinding the stack all the way to (0,0).

🚀 Key Takeaways

Full backtracking happens only when all possible moves from a position are exhausted.

• In the first case, (0,2) had no available moves left, so the backtracking continued.
• In the second case, (0,2) still had a valid move (down), so it took it instead of backtracking further.

The depth-first nature of recursion means once a path is abandoned, it won't be reconsidered.

• That's why in the first case, (0,2) didn't try moving down—because the function never reached that point before fully backtracking.

Order of movement matters.

• Right-first search heavily influences when and how backtracking occurs.
• If movement order were reversed (down first, then right), we'd see completely different solutions.