Grid Teleportation Traversal

Grid Teleportation Traversal

What is this problem about?

(Note: Assuming this relates to a standard variant like "Minimum Moves to Reach Target with Teleporters/Snakes and Ladders" or similar, based on the topics). The Grid Teleportation Traversal interview question asks you to find the shortest path from a starting cell to a target cell in a 2D matrix. You can move to adjacent cells, but the grid also contains "teleporters" (or portals) that instantly transport you from one specific cell to another. You need to find the minimum number of steps to reach the destination.

Why is this asked in interviews?

Companies like Meta and Visa use this Breadth-First Search (BFS) interview pattern to test your ability to model complex movements in a graph. It evaluates whether you can handle standard grid traversal while integrating "instantaneous" edges (teleports) without getting stuck in infinite loops.

Algorithmic pattern used

This is solved using Breadth-First Search (BFS) with a Visited Set.

1. Initialize a queue with the starting cell and a step count of 0.
2. Use a boolean matrix or a Hash Set to track visited cells.
3. In each BFS step, pop the current cell.
4. Generate all possible next moves (up, down, left, right).
5. For each valid move, check if it contains a teleporter. If it does, the "next cell" becomes the teleporter's destination.
6. If the next cell hasn't been visited, mark it as visited and push it to the queue with steps + 1.

Example explanation

Start: (0, 0). Target: (2, 2). Teleporter at (0, 1) takes you to (2, 1).

1. Queue: [((0, 0), 0)].
2. Pop (0, 0). Neighbors: (1, 0) and (0, 1).
3. Neighbor (0, 1) has a teleporter to (2, 1). Add ((2, 1), 1) to queue. Add ((1, 0), 1) to queue.
4. Pop ((2, 1), 1). Neighbors include (2, 2).
5. Target (2, 2) reached in $1 + 1 = 2$ steps.

Common mistakes candidates make

• Teleporter Loops: If a teleporter at A goes to B, and B teleports to A, not marking A and B as visited correctly can cause an infinite BFS loop.
• Counting Teleports as Steps: Usually, moving into a teleporter costs 1 step, but the teleportation itself is instantaneous. Miscounting this leads to off-by-one errors.
• DFS instead of BFS: Using Depth-First Search. DFS will find a path, but not necessarily the shortest path, unless you check all paths, which is exponential.

Interview preparation tip

Whenever a problem asks for the "shortest path" or "minimum steps" in an unweighted graph or grid, BFS is the mandatory approach. Be sure to mark nodes as visited when you add them to the queue, not when you pop them, to avoid redundant queue growth.