Hard

Google-styleMicrosoft-style

Fewest Moves to Solve a Sliding Tile Puzzle DSA Interview

Given a small 2-by-3 sliding tile puzzle board with one blank space, find the minimum number of adjacent tile slides needed to reach a specified target arrangement, or report it is unreachable.

Mock Interview with AI

1. Problem Statement

You are given a 2x3 sliding tile board (6 cells, one of which is blank, represented as 0) in a start arrangement and a target arrangement. Each move slides a tile adjacent to the blank into the blank space. Return the minimum number of moves to reach the target arrangement from the start, or -1 if it cannot be reached.

2. Live Coding Format

Choose Python, JavaScript, Java, or C++, then solve while explaining your reasoning to the live interviewer.

Validation uses handwritten tests only. The MVP does not compile or run code, and it does not provide AI algorithm completion.

3. Key Focus Areas

1
Problem clarification and contract
2
Approach exploration and optimality
3
Think-aloud communication and pacing
4
Implementation correctness
5
Code quality and language fluency
6
Handwritten tests and dry run
7
Debugging and self-correction
8
Complexity analysis
9
Follow-up performance

4. What Strong Candidates Should Demonstrate

✓Clarify board encoding, move rules, and unreachable-case behavior before coding.
✓Explain an unbounded DFS baseline and improve to visited-state BFS over the configuration graph.
✓Think aloud while implementing careful state encoding and neighbor generation.
✓Validate with explicit expected outputs and a top-to-bottom handwritten dry run.
✓Analyze time and space complexity and handle a focused follow-up extension.

Evaluation Guide

This is an evaluation framework, not a single model answer. Strong designs may make different choices when their assumptions and trade-offs are explicit.

Problem clarification and contract

10%

Senior signals

✓Clarifies the board encoding (flat array representing a 2x3 grid, with 0 as the blank), confirms which positions are adjacent for sliding, and asks what to return if start already equals target.
✓Confirms both boards are guaranteed to contain the same set of tile values (a valid permutation), so the only question is reachability via legal moves.

Staff-level signals

◆Asks whether the total configuration space is small enough to enumerate exhaustively, to justify a full-state BFS.

Common red flags

×Codes immediately while assuming any arrangement is reachable from any other without confirming or discussing reachability.

Approach exploration and optimality

20%

Senior signals

✓Explains a naive baseline that explores move sequences via DFS without tracking visited states, identifies the risk of revisiting the same configuration indefinitely or doing redundant exponential work, and improves to BFS over the state-space graph where each node is a board configuration and edges are legal single slides, tracking visited configurations.
✓Explains why BFS (not DFS) guarantees the first time the target is reached corresponds to the minimum number of moves.

Staff-level signals

◆Discusses how encoding a board configuration as a single string or tuple enables an efficient visited-set lookup.

Common red flags

×Starts implementation without explaining an approach even after one interviewer prompt.
×Proposes DFS for a shortest-path count without acknowledging it does not guarantee minimality.

Think-aloud communication and pacing

10%

Senior signals

✓Explains the plan before coding and narrates state encoding and neighbor-generation logic while implementing.
✓Paces the core solution to leave time for validation and the follow-up.

Common red flags

×Writes substantial code silently and cannot explain what the code is doing.

Implementation correctness

25%

Senior signals

✓Implements a correct BFS from the start configuration, generating neighbor configurations by sliding the blank into each valid adjacent position, tracking visited configurations, and returning the level at which the target is first reached, or -1 if the queue empties first.
✓Handles start already equal to target (0 moves), an unreachable target, and correct adjacency for all six board positions (including corner and edge positions with fewer neighbors).
✓Provides a convincing invariant argument for why BFS level order gives the minimum move count.

Common red flags

×Misses one or more valid adjacent-slide positions for a given blank location, producing incorrect neighbor generation.
×Final code contains a material correctness bug that the candidate does not identify.

Code quality and language fluency

15%

Senior signals

✓Produces readable, language-appropriate code with a clear board-to-key encoding, a defined adjacency map for blank positions, and a well-structured BFS queue.

Common red flags

×Contains adjacency-mapping errors or syntax-level incoherence that prevents credible reasoning.

Handwritten validation, dry run, and debugging

10%

Senior signals

✓Provides explicit inputs and expected outputs before tracing the code from top to bottom, showing a few BFS levels of explored configurations.
✓Covers start equal to target, a one-move solution, and a target that is unreachable (if the candidate agrees such cases exist for a 2x3 board, or discusses why they may not).
✓Finds and fixes an error independently, then re-validates the affected path.

Common red flags

×Claims the code works without a representative trace.

Complexity analysis and follow-up

10%

Senior signals

✓States time and space complexity in terms of the total number of distinct board configurations (bounded by 6! for a 2x3 board) and the branching factor per state, comparing this with the unbounded DFS baseline.

Staff-level signals

◆Discusses how the approach would need to change for a larger board where the full configuration space is too large to enumerate exhaustively.

Common red flags

×Cannot state the complexity of the implemented solution.
×Fails a reasonable follow-up despite having at least five minutes and receiving bounded clarification.

Trade-offs to articulate

DFS without visited-state tracking can revisit the same configuration repeatedly and does not guarantee finding the minimum number of moves even if it terminates.
BFS over the state-space graph with a visited set guarantees the minimum move count, bounded by the total number of distinct reachable configurations, which is small and fixed for a 2x3 board.
Bidirectional BFS from both start and target can reduce the explored state count further but adds implementation complexity that is only worthwhile for much larger configuration spaces.

Practice follow-up questions

1.Coding follow-up: extend the solution to also return one shortest sequence of moves (e.g., the blank's path or the sequence of board configurations), not just the move count, achieving the target.
2.Verbal extension: how would the approach need to change for a larger board (e.g., 3x3 or 4x4) where the full configuration space is too large to explore exhaustively?

Want interactive feedback?

Practice this problem in the live coding workspace while the interviewer probes your clarification, algorithm, implementation, complexity, and handwritten tests.

Start Interview

Core Concepts

State-Space SearchBFSGraphsComplexity Analysis