How to Solve Mazes: From Right-Hand Rule to A* (With Visuals)

Want to solve mazes systematically? This guide covers intuitive and algorithmic approaches, explains when each works best, and offers speedrun tips.

1) Right-Hand Rule (Wall Following)

• Intuition: keep your right hand on the wall and keep moving

• Best for: simple, connected planar mazes; does not guarantee shortest path

• Limitation: can loop in mazes with cycles

Practice

• Try it in /maze; zoom in slightly and focus on consistent wall contact

2) Junction Mapping

• Mark each junction (on paper or mentally) to avoid revisiting explored branches

• Ideal for medium-complexity mazes

3) BFS (Breadth-First Search)

• Guarantees the shortest path (if edges are unweighted)

• Works well for grid mazes; time O(V+E)

Pseudocode

```text queue = [start] visited = {start: null} while queue not empty: cur = queue.pop_front() if cur == goal: break for each neighbor in neighbors(cur): if neighbor not in visited: visited[neighbor] = cur queue.push_back(neighbor)

path = reconstruct from visited[goal]
```

4) Dijkstra (equivalent to BFS when edges are equal)

• Use for weighted terrains (different movement costs)

• Priority queue recommended; complexity O(E log V)

5) A* (Heuristic Search)

• f(n)=g(n)+h(n); use Manhattan distance for grid mazes

• Reduces expansions and speeds up search under similar heuristics

Speedrun Tips

• Route review: after finishing, revisit key junctions to find potential shortcuts

• Visualization: keep an active mental boundary of unexplored regions

• Rhythm: avoid excessive backtracking; prioritize frontier expansion

Common Pitfalls

• Overusing wall-following in complex mazes

• Failing to mark junctions, leading to repeated exploration

Practice & Tools

• Play online: /maze · /maze-runner

• Algorithm demos: /maze-algorithms

FAQ

Is A* always faster than BFS? Not necessarily. BFS can be very fast on certain structures; A* shines by expanding fewer nodes.

How to practice on mobile?
Use touch swipe controls; start with low complexity and ramp up gradually.