Maze complexity is how we measure how difficult a maze is to solve. It's not just about size — a tiny maze with many deceptive branches can be harder than a huge maze with a clear path. Complexity comes from the interplay of solution length, junction count, dead-end density, and the branching factor at each decision point.
The length of the shortest solution divided by the maze dimensions. A 10×10 maze with a 50-step solution is more complex than one with a 15-step solution. We use BFS to compute this because it guarantees finding the true shortest path.
Junctions where you must choose between two or more paths. More junctions mean more chances to go wrong. The branching factor at each junction matters too: a 4-way crossroads is harder than a simple T-junction.
The percentage of cells that are dead ends. More dead ends = more wrong turns. But length matters too: a 20-cell dead end wastes more time than a 2-cell dead end. The product of count × length is the real penalty.
What fraction of the maze is on the solution path? If only 10% of cells are on the correct route, there's a 90% chance any random turn leads to a dead end. This ratio is the single best predictor of perceived difficulty for human players.
| Algorithm | Corridor Length | Dead Ends | Branching | Difficulty |
|---|---|---|---|---|
| Recursive Backtracking | Long | Fewer, longer | Low | ⭐⭐⭐⭐ |
| Prim's Algorithm | Short | More, shorter | High | ⭐⭐⭐ |
| Kruskal's | Medium | Balanced | High | ⭐⭐⭐ |
| Wilson's | Varied | Uniform | Uniform | ⭐⭐⭐⭐ |
Try our mazes at different difficulty levels and feel how complexity changes the experience.
A combination of long solution paths, many junctions with multiple choices, long dead ends that waste time, and a low ratio of correct-path cells to total cells. The hardest mazes combine all of these.
No. Structure matters more than size. A small maze with deceptive branches can be harder than a large maze with a simple layout. Size contributes, but the algorithm and parameters have a bigger impact.
By choosing the algorithm (recursive backtracking for hard, Prim's for easier), adjusting grid size, adding/removing loops, and tuning dead-end length.