Maze Solver Museum

Generation Topology

Solver

Loading algorithms

Rows Cols

Seed Speed Fresh maze on solver change

start goal visited frontier goal-wave path

Selected Algorithm

Breadth-First Search

native Unweighted graph search

Breadth-first search explores the maze in distance layers, so the first time it reaches the goal is the shortest unweighted route.

How To Read It Cyan cells are explored by layer; amber cells are waiting in the frontier.

Best Use Use it when every move has the same cost and shortest path length matters.

Trade-Off It is reliable but can visit a wide area before the goal is reached.

Core Procedure

enqueue start
pop by FIFO layer
record parent
trace goal path

Breadth-First Search

Shortest path by edge count in unweighted mazes.

TimeO(V + E)

SpaceO(V)

CompleteYes

OptimalYes

Path0

Visited0

Frontier0

Steps0

Coverage0%

Work / Path0.00

Events0

Calculated Bound0

V / E0 / 0

Open Cells0

Walls0%

Dead Ends0

Junctions0

Corridor Bias0.00

Algorithm Anatomy

Unweighted graph search native

Frontier FIFO queue by distance layer

Cost Model Unit edge cost

Guarantee Complete and shortest on unweighted grids

Trace Start-origin expansion

Why It Works

Layered graph expansion over a grid graph G = (V, E).

dist[v] = dist[u] + 1 The cyan wave grows in distance layers.

Recursive Backtracker

Depth-first spanning-tree construction over odd grid cells.

Spanning tree Perfect maze O(V + E)

Model Randomized DFS on the cell graph.

Bias Long corridors and low branching.

Invariant Every carved cell is connected to the start tree.

Procedure

push start
choose unvisited neighbor
carve wall
backtrack on dead ends

Mathematical Breakdown

Layered graph expansion over a grid graph G = (V, E).

Grid graph Unit cost

Recurrence / Score dist[v] = dist[u] + 1

Invariant The first time a cell is dequeued, its edge-count distance is minimal.

Procedure

enqueue start
pop by FIFO layer
record parent for every new cell
trace parents from goal

What to Watch The cyan wave grows in distance layers; magenta appears only after the route is reconstructed.