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Maze generation: Difference between revisions
Mathematica
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<a id='solve' style='display:none' href='javascript:solve(); void(0)'>Solve</a>
</fieldset></form><table id='maze'/></body></html></lang>
=={{header|Mathematica}}==
<lang mathematica>MazeGraphics[m_, n_] :=
Block[{$RecursionLimit = Infinity,
unvisited = Tuples[Range /@ {m, n}], maze},
maze = Graphics[{Line[{{#, # - {0, 1}}, {#, # - {1, 0}}}] & /@
unvisited,
Line[{{0, n}, {0, 0}, {m, 0}}]}]; {unvisited =
DeleteCases[unvisited, #];
Do[If[MemberQ[unvisited, neighbor],
maze = DeleteCases[
maze, {#,
neighbor - {1, 1}} | {neighbor, # - {1, 1}}, {5}]; #0@
neighbor], {neighbor,
RandomSample@{# + {0, 1}, # - {0, 1}, # + {1, 0}, # - {1,
0}}}]} &@RandomChoice@unvisited; maze];
maze = MazeGraphics[13, 21]</lang>
{{Out}}
[[File:MathematicaMazeGraphics.png]]
===Graph===
{{Works with|Mathematica|9.0}}
Here I generate a maze as a graph. Vertices of the graph are cells and edges of the graph are removed walls. This version is mush faster and is convenient to solve.
<lang mathematica>MazeGraph[m_, n_] :=
Block[{$RecursionLimit = Infinity, grid = GridGraph[{m, n}],
visited = {},
edges = {}}, {AppendTo[visited, #];
Do[If[FreeQ[visited, neighbor],
AppendTo[edges, # <-> neighbor]; #0@neighbor], {neighbor,
RandomSample@AdjacencyList[grid, #]}]} &@
RandomChoice@VertexList@grid;
Graph[Range[m n], edges,
GraphLayout -> {"GridEmbedding", "Dimension" -> {m, n}}]];
maze = MazeGraph[13, 21]</lang>
{{Out}}
[[File:MathematicaMazeGraph.png]]
=={{header|MATLAB}}==
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