![]() ![]() Starting from a random cell, the computer then selects a random neighbouring cell that has not yet been visited. Consider the space for a maze being a large grid of cells (like a large chess board), each cell starting with four walls. ![]() Frequently implemented with a stack, this approach is one of the simplest ways to generate a maze using a computer. ![]() This algorithm is a randomized version of the depth-first search algorithm. Finally, when all vertices of F have been visited, F is erased and two edges from G, one for the entrance and one for the exit, are removed. During the traversal, whenever a red edge crosses over a blue edge, the blue edge is removed. Second, computer traverses F using a chosen algorithm, such as a depth-first search, coloring the path red. First, the computer creates a random planar graph G shown in blue, and its dual F shown in yellow. The animation shows the maze generation steps for a graph that is not on a rectangular grid. Loops, which can confound naive maze solvers, may be introduced by adding random edges to the result during the course of the algorithm. Because of this, maze generation is often approached as generating a random spanning tree. If the graph contains loops, then there may be multiple paths between the chosen nodes. ![]() If the subgraph is not connected, then there are regions of the graph that are wasted because they do not contribute to the search space. The purpose of the maze generation algorithm can then be considered to be making a subgraph in which it is challenging to find a route between two particular nodes. This predetermined arrangement can be considered as a connected graph with the edges representing possible wall sites and the nodes representing cells. A maze can be generated by starting with a predetermined arrangement of cells (most commonly a rectangular grid but other arrangements are possible) with wall sites between them. ![]()
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May 2023
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