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Implementing the Aldous-Broder Algorithm

Explore how to implement the Aldous-Broder algorithm to generate unbiased mazes using random walks. Understand the step-by-step process, how to detect visited cells, and how to analyze the maze's textures to confirm lack of bias. Learn about its practical drawbacks, such as inefficiency on large grids, and why its uniformity is important despite those challenges.

We'll cover the following...

The AldousBroder class

As might be expected, the random walk forms the core of our implementation, repeatedly visiting neighboring cells until no unvisited cells remain. It comes together without any surprises, just as described.

We'll create a new file named aldous_broder.rb. As before, we’ll put the algorithm in its own class so we can reuse it more easily.

C++
class AldousBroder
  def self.on(grid)
    cell = grid.random_cell 
    unvisited = grid.size - 1 
    while unvisited > 0 
      neighbor = cell.neighbors.sample 
      if neighbor.links.empty?
        cell.link(neighbor) 
        unvisited -= 1 
      end
      cell = neighbor 
    end
    grid
  end
end

Code explanation

Lines 4–5: We start everything off by choosing one cell at random. The random walk will begin at that cell. To make sure the algorithm knows when everything has been visited, line 5 ...