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Mazes for Programmers

Solution: Optimizing Aldous-Broder

Explore the process of optimizing the Aldous-Broder algorithm for maze generation by using random walks and careful tracking of cell visits. Learn how to select neighbors wisely and link cells to ensure an unbiased and complete maze, improving maze generation efficacy through code implementation.

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Solution

Let's execute the following solution code and see how it works:

C++
# This is a modified---and biased!---version of the Aldous- Broder
# algorithm. If you thought the result was unbiased, consider that
# this version now *prefers* a least-visited neighbor over other
# neighbors; the result may or may not exhibit a tell-tale texture, but
# it's still biased!
class ModifiedAldousBroder
# Write your code here
  def self.on(grid)
    cell = grid.random_cell 
    unvisited = grid.size - 1 
    visits = Hash.new(0)
    while unvisited > 0
      visits[cell]+=1
      # find the set of least-visited neighbors, and pick one randomly
      neighbors_by_visit = cell.neighbors.group_by { |n| visits[n] }
      min = neighbors_by_visit.keys.min 
      neighbor = neighbors_by_visit[min].sample 
      if neighbor.links.empty?
        cell.link(neighbor)
        unvisited -= 1
      end
      cell = neighbor
    end
    grid
  end
end

Code explanation

Lines 8–25: We define the class method self.on, which takes a grid object as an argument and generates the maze using the modified Aldous-Broder algorithm.

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