Building a Maze by Destroying Walls Efficiently

I wrote a maze-generation program [0] in 1999 that used disjoint-set forests with path compression to generate mazes. Wikipedia didn't exist yet, so I didn't know what they were called, but I'm pretty sure I'd heard of them somewhere before.

[0]: http://lists.canonical.org/pipermail/kragen-hacks/1999-Febru... "mazewiz in C (second iteration), posted to kragen-hacks 1999-02-16"

Joe Allen's three-lines-of-C maze generator (included in the post), however, blows the hell out of my program for coolness.

This "efficient" algorithm takes O(n^2) time (where n is the number of grid squares) because it has to repeatedly remove elements from the middle of a list. It can easily be improved to O(n) by simply shuffling the list once and traversing it in order.

For those interested in maze generation, Jamis Buck's maze series (http://weblog.jamisbuck.org/2011/2/7/maze-generation-algorit...) covers the whole spectrum of algorithms and has recently started on weave mazes.

To build and run (I expected a build.xml file):

    cd ai4u-read-only/com.ai4u.util/trunk/src
    javac com/ai4u/util/*.java com/ai4u/util/disjointSet/*.java com/ai4u/util/games/maze/Maze.java
    java com.ai4u.util.games.maze.Maze

I like the output of this maze algo even more than the standard recursive backtracker, plus it's more efficient; from a few walkthroughs it seems to generate slightly more challenging mazes as well. (A solver line would help showing this and any bias.)

Also to make more fun (Maze.java):

    final int rows, cols;
    if (args.length == 2) {
      rows = Integer.parseInt(args[0]); cols = Integer.parseInt(args[1]);
    } else {
      rows = cols = 30;
    }
    final Maze m = createRandomMaze(rows, cols);
    ...
    .addGap(0, 13 * cols,
    ...
    .addGap(0, 13 * rows,

I'm still puzzled how the Fulfillment[1] game builds a board by doing the opposite of this. Naively adding random walls clearly doesn't lead to a board filled with tetris pieces.

[1] http://homokaasu.org/gasgames/game.gas?27

And a simple example of how to solve them: http://thinkcode.tv/catalog/amazing-python/