Wilson’s Algorithm IV

Applying a tree layout on Wilson’s algorithm.

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<style>

.link {
  fill: none;
  stroke: #000;
  stroke-width: 1.5px;
}

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<body>
<script src="//d3js.org/d3.v3.min.js"></script>
<script>

var margin = {top: 20, right: 20, bottom: 20, left: 20},
    width = 960 - margin.left - margin.right,
    height = 500 - margin.top - margin.bottom;

var N = 1 << 0,
    S = 1 << 1,
    W = 1 << 2,
    E = 1 << 3;

var root = generateTree(40, 40);

var tree = d3.layout.tree()
    .size([height, width]);

var nodes = tree.nodes(root),
    links = tree.links(nodes);

var svg = d3.select("body").append("svg")
    .attr("width", width + margin.left + margin.right)
    .attr("height", height + margin.top + margin.bottom)
  .append("g")
    .attr("transform", "translate(" + margin.left + "," + margin.top + ")");

svg.selectAll(".link")
    .data(links)
  .enter().append("path")
    .attr("class", "link")
    .attr("d", function(d) { return "M" + d.source.y + "," + d.source.x + "L" + d.target.y + "," + d.target.x; });

function generateTree(width, height) {
  var cells = generateMaze(width, height), // each cell’s edge bits
      visited = d3.range(width * height).map(function() { return false; }),
      root = {index: cells.length - 1, children: []},
      frontier = [root],
      parent,
      child,
      childIndex,
      cell;

while ((parent = frontier.pop()) != null) {
    cell = cells[parent.index];
    if (cell & E && !visited[childIndex = parent.index + 1]) visited[childIndex] = true, child = {index: childIndex, children: []}, parent.children.push(child), frontier.push(child);
    if (cell & W && !visited[childIndex = parent.index - 1]) visited[childIndex] = true, child = {index: childIndex, children: []}, parent.children.push(child), frontier.push(child);
    if (cell & S && !visited[childIndex = parent.index + width]) visited[childIndex] = true, child = {index: childIndex, children: []}, parent.children.push(child), frontier.push(child);
    if (cell & N && !visited[childIndex = parent.index - width]) visited[childIndex] = true, child = {index: childIndex, children: []}, parent.children.push(child), frontier.push(child);
  }

return root;
}

function generateMaze(width, height) {
  var cells = new Array(width * height), // each cell’s edge bits
      remaining = d3.range(width * height), // cell indexes to visit
      previous = new Array(width * height); // current random walk

// Add the starting cell.
  var start = remaining.pop();
  cells[start] = 0;

// While there are remaining cells,
  // add a loop-erased random walk to the maze.
  while (!loopErasedRandomWalk());

return cells;

function loopErasedRandomWalk() {
    var i0,
        i1,
        x0,
        y0;

// Pick a location that’s not yet in the maze (if any).
    do if ((i0 = remaining.pop()) == null) return true;
    while (cells[i0] >= 0);

// Perform a random walk starting at this location,
    previous[i0] = i0;
    while (true) {
      x0 = i0 % width;
      y0 = i0 / width | 0;

// picking a legal random direction at each step.
      i1 = Math.random() * 4 | 0;
      if (i1 === 0) { if (y0 <= 0) continue; --y0, i1 = i0 - width; }
      else if (i1 === 1) { if (y0 >= height - 1) continue; ++y0, i1 = i0 + width; }
      else if (i1 === 2) { if (x0 <= 0) continue; --x0, i1 = i0 - 1; }
      else { if (x0 >= width - 1) continue; ++x0, i1 = i0 + 1; }

// If this new cell was visited previously during this walk,
      // erase the loop, rewinding the path to its earlier state.
      if (previous[i1] >= 0) eraseWalk(i0, i1);

// Otherwise, just add it to the walk.
      else previous[i1] = i0;

// If this cell is part of the maze, we’re done walking.
      if (cells[i1] >= 0) {

// Add the random walk to the maze by backtracking to the starting cell.
        // Also erase this walk’s history to not interfere with subsequent walks.
        while ((i0 = previous[i1]) !== i1) {
          if (i1 === i0 + 1) cells[i0] |= E, cells[i1] |= W;
          else if (i1 === i0 - 1) cells[i0] |= W, cells[i1] |= E;
          else if (i1 === i0 + width) cells[i0] |= S, cells[i1] |= N;
          else cells[i0] |= N, cells[i1] |= S;
          previous[i1] = NaN;
          i1 = i0;
        }

previous[i1] = NaN;
        return;
      }

i0 = i1;
    }
  }

function eraseWalk(i0, i2) {
    var i1;
    do i1 = previous[i0], previous[i0] = NaN, i0 = i1; while (i1 !== i2);
  }
}

</script>

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