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@mbostock
Last active Feb 9, 2016
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Wilson’s Algorithm IV
license: gpl-3.0
<!DOCTYPE html>
<meta charset="utf-8">
<style>
.link {
fill: none;
stroke: #000;
stroke-width: 1.5px;
}
</style>
<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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