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@mbostock /.block
Last active Feb 9, 2016

Prim’s Algorithm III
license: gpl-3.0

A spanning tree of the canvas is generated using Prim’s algorithm and then flooded with color. Hue encodes Manhattan distance from the root of the tree. (This is not an optimal visual encoding, but it suffices and is pretty.)

Spanning trees can also be used to generate mazes. See a maze generated with Prim’s algorithm flooded with color, and compare color floods of spanning trees generated with Prim’s algorithm to random traversal, randomized depth-first traversal and Wilson’s algorithm.

var N = 1 << 0,
S = 1 << 1,
W = 1 << 2,
E = 1 << 3;
self.addEventListener("message", function(event) {
postMessage(generateMaze(event.data.width, event.data.height));
});
function generateMaze(cellWidth, cellHeight) {
var cells = new Array(cellWidth * cellHeight),
frontier = minHeap(function(a, b) { return a.weight - b.weight; }),
startIndex = (cellHeight - 1) * cellWidth;
cells[startIndex] = 0;
frontier.push({index: startIndex, direction: N, weight: Math.random()});
frontier.push({index: startIndex, direction: E, weight: Math.random()});
while ((edge = frontier.pop()) != null) {
var edge,
i0 = edge.index,
d0 = edge.direction,
i1 = i0 + (d0 === N ? -cellWidth : d0 === S ? cellWidth : d0 === W ? -1 : +1),
x0 = i0 % cellWidth,
y0 = i0 / cellWidth | 0,
x1,
y1,
d1,
open = cells[i1] == null; // opposite not yet part of the maze
if (d0 === N) x1 = x0, y1 = y0 - 1, d1 = S;
else if (d0 === S) x1 = x0, y1 = y0 + 1, d1 = N;
else if (d0 === W) x1 = x0 - 1, y1 = y0, d1 = E;
else x1 = x0 + 1, y1 = y0, d1 = W;
if (open) {
cells[i0] |= d0, cells[i1] |= d1;
if (y1 > 0 && cells[i1 - cellWidth] == null) frontier.push({index: i1, direction: N, weight: Math.random()});
if (y1 < cellHeight - 1 && cells[i1 + cellWidth] == null) frontier.push({index: i1, direction: S, weight: Math.random()});
if (x1 > 0 && cells[i1 - 1] == null) frontier.push({index: i1, direction: W, weight: Math.random()});
if (x1 < cellWidth - 1 && cells[i1 + 1] == null) frontier.push({index: i1, direction: E, weight: Math.random()});
}
}
return cells;
}
function minHeap(compare) {
var heap = {},
array = [],
size = 0;
heap.empty = function() {
return !size;
};
heap.push = function(value) {
up(array[size] = value, size++);
return size;
};
heap.pop = function() {
if (size <= 0) return;
var removed = array[0], value;
if (--size > 0) value = array[size], down(array[0] = value, 0);
return removed;
};
function up(value, i) {
while (i > 0) {
var j = ((i + 1) >> 1) - 1,
parent = array[j];
if (compare(value, parent) >= 0) break;
array[i] = parent;
array[i = j] = value;
}
}
function down(value, i) {
while (true) {
var r = (i + 1) << 1,
l = r - 1,
j = i,
child = array[j];
if (l < size && compare(array[l], child) < 0) child = array[j = l];
if (r < size && compare(array[r], child) < 0) child = array[j = r];
if (j === i) break;
array[i] = child;
array[i = j] = value;
}
}
return heap;
}
<!DOCTYPE html>
<meta charset="utf-8">
<canvas width="960" height="500"></canvas>
<script src="//d3js.org/d3.v3.min.js"></script>
<script>
var canvas = d3.select("canvas"),
context = canvas.node().getContext("2d"),
width = canvas.property("width"),
height = canvas.property("height");
var worker = new Worker("generate-prims.js");
worker.postMessage({width: width, height: height});
worker.addEventListener("message", function(event) {
worker.terminate();
var N = 1 << 0,
S = 1 << 1,
W = 1 << 2,
E = 1 << 3;
var cells = event.data,
distance = 0,
visited = new Array(width * height),
frontier = [(height - 1) * width],
image = context.createImageData(width, height);
function flood() {
var frontier1 = [],
i0,
n0 = frontier.length,
i1,
color = d3.hsl((distance += .5) % 360, 1, .5).rgb();
for (var i = 0; i < n0; ++i) {
i0 = frontier[i] << 2;
image.data[i0 + 0] = color.r;
image.data[i0 + 1] = color.g;
image.data[i0 + 2] = color.b;
image.data[i0 + 3] = 255;
}
for (var i = 0; i < n0; ++i) {
i0 = frontier[i];
if (cells[i0] & E && !visited[i1 = i0 + 1]) visited[i1] = true, frontier1.push(i1);
if (cells[i0] & W && !visited[i1 = i0 - 1]) visited[i1] = true, frontier1.push(i1);
if (cells[i0] & S && !visited[i1 = i0 + width]) visited[i1] = true, frontier1.push(i1);
if (cells[i0] & N && !visited[i1 = i0 - width]) visited[i1] = true, frontier1.push(i1);
}
frontier = frontier1;
return !frontier1.length;
}
d3.timer(function() {
for (var i = 0, done; i < 3 && !(done = flood()); ++i);
context.putImageData(image, 0, 0);
return done;
});
});
</script>
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