Prim’s Algorithm II

This maze is generated using Prim’s algorithm and then flooded with color. Hue encodes Manhattan distance from the starting cell. (This is not an optimal visual encoding, but it suffices and is pretty.)

Color is useful to visually compare the structure of mazes; without color, the black and white alternating cells are too noisy to offer any pre-attentive comparisons. Compare a maze generated by Prim’s algorithm to random traversal, randomized depth-first traversal and Wilson’s algorithm.

See this color flood applied directly to the pixel grid.

<!DOCTYPE html>
<meta charset="utf-8">
<style>

body {
  background: #000;
}

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

var width = 960,
    height = 960;

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

var cellSize = 4,
    cellSpacing = 4,
    cellWidth = Math.floor((width - cellSpacing) / (cellSize + cellSpacing)),
    cellHeight = Math.floor((height - cellSpacing) / (cellSize + cellSpacing)),
    cells = generateMaze(cellWidth, cellHeight), // each cell’s edge bits
    distance = 0,
    visited = new Array(cellWidth * cellHeight),
    frontier = [(cellHeight - 1) * cellWidth];

var canvas = d3.select("body").append("canvas")
    .attr("width", width)
    .attr("height", height);

var context = canvas.node().getContext("2d");

context.translate(
  Math.round((width - cellWidth * cellSize - (cellWidth + 1) * cellSpacing) / 2),
  Math.round((height - cellHeight * cellSize - (cellHeight + 1) * cellSpacing) / 2)
);

context.fillStyle = "#fff";
for (var y = 0, i = 0; y < cellHeight; ++y) {
  for (var x = 0; x < cellWidth; ++x, ++i) {
    fillCell(i);
    if (cells[i] & S) fillSouth(i);
    if (cells[i] & E) fillEast(i);
  }
}

d3.timer(function() {
  if (!(n0 = frontier.length)) return true;

context.fillStyle = d3.hsl(distance++ % 360, 1, .5) + "";

if (distance & 1) {
    for (var i = 0; i < n0; ++i) {
      fillCell(frontier[i]);
    }
  } else {
    var frontier1 = [],
        i0,
        i1,
        n0;

for (var i = 0; i < n0; ++i) {
      i0 = frontier[i];
      if (cells[i0] & E && !visited[i1 = i0 + 1]) visited[i1] = true, fillEast(i0), frontier1.push(i1);
      if (cells[i0] & W && !visited[i1 = i0 - 1]) visited[i1] = true, fillEast(i1), frontier1.push(i1);
      if (cells[i0] & S && !visited[i1 = i0 + cellWidth]) visited[i1] = true, fillSouth(i0), frontier1.push(i1);
      if (cells[i0] & N && !visited[i1 = i0 - cellWidth]) visited[i1] = true, fillSouth(i1), frontier1.push(i1);
    }

frontier = frontier1;
  }
});

function fillCell(i) {
  var x = i % cellWidth, y = i / cellWidth | 0;
  context.fillRect(x * cellSize + (x + 1) * cellSpacing, y * cellSize + (y + 1) * cellSpacing, cellSize, cellSize);
}

function fillEast(i) {
  var x = i % cellWidth, y = i / cellWidth | 0;
  context.fillRect((x + 1) * (cellSize + cellSpacing), y * cellSize + (y + 1) * cellSpacing, cellSpacing, cellSize);
}

function fillSouth(i) {
  var x = i % cellWidth, y = i / cellWidth | 0;
  context.fillRect(x * cellSize + (x + 1) * cellSpacing, (y + 1) * (cellSize + cellSpacing), cellSize, cellSpacing);
}

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;
}

d3.select(self.frameElement).style("height", height + "px");

</script>

https://d3js.org/d3.v3.min.js